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PhD Dissertation

December 2006

International Doctorate School in Information and Communication Technologies

DIT - University of Trento

ADVANCED METHODS FOR AUTOMATIC CHANGE DETECTION IN MULTITEMPORAL REMOTE SENSING IMAGES ACQUIRED BY

SAR AND MULTISPECTRAL SENSORS

Francesca Bovolo

Advisor:

Prof. Lorenzo Bruzzone

Università degli Studi di Trento

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“Sognate e mirate sempre più in alto di quello che ritenete alla vostra portata. Non cercate solo di superare i vostri contemporanei o i vostri predecessori. Cercate, piuttosto, di superare voi stessi”.

William Faulkner

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Trento, 4 dicembre 2006 Alla mia mamma, per tutti quei piccoli gesti che alle volte passano inosservati, ma che spesso fanno la differenza.

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Acknowledgments Per ricordare tutti quelli che in questi anni di università

hanno occupato un ruolo nella mia vita non basterebbe un’altra tesi. Ciascuno di loro con la propria presenza ha contribuito a farmi crescere e maturare e per questo lo ringrazio.

Tra tutti devo cominciare dalla mamma che in questi anni di studio non ha mai smesso un momento di ascoltarmi, incoraggiarmi e sostenermi. Il suo aiuto è stato concreto e fondamentale. Come dimenticare tutte le volte in cui mi ha detto “Parlami pure, ma non so se posso aiutarti” e io le spiegavo matematica, fisica, comunicazioni, statistica, ecc. e lei riusciva sempre a dirmi la parola magica che sbrogliava la matassa. Come dimenticare i piccoli gesti quotidiani, quelle piccole attenzioni, che ti tirano su il morale e “le nostre colazioni” che sono state momenti di confronto e di crescita. Questo traguardo te lo sei meritato tanto quanto me, voglio che tu sia orgogliosa.

In secondo luogo, ma con altrettanta intensità, devo ringraziare mia sorella Barbara, che ha sempre trovato il tempo per ascoltarmi e per consigliarmi, per aiutarmi e sostenermi. La ringrazio soprattutto per non essere la sorella “maggiore” ma per essere una sorella che si è confrontata alla pari con me su vari aspetti della vita. Insieme a lei ringrazio Mirko perché i suoi discorsi “scientifici” sono un modo per staccare un po’ dalla scienza lavorativa, e la piccola Emma.

Un grazie davvero particolare va a Lorenzo (il prof), che dopo due tesi di laurea mi ha stupito non poco con la sua proposta di fare il dottorato, e al quale non avrò mai dimostrato abbastanza la mia riconoscenza per aver creduto nelle mie capacità scientifiche. Lo ringrazio per aver sempre trovato il tempo, anche quando tempo non ce n’era, per intavolare lunghe discussioni in cui le idee hanno trovato lo spazio giusto per confrontarsi e concretizzarsi in soluzioni e nuovi progetti che hanno portato allo

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sviluppo dell’attività di ricerca documentata in questa tesi. La sua guida è stata fondamentale per la mia crescita sia sul piano lavorativo che personale. Lo ringrazio per aver sempre seguito con attenzione il mio lavoro e per avermi lasciato allo stesso tempo la libertà di svolgerlo in autonomia. Grazie alla sua impostazione e al suo appoggio ho stretto i denti quando avrei pensato di non farcela e ho potuto maturare e raggiungere importanti risultati nel lavoro di ricerca. Insieme a lui ringrazio gli altri membri dell’RSLab, Lorenzo e Matita, per essere stati fonte di innumerevoli spunti di riflessione e di confronto.

Con estremo calore e affetto devo ringraziare Barbara per la sua sincerità, la sua lealtà e la sua amicizia incondizionata che hanno rappresentato per me un punto fermo in questi anni di studio. La ringrazio per avermi sempre ascoltata e consigliata; per aver espresso il proprio parere senza giri di parole e con senso critico tenendo acceso il cervello (non è da tutti); per aver difeso le proprie opinioni senza ipocrisia e falsità. Infine, grazie per tutti i percorsi “casa-facoltà” in cui abbiamo condiviso molto di noi (non sono ancora finiti, tranquilla) e per il tempo trascorso (anche con Laura, Paolo e Nicola) nei seminterrati della facoltà, in mezzo a tutti quegli oggetti affascinanti per me che di strumentazione “hardware” ho solo un pc.

Un pensiero dolce e riconoscente va alle mie “bandite” Barbara (con Gianluca) e Nicoletta per l’essere le mie più fidate oratici. La loro partecipazione alle mie fatiche ha reso tutto più facile. Le ringrazio per avermi accompagnato con la musica e le belle serate per sole donne che rendono più bella la vita.

Infine, un pensiero lo dedico a Martino che, sebbene non più al mio fianco, ha condiviso con me l’inizio di questo lungo percorso.

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Abstract

Automatic analysis of multitemporal remote sensing images represents a useful support for an efficient management of envi-ronmental resources and a proper definition of intervention plans in many different application domains, such as environmental monitoring, study on land-use/land-cover dynamics, analysis of forest or vegetation changes, damage assessment, agricultural surveys, and analysis of urban changes. In this context, in order to properly exploit the huge amount of data acquired by the new generation of remote sensing satellites, it is mandatory to develop effective unsupervised and automatic change-detection tech-niques.

Change detection is a process that analyzes a pair of remote sensing images acquired on the same geographical area at differ-ent times in order to identify changes that may have occurred be-tween the considered acquisition dates. In the literature many dif-ferent techniques have been proposed for performing both supervised and unsupervised change detection. In supervised change detection, in addition to the multitemporal images, also multitemporal ground truth information is needed. However, in the most of the applications no ground truth information is avail-able and the use of unsupervised change-detection techniques is mandatory. For this reason, in this thesis the attention is focused on the development of novel automatic and unsupervised change-detection techniques.

The proposed techniques can analyze both multispectral im-ages acquired by passive sensors and SAR data acquired by ac-tive sensors. Independently on the acquisition sensor, two differ-ent kinds of approaches to change detection are proposed: a single-scale approach and a multiscale approach.

Within the single-scale approach, we propose: i) a novel theo-retical framework for a formal definition and a theoretical study

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of the change vector analysis (CVA) technique, which is based on the representation of the CVA in polar coordinates and that al-lows defining a solid background for the development of ad-vanced and accurate automatic change-detection algorithms in the polar domain; and ii) a novel split-based approach to auto-matic and unsupervised change detection in large-size multitem-poral remote sensing images; which can detect in a consistent and reliable way changes in images of large size also when the extension of the changed area is small (and therefore the prior probability of the class of changed pixels is very small).

In the context of the multiscale approach we propose: i) a novel method for change detection in multitemporal SAR images, which exploits a wavelet-based multiscale decomposition of the log-ratio image aimed at improving the accuracy and the geomet-ric fidelity of the change-detection map with respect to single-scale techniques; and ii) a parcel-based context-sensitive tech-nique for unsupervised change detection in very high geometrical resolution images, which properly models complex objects in the investigated scene on the basis of multitemporal and multilevel homogeneous regions.

Quantitative and qualitative experimental results obtained on real SAR and/or multispectral images confirmed the effectiveness of all the proposed techniques. Keywords

Change detection, unsupervised techniques, multitemporal im-ages, multispectral images, synthetic aperture radar images, change vector analysis, context-sensitive analysis, multiresolution and multiscale analysis, large-size image analysis, damage as-sessment, remote sensing, image processing.

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Contents 1. CHANGE DETECTION IN MULTITEMPORAL REMOTE

SENSING IMAGES .........................................................................1 1.1. INTRODUCTION.............................................................................1 1.2. CHANGE DETECTION: GENERAL OVERVIEW ................................6 1.3. UNSUPERVISED CHANGE DETECTION IN MULTITEMPORAL

REMOTE SENSING IMAGES .........................................................10 1.3.1. Pre-processing .....................................................................10 1.3.2. Multitemporal Image Comparison ......................................13 1.3.3. Analysis of the Image after Comparison .............................16

1.4. NOVEL CONTRIBUTIONS OF THE THESIS.....................................18 1.5. THESIS OVERVIEW .....................................................................21 REFERENCES .....................................................................................21

2. A THEORETICAL FRAMEWORK FOR UNSUPERVISED CHANGE DETECTION BASED ON CHANGE VECTOR ANALYSIS IN POLAR DOMAIN ...............................................31 2.1. INTRODUCTION...........................................................................32 2.2. PROPOSED POLAR REPRESENTATION FRAMEWORK FOR CVA ...33

2.2.1. Background and CVA Formulation ....................................33 2.2.2. General Framework for Hyperspherical Representation .....36 2.2.3. Proposed Polar Framework for the CVA Technique:

Definitions...........................................................................38 2.3. ANALYSIS OF THE JOINT CONDITIONAL DISTRIBUTIONS OF

CLASSES.....................................................................................43 2.3.1. Class Distributions in the Cartesian Domain.......................43 2.3.2. Class Distributions in the Polar Domain .............................44

2.4. ANALYSIS OF THE MARGINAL CONDITIONAL DISTRIBUTIONS OF MAGNITUDE AND DIRECTION................................................46

2.4.1. Statistical Models for the Class of Unchanged Pixels .........49 2.4.2. Statistical Models for the Classes of Changed Pixels..........50 2.4.3. Discussion ...........................................................................52

2.5. EXPERIMENTAL RESULTS: SINGLE-CHANGE CASE.....................55 2.5.1. Data Set Description and Experiment Design .....................55 2.5.2. Qualitative Analysis of the Class Distributions in the

Polar Domain ......................................................................59 2.5.3. Quantitative Analysis of the Accuracy of the Statistical

Models of Class Distributions in the Polar Domain ............62 2.5.3.1 Statistical Models for the Class of No-Changed Pixels ............ 63

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2.5.3.2 Statistical Models for the Class of Changed Pixels...................65 2.5.4. Analysis of the Effectiveness of the Proposed Framework

for Solving Change-Detection Problems ............................66 2.6. EXPERIMENTAL RESULTS: DOUBLE-CHANGE DATA SET ...........68

2.6.1. Data Set Description and Experiment Design.....................68 2.6.2. Qualitative and Quantitative Analysis of the Class

Distributions in the Polar Domain ......................................70 2.6.3. Analysis of the Effectiveness of the Proposed Framework

for Solving Change-Detection Problems ............................73 2.7. DISCUSSION AND CONCLUSIONS................................................76 APPENDIX.........................................................................................79 REFERENCES.....................................................................................81

3. A SPLIT-BASED APPROACH TO UNSUPERVISED CHANGE DETECTION IN LARGE-SIZE MULTITEMPORAL IMAGES....................................................85 3.1. INTRODUCTION ..........................................................................86 3.2. PROPOSED SPLIT-BASED APPROACH TO CHANGE DETECTION

IN LARGE-SIZE MULTITEMPORAL IMAGES.................................89 3.2.1. Image Comparison ..............................................................89 3.2.2. Image Split and Adaptive Split Selection ...........................91 3.2.3. Split-Based Threshold Selection.........................................93

3.3. A NOVEL SPLIT-BASED SYSTEM FOR TSUNAMI DAMAGE ASSESSMENT..............................................................................95

3.3.1. Dataset and Problem Description........................................96 3.3.2. Proposed System for Tsunami Damage Assessment ..........97

3.4. EXPERIMENTAL RESULTS.........................................................100 3.4.1. Design of Experiments......................................................100 3.4.2. Change-Detection Results: Single-Change Identification.107 3.4.3. Change-Detection Results: Double-Change Identification110

3.5. DISCUSSION AND CONCLUSIONS..............................................116 ACKNOWLEDGMENTS .....................................................................118 REFERENCES...................................................................................118

4. A DETAIL-PRESERVING SCALE-DRIVEN APPROACH TO CHANGE DETECTION IN MULTITEMPORAL SAR IMAGES .......................................................................................125 4.1. INTRODUCTION ........................................................................125 4.2. PROBLEM FORMULATION AND ARCHITECTURE OF THE

PROPOSED TECHNIQUE .............................................................128

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4.3. PROPOSED ADAPTIVE SCALE-DRIVEN CHANGE DETECTION TECHNIQUE...............................................................................131

4.3.1. Multiresolution decomposition of the log-ratio image ......131 4.3.2. Adaptive scale identification .............................................135 4.3.3. Scale-driven fusion............................................................137

4.4. EXPERIMENTAL RESULTS.........................................................140 4.4.1. Data set description ...........................................................140 4.4.2. Results ...............................................................................142

4.5. DISCUSSION AND CONCLUSION.................................................150 ACKNOWLEDGMENT .......................................................................151 REFERENCES ...................................................................................152

5. A MULTILEVEL PARCEL-BASED APPROACH TO CHANGE DETECTION IN VERY HIGH RESOLUTION MULTITEMPORAL IMAGES ..................................................157 5.1. INTRODUCTION.........................................................................158 5.2. PROPOSED PARCEL-BASED CHANGE-DETECTION TECHNIQUE.159 5.3. EXPERIMENTAL RESULTS.........................................................163 5.4. DISCUSSION AND CONCLUSIONS ..............................................167 REFERENCES ...................................................................................168

6. CONCLUSIONS ..........................................................................171

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Chapter 1

1. Change Detection in Multitemporal Remote Sensing Images

Analysis of multitemporal remote-sensing images represents a useful support for an efficient management of environmental re-sources and a proper definition of intervention plans in many dif-ferent application domains. This chapter addresses the problem of change detection in temporal series of images, by focusing on automatic change-detection methods. After a brief survey on the main change-detection techniques present in the remote sensing literature, the chapter focuses the attention on unsupervised methods. On the basis of the general description of the problem, the main objectives, the novelties and the structure of the thesis are presented.

1.1. Introduction The recent natural disasters (e.g., tsunami, hurricanes, erup-

tions, earthquakes, etc.) and also the increasing amount of anthro-pogenic changes (e.g., due to wars, pollution, urban growth, etc.) gave prominence to the topics related to environment monitoring and damage assessment. The study of environmental variations due to the time evolution of the aforementioned phenomena is of fundamental interest from a political point of view. Such kind of applications requires the availability of information regularly ac-quired over the area of interest. In this context, remote-sensing images acquired by sensors mounted on board of satellites that

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periodically pass over the same geographical area become an im-portant tool for performing Earth monitoring. Information extrac-tion from such a large amount of data needs the development of ad hoc change-detection techniques capable of automatically identifying land-cover variations occurred on the ground by ana-lyzing remote sensing images.

The change-detection process considers images acquired at different times over the same geographical area of interest. This requirement makes images acquired from repeat-pass satellite sensors an effective input for addressing change-detection prob-lems. Several different Earth-observation satellite missions are currently operative, with different kind of sensors mounted on board (e.g., MODIS and ASTER on board of the NASA's TERRA satellite, MERIS and ASAR on board of the ESA’s ENVISAT satellite, Hyperion on board of the EO-1 NASA's satellite, SAR sensors on board of RADARSAT-1 and RADARSAT-2 CSA’s satellites, Ikonos and Quickbird satellites that acquire very high-resolution pancromatic and multispectral images, etc.). Each sen-sor has specific properties with respect to image acquisition mode (e.g., passive or active), geometrical, spectral and radiometric resolutions, etc. In the development of automatic change-detection techniques, it is mandatory to take into account the sen-sors properties to properly extract information from the consid-ered data.

Let us consider in greater detail the main characteristics of dif-ferent kinds of sensors (Table 1.1 summarizes some advantages and disadvantages of different sensors for change-detection appli-cations according to their characteristics).

Images acquired by passive sensors are obtained measuring the land-cover reflectance on the basis of the energy emitted from the sun and reflected from the ground1. Usually, the measured signal can be modeled as the desired reflectance (measured as a radiance) altered from an additive gaussian noise. This noise 1 Also the emission of Earth affects the measurements in the infrared portion of the

spectrum.

CHAPTER 1 - CHANGE DETECTION IN MULTITEMPORAL REMOTE SENSING IMAGES

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model makes relatively easy to process the signal when designing data analysis techniques. Passive sensors can acquire two differ-ent kinds of images: panchromatic (PAN) images and multispec-tral (MS) images, by defining different trade-offs between geo-metrical and spectral resolution according to the radiometric resolution of the adopted detectors. PAN images are characterized by a poorer spectral resolution but a significantly higher geomet-rical resolution with respect to MS images acquired

TABLE 1.1 ADVANTAGES AND DISADVANTAGE OF DIFFERENT KINDS OF SENSORS FOR CHANGE-

DETECTION APPLICATIONS

Sensor Advantages Disadvantages

Multispectral (passive)

• characterization of the spec-tral signature of land-covers

• the noise has an additive model

• atmospheric conditions strongly affect the acquisi-tion phase

Panchromatic (passive)

• high geometrical resolution • high content of spatial-

context information

• atmospheric conditions strongly affect the acquisi-tion phase

• poor characterization of the spectral signature of land-covers

SAR (active)

• not affected by sun light and atmospheric conditions

• complexity of data pre-processing

• presence of multiplicative speckle noise

by the same sensor. On the opposite, MS images show lower geometrical resolution but higher spectral resolution. From the perspective of change detection, PAN images should be used when the expected size of the changed areas is too small for adopting MS data. For example, this is the case of the analysis of changes in urban areas, when detailed urban studies should be carried out. Change detection in PAN images requires the defini-tion of techniques capable to capture the richness of information present both in the spatial-context relations between neighboring pixels and in the geometrical shapes of objects. MS data should be used when a lower geometrical resolution is sufficient for characterizing the size of the changed areas and a detailed model-

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ing of the spectral signature of the land-covers is necessary for identifying the investigated change. Change-detection methods in MS images should be able to properly exploit the available mul-tispectral information in the analysis process. A very critical problem related to the use of passive sensors in change detection consists in the sensitivity of the image acquisition phase to at-mospheric conditions. This problem has two possible effects: i) atmospheric conditions may result in the impossibility to measure land-cover spectral signatures depending on the presence of clouds; ii) variations in illumination and atmospheric conditions at different acquisition times may be a potential source of errors, which should be taken into account in order to avoid the identifi-cation of false changes (or the missed detection of true changes).

The working principle of active Synthetic Aperture Radar (SAR) sensors is completely different from that of the passive ones and allows overcoming some of the drawbacks that affect optical images. The signal measured by active sensors is the Earth backscattering of an electromagnetic pulse emitted from the sen-sor itself. SAR instruments acquire different kinds of signals that result in different images: medium or high resolution images; sin-gle-frequency or multi-frequency and single-polarimetric or fully-polarimetric images. As for optical data, the proper geometrical resolution should be chosen according to the size of the expected investigated changes. The SAR signal can have different geomet-rical resolutions and has a different penetration capability depend-ing on the signal wavelength, which is usually included between band X and band L (i.e., between 2 and 30[cm]). All the wave-lengths adopted for SAR sensors do not suffer from atmosphere and sunlight conditions, as well as from the presence of clouds; thus multitemporal radar backscattering does not change with at-mospheric conditions. The main problem related to the use of ac-tive sensors is the coherent nature of the SAR signal, which re-sults in a multiplicative speckle noise that makes acquired data intrinsically complex to be analyzed. A proper handling of speckle requires both an intensive pre-processing phase and the development of effective data analysis techniques.


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The different properties and statistical behaviors of signals ac-quired by active and passive sensors require the definition of dif-ferent change-detection techniques capable to properly exploit the specific data peculiarities.

In the literature, many different techniques for change detec-tion in images acquired by passive sensors have been presented [1]-[8], and many applications of these techniques have been re-ported. This is due to both the amount of information present in MS images and the relative simplicity of data analysis, which re-sults from the additive noise model adopted for MS data (the ra-diance of natural classes can be approximated with a Gaussian distribution). Less attention has been devoted to change detection in SAR images. This is explained by the intrinsic complexity of SAR data, which require both an intensive pre-processing phase and the development of effective data analysis techniques capable of dealing with multiplicative speckle noise. Nonetheless, in the last few years the remote-sensing community increased its inter-est in the use of SAR images in change-detection problems, thanks to their independence from atmospheric conditions that re-sults in excellent operational properties. This scenario is com-pleted from the recent technological developments in sensors and satellites, which resulted in the design of evermore sophisticated systems with increased geometrical resolution. Independently from the active or passive nature of the sensor, the very high geometrical resolution images acquired by these systems (e.g. PAN images) require the development of specific techniques ca-pable to take advantage from the richness of geometrical informa-tion they contain. In particular, both the high correlation between neighboring pixels and the object shapes should be considered in the design of data-analysis procedures.

The chapter is organized into four sections. Section 1.2 gives a brief survey on change detection in multitemporal remote sensing images, section 1.3 focuses attention on unsupervised change-detection techniques for both multitemporal SAR and multispec-tral images. Finally, section 1.4 presents the main objectives, the novelties and the structure of this thesis.

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1.2. Change Detection: General Overview A very important preliminary step to the development of a

change-detection system based on automatic ore semi-automatic procedures, consists in the design of a proper phase of data col-lection. The phase of data collection aims at defining: i) the kind of satellite to be used (on the basis of the repetition time and of the characteristics of the sensors mounted on-board); ii) the kind of sensor to be considered (on the basis of the desired properties of the images and of the system); iii) the end-user requirements (which are of basic importance for the development of a proper change-detection technique); and iv) the kinds of available ancil-lary data (all the available information that can be used for con-straining the change-detection procedure).

The outputs of the data-collection phase should be used for de-fining the automatic change-detection technique. In the literature, many different techniques have been proposed. We can distin-guish between two main categories: supervised and unsupervised methods [9],[10].

When performing supervised change detection, in addition to the multitemporal images, also multitemporal ground truth infor-mation is needed. This information is used for identifying, for each possible land-cover class, spectral signature samples for per-forming supervised data classification and also for explicitly iden-tifying what kinds of land-cover transitions have taken place. Three main general approaches to supervised change detection can be found in the literature: Post-Classification Comparison, Supervised Direct Multidata Classification [10] and Compound Classification [11]-[13]. Post-Classification Comparison com-putes the change-detection map by comparing the classification maps obtained by classifying independently two multitemporal remote-sensing images. On the one hand, this procedure avoids data normalization aimed at reducing atmospheric conditions, sensor differences, etc. between the two acquisitions; on the other hand, it critically depends on the accuracies of the classification maps computed at the two acquisition dates. As Post-Classification Comparison does not take into account the depend-


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ence existing between two images of the same area acquired at two different times, the global accuracy is close to the product of the accuracies yielded at the two times [10]. Supervised Direct Multidata Classification [10] performs change detection by con-sidering each possible transition (according to the available a pri-ori information) as a class and by training a classifier to recognize the transitions. Although this method exploits the temporal corre-lation between images in the classification process, its major drawback is that training pixels should be related to the same points on the ground at the two times and should accurately repre-sent the proportions of all the transitions in the whole images. Compound Classification overcomes the aforementioned draw-backs of Supervised Multidate Classification technique, by re-moving the constraint that training pixels should be related to the same area on the ground [11]-[13]. In general, the approach based on supervised classification is more accurate and detailed than the unsupervised one; nevertheless, the latter approach is often pre-ferred in real-data applications. This is due to the difficulties in collecting proper ground-truth information (necessary for super-vised techniques), which is a complex, time consuming and ex-pensive process (in many cases this process is not consistent with the application constraints).

Unsupervised change-detection techniques are based on the comparison of the spectral reflectances (or backscattering coeffi-cient) of multitemporal raw images and a subsequent analysis of the comparison output. In the literature, the most widely used un-supervised change-detection techniques are based on a 3-step pro-cedure [10],[14]: i) pre-processing; ii) pixel-by-pixel comparison of two raw images; and iii) image analysis/thresholding (Fig. 1.1).

The aim of the pre-processing step is to make the two consid-ered images as more comparable as possible. In general, pre-processing operations include: co-registration, radiometric and geometric corrections and noise reduction. From the practical point of view, co-registration is a fundamental step as it allows

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obtaining a pair of images where corresponding pixels are associ-ated to the same position on the ground2. Radiometric corrections reduce differences between the two acquisitions due to sunlight and atmospheric conditions. These procedures are applied to opti-cal images, but they are not necessary with SAR images (as SAR data are not affected from atmospheric conditions). Also noise re-duction is performed differently according to the kind of remote-sensing images considered. In optical images common low-pass filters can be used, whereas in SAR images proper despeckling filters should be applied. However, the need of this step should be carefully evaluated because it reduces the geometrical details pre-sent in the images.

Figure 1.1 Block scheme of a standard unsupervised change detection approach.

2 It is worth noting that usually it is not possible to obtain a perfect alignment between

temporal images. This may considerably affect the change-detection process [31]. Consequently, if the amount of residual misregistration noise is significant, proper techniques aimed at reducing its effects should be used for change detection [1],[4].

Change-detection map (M)

Analysis of the im-age after comparison

Remote Sensing Image (date t1)

Remote Sensing Image (date t2)

Comparison

Pre-processing Pre-processing


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The comparison step aims at producing a further image where differences between the two considered acquisitions are high-lighted. Different mathematical operators (see next section for a summary) can be adopted to perform image comparison; this choice gives rise to different kinds of techniques [10],[15]-[19]. Performances of the above mentioned techniques can be degraded by several factors like differences in illumination at two dates, differences in atmospheric conditions and in sensor calibration that make difficult a direct comparison between raw images ac-quired at different times. It is worth noting that, differences in il-lumination and atmospheric conditions do not affect SAR data; however, distortions due to the range antenna pattern, the eleva-tion pointing angle of the sensor should be corrected when active sensors are used.

After image comparison, a new image is obtained where changes occurred on the ground are empathized. In order to ex-tract the change information, a proper unsupervised image analy-sis technique should be adopted. Among unsupervised techniques, the most widely used is based on the selection of a decision threshold that aims separating changed from unchanged pixels. The decision threshold can be selected either with a manual trial-and-error procedure (according to the desired trade-off between false and missed alarms) or with automatic techniques (e.g., by analyzing the statistical distribution of the image obtained after comparison, by fixing the desired false alarm probability [20],[21], or following a Bayesian minimum-error decision rule [14]).

The remote-sensing community attention has devoted to change-detection techniques for images acquired by both passive multispectral [6]-[8] and active SAR sensors [22]-[30]. From an operational point of view, it is obvious that unsupervised change-detection techniques are more attractive (as suitable ground-truth information is not always available) approach. For this reason, in the following we focus the attention on unsupervised change-detection methods for both SAR and multispectral images.

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1.3. Unsupervised Change Detection in Multitemporal Remote Sensing Images

Let us consider two remote sensing images, X1 and X2 ac-quired over the same area at different times t1 and t2. Let

uc ωω ,=Ω be the set of classes associated with changed and un-changed pixels. Let us assume that no ground-truth information is available for the design of the change-detection algorithm, i.e. the statistical analysis of change and no-change classes should be per-formed only on the basis of the raw data. The change-detection process aims at generating a change-detection map that represents changes occurred on the ground between the two considered ac-quisition dates. In other words one of the possible labels in Ω should be assigned to each pixel (i,j) in the scene.

1.3.1. Pre-processing The first step for properly performing change detection based

on direct image comparison is image pre-processing. This proce-dure aims at generating two images that are as similar as possible unless in changed areas. Pre-processing consists usually in four steps: i) radiometric and atmospheric correction, ii) geometric correction; iii) co-registration; and iv) noise reduction.

The first step aims at reducing the differences in multitemporal images due to changes in light and atmospheric conditions be-tween the two acquisition dates, that may result in undesired false alarms [11],[14],[31],[32]. Two different approaches are present in the literature: absolute calibration and relative calibration. The first one converts gray-level values in the multitemporal images into a corresponding reflectance value, i.e. to meaningful physical units [15],[26],[33]. The second one adjusts the radiometric prop-erties of an image to those of a reference image, such that the same gray-level values in the two images represent the same re-flectance value, whatever the reflectance values on the ground may be [13],[14],[17]. The choice of one of the two approaches depends on the specific application considered. As SAR data are not corrupted by differences in atmospheric and sunlight condi-


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tions, radiometric and atmospheric corrections are not required. However, in order to estimate a stable backscattering coefficient from the measured signal over multitemporal acquisitions, the ef-fects of the range antenna pattern and of the elevation pointing angle should be corrected. This process can be addressed on the basis of the known sensor’s parameters and by using targets with known scattering characteristics (e.g. trihedral corner reflectors).

The second step aims at reducing distortions that are due to the ground topography and becomes relevant especially when the study area is mountainous [34]-[37]. This process compensates the different response to illumination due to the irregular shape of the terrain this is of particular importance for very high resolution multispectral images and for SAR images. In SAR images, it al-lows to reduce specific geometric distortion effects like layover and foreshortening due to the active nature of the SAR signal. Among all methods present in the literature, two categories may be distinguished: i) methods based on band ratios; and ii) methods based on digital elevation models (DEMs). The former are much simpler and do not require additional input data. The reflectance is assumed to increase or decrease proportionally in the two ratio bands. Therefore, the quotient between them will compensate for topographic effects [36]. The methods belonging to the second group are based on illumination conditions models and require a DEM of the same resolution as the image to be corrected [34],[35]. The DEM is required to compute the incident angle [35].

The third step is very important, as it allows aligning temporal images in order to have that corresponding pixels in the spatial domain are associated to the same geographical position on the ground. In the literature two kinds of methods to image registra-tion can be found: i) semi-manual registration methods and ii) automatic methods. Semi-manual methods are based on a two step procedure [38],[39]. In the first step a set of matching control points (CPs) are manually identified in the two images to be co-registered. Alternatively, pairs of structures (objects or other primitives) that correspond to each other may used as a set of

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control points [40]. Step two uses corresponding control points to estimate parameters of the polynomial mapping function such that CPs in multitemporal images overlay as closely as possible. Automatic methods can be classified into two types, those which follow a human approach and those which exploit a global match-ing approach. The first type of methods follows the semiauto-matic two-step procedure described above, but CPs are automati-cally identified. The second type of methods, widely used in SAR images, is based on correlation-like techniques, such as cross cor-relation in the spatial or frequency domain [41],[42], absolute dif-ferences, and moments calculus [40],[43],[44]. The most signifi-cant drawback of these techniques is the high computational complexity due to the need of performing backscattering values interpolation, which is a time consuming process. The reader is referred to [45] for more details on image registration techniques and to [15] for details on the impact of registration noise on the accuracy of the change-detection process.

Finally, the last step is aimed at reducing the noise present in the images. In optical images common low-pass or edge-preserving image-smoothing filters can be used. The choice of the specific filter is application dependent. In SAR images the pres-ence of the multiplicative speckle noise makes the task more complex. Many different techniques have been developed in the literature for reducing the speckle, one of the most attractive is multilooking [46]. This procedure, which is used for generating images with the same resolution along azimuth and range direc-tions, allows contemporarily to reducing the effect of the coherent speckle components. However, a further filtering step is usually applied to the images for making them suitable to the desired analysis. Usually, adaptive despeckling procedures are exploited, among those we mention the following filtering techniques: Frost [47], Lee [48], Kuan [49], Gamma Map [50],[51], and Gamma WMAP [52] (i.e., the Gamma MAP filter applied in the wavelet domain). However, the real need of filtering should be carefully evaluated on the basis of the specific application considered, as filtering degrade the spatial resolution of the resulting image.


13

1.3.2. Multitemporal Image Comparison As mentioned in section 1.2, image pixel-by-pixel comparison

can be performed by means of many different mathematical op-erators (see Table 1.2).

One of the most widely used operator is the difference one. The difference can be applied: i) to a single spectral band (Uni-variate Image Differencing) [10],[17]-[19]; ii) to multiple spectral bands (Change Vector Analysis) [10],[53]; iii) to vegetation indi-ces (Vegetation Index Differencing) [10],[15] or other linear (e.g., Tasselled Cap Transformation [18]) or non liner combinations of spectral bands. A different approach is based on the use of the Principal Component Analysis (PCA) [10],[16],[19]. PCA can be applied separately to the feature space at single times or jointly to both images. In the first case comparison should be performed in the transformed feature space before performing change detec-tion, in the second case the minor components of the transformed feature space contain change information. Another widely used operator is the ratio operator (Image Ratioing) [10]. More com-plex strategies are based on context-sensitive dissimilarity meas-ures computed between statistical distributions [29].

TABLE 1.2

SUMMARY OF THE MOST WIDELY USED COMPARISON OPERATORS. fk IS THE CONSID-ERED FEATURE AT TIME tk THAT CAN BE: I) A SINGLE SPECTRAL BAND

bkX ; II) A VEC-

TOR OF M SPECTRAL BANDS 1[ ,..., ]mk kX X ; III) A VEGETATION INDEX Vk; OR IV) A VEC-

TOR OF FEATURES 1[ ,..., ]mk kP P OBTAINED AFTER PCA. XD AND XR ARE THE IMAGES

AFTER COMPARISON WITH THE DIFFERENCE OR RATIO OPERATORS, RESPECTIVELY

Technique Feature vector fk at the time tk

Comparison operator

Univariate image differencing

bkk X=f XD = f2 - f1

Vegetation index differencing fk = Vk XD = f2 - f1

Image rationing bkk X=f XD = f2 / f1

Change vector analysis ],..,[ 1 m

kk XX=kf XD = || f2 - f1 ||

Principal compo-nent Analysis

1[ ,.., ]= mk kP Pkf XD = || f2 - f1 ||

14

It has been shown in the literature that the difference operator is the most effective one when dealing with multispectral images due to the commonly adopted additive model of the noise. The resulting difference image is such that pixels associated with land-cover changes present gray-level values significantly differ-ent from those of pixels associated to unchanged areas [10]. Both change and no-change classes are a priori assumed to follow a gaussian or almost gaussian statistical distribution. Although, this assumption is reasonable in many applications, the true statistical distribution of classes depends on the kind of feature subtracted and thus on the specific technique adopted. In chapter 2 an in-depth study is carried out that analytically determines the statisti-cal distribution of change and no change classes when applying the CVA technique.

Unlike in optical image processing, in SAR image analysis the ratio operator demonstrated to be more effective than the differ-ence one [14],[46],[54] due to the multiplicative noise model commonly adopted for this kind of data. Let us consider two mul-tilook intensity images. It is possible to show that the difference image XD obtained by subtracting them has a statisical distribution given by [46],[54]:

j112 1 2

1 2j 01 2

exp( 1 j)!( ) .X( 1)! j!( 1 j)! ( )( )

−− −

=

−− + ⎡ ⎤= ⎢ ⎥− − − ++ ⎣ ⎦

∑D

L LL J

D DL

XL m L m mLp X L L L m mm m (1.1)

where XD is a random variable that represents the values of the pixels in XD. The distribution in (1.1) depends on both the relative change between the intesity values in the two images and also a reference intensity value (i.e., the intensity at t1 or t2). This leads to a higher change-detection error for changes occurred in high intensity regions of the image than in low intensity regions. Although in some applications the difference operator was used with SAR data [55], the aforementoined behaviour is an undesired effect that renders the difference operator intrinsecally not suited to the statistics of SAR images. On the other hand it is possible to prove that the distribution of the ratio image XR can be written as follows [46],[54]:


15

LRR

LR

LR

R XXXX

LLXp 2

1

2 )()!1()!12()(

+−−=

−

(1.2)

where XR is a random variable that represents the values of the pixels in XR and RX is the true change in the radar cross section. The ratio operator shows two main advantages over the difference operator. The first one is that the ratio-image distribution depends only on the relative change 12 / mmX R = in the average intensity between the two dates and not on a reference intensity level. Thus changes are detected in the same manner both in high- and low-intensity regions. The second advantage is that the rationing allows to reduce common multiplicative error components (which are due to both multiplicative sensor calibration errors and to the multiplicative effects of the interaction of the coherent signal with the terrain geometry [46],[56]), as far as these components are the same for images acquired with the same geometry. It is worth noting that, in the literature, the ratio image is usually expressed in a logarithmic scale. With this operation the distribution of the two classes of interest in the ratio image can be made more sym-metrical and the residual multiplicative speckle noise can be transformed in an additive noise component [14]. Thus the log-ratio operator is typically preferred when dealing with SAR images and change detection is performed analyzing the log-ratio image XLR defined as:

2

12 1log log log log= = = −LR R

XX X X XX

(1.3)

Based on the abovementioned considerations, the ratio and log-ratio operators are more used than the difference one in SAR change-detection applications [14],[22],[54],[56]-[58]. It is worth noting that for keeping the changed class on one side of the histo-gram of the ratio (or log-ratio) image, a normalized ratio can be computed pixel-by-pixel, i.e.,

1 2

2 1

min ,⎧ ⎫⎨ ⎬⎩ ⎭

=NRX XXX X

(1.4)

16

This operator allows all changed areas (independently of the in-creasing or decreasing value of the backscattering coefficient) to play a similar role in the change-detection problem.

1.3.3. Analysis of the Image after Comparison The most widely used approach to extract change information

from the image XC obtained after comparison (independently on the adopted comparison operator) is based on histogram thresh-olding. In this context, the most difficult task is to properly define the threshold value.

In classical techniques, such an analysis is performed by thresholding the image after comparison according to empirical strategies [59] or manual trial-and-error procedures, which sig-nificantly affect the reliability and accuracy of the final change-detection map. According to the assumption that changed pixels are few and show gray-level values significantly different from the unchanged ones, a reasonable solution is to label as changed those pixels that are far from the mean of the density function as-sociated to the image to be thresholded. One strategy consists in fixing the decision threshold as nμ +σ, being μ and σ the mean value and the standard deviation of the considered image respec-tively, and n a real number derived by a trial-and-error procedure. In this context, the selection of the parameter strongly depends on the end-user’s subjective criteria, which may lead to unreliable change-detection results. In addition, such a selection usually re-quires several trials and hence, a non negligible computation time [60],[61]. An alternative strategy, which is typically adopted in SAR image processing, is to label as changed pixels the ones that modified their backscattering more than dB x± , where x is a real number depending on the considered scene. The value of x is fixed according to the kind of change and the expected magnitude variation in order to obtain a desired probability of correct detec-tion Pd (which is the probability to be over the threshold if a change occurred) or false alarm Pfa (which is the probability to be over the threshold if no change occurred). It has been shown that the value of x can be analytical defined as a function of the true


17

change in the radar backscattering RX and of the equivalent number of looks L [46],[54], once Pd and Pfa are fixed. A similar approach is presented [55]; it identifies the decision threshold on the basis of predefined values on the cumulative histogram of the difference image. It is worth noting that these approaches are not fully automatic and objective from an application point of view, as they depend on the user sensibility in constraint definition with respect to the considered kind of change.

The dependence on subjective and empirical criteria represents a critical limitation of the aforementioned approaches to image thresholding. An interesting alternative consists in formulating the change-detection problem in the framework of the Bayesian decision theory in order to optimize the separation between changed and unchanged pixels in an unsupervised way. The main problem to be solved for the application of the Bayes decision theory consists in the explicit estimation of the statistical terms associated to the classes of change and no-change (i.e., the prior probabilities P(ωc) and P(ωn); and the probability density func-tions p(XC /ωn) and p(XC /ωc)) [62],[63] without any ground-truth information (i.e. without any training set). The starting point of methodologies based on the Bayesian decision theory is the hy-pothesis that the statistical distributions of pixels in the analyzed image can be modeled as a mixture of two densities associated with the classes of changed and unchanged pixels, i.e.,

( ) ( ) ( ) ( ) ( )= +C C n n C c cp X p X /ω P ω p X /ω P ω (1.5)

In the literature, explicit estimation of class statistical parameters has been addressed with the Expectation-Maximization (EM) al-gorithm which is an iterative approach to maximum-likelihood (ML) estimation for incomplete data problems [64]-[66]. The it-erative equations that characterize the EM algorithm are different according to the statistical model adopted for the distributions of the change and no-change classes. The more suitable statistical model varies according to the kind of data to be analyzed. For ex-ample, in the difference image obtained from multispectral pas-sive images the change and no-change classes are commonly as-

18

sumed to follow a gaussian distribution [3],[5],[19] or a mixture of guassian distribution [67]. When dealing with a log-ratio image obtained comparing SAR multitemporal images, it is possible to show [14],[58],[68],[69] that the Generalized Gaussian distribu-tion is a more flexible statistical model that allows handling the complexity of the class distributions better than the more com-monly used Gaussian distribution. The iterative equations needed for performing EM parameter optimization under the Gaussian, mixture of Gaussian and Generalized Gaussian class models can be found in [53],[58] and [67], respectively. Once the statistical parameters are computed, pixel-based or context-based decision rules can be applied. In the former group, we find: the Bayes rule for minimum error, the Bayes rule for minimum cost, the Ney-man-Pearson criterion, etc. [3],[5],[53],[63]. In the latter group, we find the contextual Bayes rule for minimum error formulated in the Markov Random Field (MRF) framework [53],[69].

Statistical parameters estimation under hypothesis in (1.5) may be also performed adopting an implicit approach [70]-[73]. As for the EM algorithm, the mathematical formulation changes accord-ing to the statistical model adopted for the change and no-change class distribution. As an example, we mention here the well-known Kittler and Illingworth (KI) thresholding technique which can be used under both the Gaussian [70] and the Generalized Gaussian [14],[68] assumption for the statistical distributions of the change and no-change classes. Despite its simplicity (the change-detection map is computed in a one-step procedure), the KI technique produces satisfactory change-detection results.

1.4. Novel Contributions of the Thesis On the basis of the analysis of the literature carried out in the

previous section, in this thesis the attention is focused on the de-velopment of advanced techniques for unsupervised change de-tection that take into account the peculiar properties of both mul-tispectral images acquired by passive sensors and SAR images acquired by active sensors. Both single-scale and multiscale novel approaches to change detection will be presented, which allow


19

identification of changes in different operational conditions. In the following, a brief overview of the main contributions of the thesis is reported.

Single-level (single-scale) unsupervised change detection.

With respect to this topic, the work carried out in the thesis aims at addressing two main limitations of the techniques pre-sented in the literature that are related to: i) the absence a formal and theoretical framework for the widely used change vector analysis technique; and ii) the absence of change-detection meth-ods capable to deal with large size remote sensing images.

The first limitation is addressed by defining a proper frame-work for a formal definition and a theoretical study of the change vectors obtained by applying the change vector analysis (CVA) technique to multitemporal images. This framework, which is based on the representation of the CVA in polar coordinates, aims at: i) introducing a set of formal definitions in the polar domain (which are linked to the properties of the data) for a better general description (and thus understanding) of the information present in spectral change vectors; ii) analyzing from a theoretical point of view the distributions of changed and unchanged pixels in the po-lar domain; iii) driving the implementation of proper pre-processing procedures to be applied to multitemporal images on the basis of the results of the theoretical study on the distribu-tions; and iv) defining a solid background for the development of advanced and accurate automatic change-detection algorithms in the polar domain.

The second limitation is addressed by presenting a split-based approach to automatic and unsupervised change detection in large-size multitemporal remote sensing images, which is suitable for both SAR and multispectral images. The proposed approach can detect in a consistent and reliable way changes in images of large size also when the extension of the changed area is small (and therefore the prior probability of the class of changed pixels is very small). It is based on: i) a split of the large-size image into

20

sub-images; ii) an adaptive analysis of each sub-image; iii) an automatic split-based threshold-selection procedure.

Multilevel (multiscale) unsupervised change detection.

With respect to this topic two problems are considered in the thesis: i) multilevel change detection in SAR images; and ii) mul-tilevel change detection in very high geometrical resolution opti-cal images.

The first problem is addressed by proposing a novel approach that exploits a wavelet-based multiscale decomposition of the log-ratio image (obtained by a comparison of the original multitempo-ral data) aimed at achieving different scales (levels) of representa-tion of the change signal. Each scale is characterized by a differ-ent trade-off between speckle reduction and preservation of geometrical details. For each pixel, a subset of reliable scales is identified on the basis of a local statistic measure applied to scale-dependent log-ratio images. The final change-detection result is obtained according to an adaptive scale-driven fusion algorithm. The proposed method exhibits both a high sensitivity to geometri-cal details (e.g., the borders of changed areas are well preserved) and a high robustness to noisy speckle components in homogene-ous areas.

The second problem is faced by proposing a parcel-based con-text-sensitive technique suitable for very high geometrical resolu-tion images. The proposed technique models the scene (and hence the changes occurred in the multitemporal data) at different reso-lution levels, by analyzing both the temporal and multilevel spa-tial contexts of pixels. Change detection is achieved by applying a specific comparison algorithm to each pixel of the considered im-ages, which properly analyzes the multilevel and multitemporal parcel-based context of the investigated spatial position. The adaptive nature of this representation allows to model accurately complex objects in the investigated scene as well as borders of the changed areas and change details, thus improving the pixel-based change-detection performances.


21

1.5. Thesis Overview This thesis is organized in 6 chapters. Chapters 2 and 3 present single-level (single-scale) approaches

to unsupervised change detection. Chapter 2 deals with the pro-posed theoretical framework for CVA in polar domain, while chapter 3 addresses the problem of change detection in large-size remote sensing images.

Chapters 4 and 5 present multilevel (multiscale) approaches. Chapter 4 proposes a detail-preserving scale-driven approach to change detection in multitemporal SAR images, while chapter 5 deals with a multilevel parcel-based approach to change detection suitable for very high geometrical resolution remote sensing im-ages. Finally, chapter 6 draws the conclusions of this work, and discusses future developments for the research conducted in the framework of this thesis.

All the chapters in this dissertation are to be considered as in-dependent to each other and therefore result self-consistent. Readers interested to one of the abovementioned topics can read a single chapter without the need of reading the whole dissertation.

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[62] K. Fukunaga, Introduction to Statistical Pattern Recognition, 2nd ed. London: Academic Press, 1990.

[63] R.O. Duda, P.E. Hart, and D.G. Stork, Pattern Classification, Wiley, New York, 2001.

[64] A.P. Dempster, N.M. Laird, and D.B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” Journal of Royal Statistic. Soc., Vol. 39, pp. 1-38, 1977.

[65] T.K. Moon, “The Expectation-Maximization algorithm,” Signal Processing Magazine, Vol. 13, pp. 47-60, 1996.

[66] A.P. Redner and H. F. Walker, “Mixture densities, maximum likelihood and the EM algorithm,” SIAM Review, Vol. 26, pp. 195-239, 1984.

[67] L. Bruzzone and D. Fernández Prieto, “An adaptive semi-parametric and context-based approach to unsupervised change detection in multitemporal remote-sensing images,” IEEE Trans. Image Processing, Vol. 11, pp. 452-446, 2002.

[68] Y. Bazi, L. Bruzzone, F. Melgani, “Automatic identification of the number and values of decision thresholds in the log-

28

ratio image for change detection in SAR images,” IEEE Lett. Geosci. Rem. Sens. (in press).

[69] Y. Bazi, L. Bruzzone and F. Melgani, “Change detection in multitemporal SAR images based on the EM-GA algorithm and Markov Random Fields,” Proc. IEEE 2005 Third Int. Workshop on the Analysis of Multi-Temporal Remote Sens-ing Images (Multi-Temp 2005), 2005.

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31

Chapter 2

2. A Theoretical Framework for Unsuper-vised Change Detection Based on Change Vector Analysis in Polar Do-main

This chapter addresses unsupervised change detection by pro-

posing a proper framework for a formal definition and a theoreti-cal study of the change vector analysis (CVA) technique. This framework, which is based on the representation of the CVA in polar coordinates, aims at: i) introducing a set of formal defini-tions in the polar domain (which are linked to the properties of the data) for a better general description (and thus understand-ing) of the information present in spectral change vectors; ii) analyzing from a theoretical point of view the distributions of changed and unchanged pixels in the polar domain (also accord-ing to possible simplifying assumptions); iii) driving the imple-mentation of proper pre-processing procedures to be applied to multitemporal images on the basis of the results of the theoretical study on the distributions; and iv) defining a solid background for the development of advanced and accurate automatic change-detection algorithms in the polar domain. The findings derived from the theoretical analysis on the statistical models of classes have been validated on real multispectral and multitemporal re-mote sensing images according to both qualitative and quantita-tive analyses. The results obtained confirm the interest of the pro-posed framework and the validity of the related theoretical analysis.

32

(This chapter is in press in the IEEE Transaction on Geo-science and Remote Sensing, vol. 44, March 2007. Co-author: Lorenzo Bruzzone)

2.1. Introduction Several unsupervised change-detection methodologies have

been proposed in the literature [1]-[3]. Among them, a widely used technique is the change vector analysis (CVA). CVA is typi-cally applied to multispectral images acquired by passive sensors, by considering more than one spectral channel in order to exploit all the available information about the considered event of change. However, usually CVA is used in an empirical way, without referring to a specific theoretical framework capable to properly and formally represent all the information contained in the spectral change vectors (SCVs) obtained by subtracting corre-sponding spectral bands of two images acquired at different dates. In addition, in the most of the applications, only the magnitude of the SCVs is exploited in order to identify changed pixels. Only in few applications also the direction of the vector is empirically used for deriving information on the kind of change occurred on the ground [4]-[13]. This lack of a formal framework and of a proper analysis of the statistics of data results in sub-optimal ap-plications of the CVA or, in some cases, in a non-complete under-standing of the richness of the information present in SCVs. This involves an incomplete exploitation of all the available informa-tion and/or the definition of change-detection algorithms that are not based on a solid theoretical background and on proper analy-sis procedures.

In order to address the aforementioned problems, in this chap-ter we present a consistent theoretical framework for a proper rep-resentation, modeling and exploitation of the information present in the SCVs computed according to the CVA technique. The pro-posed framework and the related analysis are developed in the context of a Polar representation of the CVA. In particular, the proposed novel contributions of this chapter consist in: i) the in-troduction of formal definitions for the characterization of the in-

CHAPTER 2 - A THEORETICAL FRAMEWORK FOR UNSUPERVISED CHANGE DETECTION BASED ON CHANGE VECTOR ANALYSIS IN POLAR DOMAIN

33

formation present in SCVs; ii) a theoretical analysis on the distri-butions of changed and unchanged pixels in the Polar domain under both general conditions and proper simplifying assump-tions; iii) the introduction of proper guidelines for defining effec-tive pre-processing strategies based on the expected properties of the theoretical distributions of changed and unchanged pixels; iv) the definition of a solid background for the development of ad-vanced and accurate automatic change-detection algorithms in the Polar domain. A validation of the theoretical analysis, carried out on two multispectral and multitemporal data sets, is also reported. The first data set is made up of two real multitemporal remotely sensed images including only one kind of change, while the sec-ond data set is obtained from the first one by properly simulating a second kind of change.

The chapter is organized into seven sections. The next section introduces the change-detection problem and the formulation of the CVA technique in both Cartesian and Hyperspherical do-mains. Section 2.3 gives some basics on the models for joint con-ditional class distributions in both Cartesian and Polar coordinate systems. Section 2.4 presents the proposed theoretical analysis on the models of marginal conditional distributions of magnitude and direction; furthermore, it proposes a critical analysis on the im-portance and the effects of image pre-processing procedures (e.g., radiometric corrections, coregistration, etc.) on the data distribu-tions. The validation of the proposed theoretical analysis carried out on single-change and double-change data sets, is reported in sections 2.5 and 2.6, respectively. Finally, Section 2.7 discusses the obtained results and draws the conclusions of this chapter.

2.2. Proposed Polar Representation Framework for CVA

2.2.1. Background and CVA Formulation Let us consider two coregistered multispectral images, X1 and

X2, of size JI ⋅ , acquired over the same area at different times t1

34

and t21. X1 and X2 be two multidimensional random variables that

represent the statistical distributions of pixels in images X1 and X2, respectively. Let Xb,t be the random variable representing the b-th component of the multispectral image Xt (t = 1, 2) in the con-sidered feature space. Let Ω=ωn, Ωc be the set of classes of un-changed and changed pixels to be identified. In greater detail, ωn represents the class of unchanged pixels and ω,...,ω

K1 cc=cΩ the set of the K possible classes (kinds) of change occurred in the considered area.

The first step of the most widely used change-detection tech-niques presented in the literature performs comparison between the two considered images according to a proper operator [1]. When dealing with multispectral images, the comparison operator is usually the vector difference, which is applied to a n-dimensional feature space in order to give as input to the change-detection process all the relevant spectral information. This tech-nique is known as change vector analysis (CVA) [1],[5] and has been successfully used in many different application domains [4]-[13]2. CVA firstly computes a multispectral difference image (XD) subtracting the spectral feature vectors associated with each corresponding spatial position in the two considered images X1 and X2. Let XD be the multidimensional random variable repre-senting the spectral change vectors (SCVs) in the difference im-age obtained as follows [1]:

2 1X = X - XD . (2.1) Each SCV is usually implicitly represented in Polar coordi-

nates with its magnitude and direction. Although the direction of the SCVs is rich of information (e.g., on the kind of changes oc-

1 In this chapter, only the case of pairs of images is discussed. It is worth noting that the

proposed framework can be applied to a multitemporal sequence made up of more than two images by analyzing separately couples of images.

2 The particular case of working with a single feature reduces the CVA to the univariate image differencing technique [1].


35

curred on the ground and on the distribution of registration noise), in the most of the applications it is not considered. Among the few studies reported in the literature where magnitude and direc-tion expressed as cosine functions are considered together for change detection, we recall [5]-[13]. In 1980, Malila [5] first for-mulated the concept of change vector and then used both magni-tude and direction in a two-dimensional space for identifying changes due to plants clearcut and regrowth in the northern Idaho (U.S.) forest. In [5]-[8] the direction variable was subdivided into a fixed number of sectors, each of them corresponding to positive or negative changes in one of the B considered features (i.e., spec-tral channels or linear combinations of them, like Tasseled-Cap transformation). This kind of quantization leads to the definition of a maximum of 2B sectors and hence of types of changes. The major drawback of this approach is that different kinds of changes could assume the same sector code. In [9], the CVA sector coding approach was extended to the solution of multivariate, full-dimensional and also multi-interval problems (i.e., applications involving more than two acquisition dates). In [10], Allen and Kupfer introduced in the CVA technique the use of direction co-sines for the description of SCV directions. They applied a hierar-chical linear discriminant analysis for testing predictive power of magnitude and vector angles in solving change-detection prob-lems. Direction cosines were used also in [11] and [12]. In these works authors firstly identified changed pixels on the basis of magnitude values, then image classification algorithms were ap-plied to direction cosines for discriminating the different kinds of change. In [13], authors defined a modified CVA (mCVA) tech-nique where Polar coordinates are transformed back into a Carte-sian coordinate system to overcome discontinuity between 0 and 2π and different kinds of changes are then detected by using ei-ther supervised or unsupervised clustering algorithms. A different approach to the use of the direction information has been pre-sented in [4], where the authors proposed a method for estimating and reducing the effects of the registration noise. The method is

36

based on a joint exploitation of the magnitude and direction com-ponents.

However, the most of the analyses reported in the literature have been carried out in an empirical way without a rigorous characterization of the statistical models of information classes and without referring to a proper theoretical framework for a completely understanding and processing the information present in SCVs. In this chapter, in order to fill the aforementioned gaps, we propose a rigorous framework for CVA in polar domain.

2.2.2. General Framework for Hyperspherical Representation Given a B-dimensional feature space, the SCV associated with

a pixel of the analyzed scene can be described with its magnitude value and B-1 directions. In this work, we propose to represent the properties of the SCVs, instead of using a Cartesian coordi-nate system, by plotting SCVs in a B-dimensional Hyperspherical coordinate system3. Thus the multidimensional random variable XD can be represented with a random variable [0, )ρ ∈ +∞ that models the statistical distribution of the change-vector magnitude, and B-1 random variables [ϑ , 1ϕ , 2ϕ ,..., 2Bϕ − ] that represent the distribution of the change vector angular coordinates ( [0,2 )ϑ π∈ and [0, ], 1,..., - 2k k Bϕ π∈ = ). It is worth noting that changing the coordinate system has a dramatic impact on the statistical distri-butions of the considered classes. This aspect will be analyzed in the next section.

Let X1,D, …, XB,D be the random variables representing the dis-tributions of SCVs along the B dimensions (spectral channels) of the considered Cartesian coordinate system; then, the relations between the random variables modeling SCVs in the Cartesian and the Hyperspherical coordinates are the following:

3 In the particular case of B=2 the Hyperspherical coordinate system is said Polar coor-

dinate system.


37

1

,1

2

1,1

2

,1

sin cos , 1 - 2

sin cos

sin sin

b

b D k bk

B

B D kk

B

B D kk

X ρ b B

X ρ

X ρ

ϕ ϕ

ϕ ϑ

ϕ ϑ

−

=

−

−=

−

=

⎛ ⎞= ≤ ≤⎜ ⎟⎝ ⎠⎛ ⎞= ⎜ ⎟⎝ ⎠⎛ ⎞= ⎜ ⎟⎝ ⎠

∏

∏

∏

(2.2)

where [0, )ρ ∈ +∞ , [0, ], 1,..., - 2k b Bϕ π∈ = and [0,2 )ϑ π∈ .

In the following, for simplicity, we will assume that the CVA technique is applied only to two spectral channels of the consid-ered multitemporal images, i.e., that a two-dimensional coordi-nate system is sufficient to completely describe SCVs. However, the analysis can be generalized to the case of more spectral chan-nels by considering more direction contributions for describing each SCV (see Appendix A). It is worth noting that, although the abovementioned generalization is possible, the assumption of working with a couple of spectral channels is reasonable in many change-detection problems [14]-[16]. This choice is often due to the need of isolating the most informative features with respect to the specific considered problem without including noisy and mis-leading spectral channels in the analysis. In the above assumption, in the Cartesian coordinate system only random variables X1,D and X2,D are necessary to describe SCVs, whereas in the Polar coordi-nate system random variables, representing the magnitude ρ and the direction ϑ are required for each SCV. The relation between Cartesian and Polar representation of the difference image is as follows:

2 21, 2,

2,

1,

( ) ( )

arctan .

D D

D

D

ρ X X

XXϑ

⎧ = +⎪⎨ ⎛ ⎞=⎪ ⎜ ⎟

⎝ ⎠⎩

(2.3)

38

2.2.3. Proposed Polar Framework for the CVA Technique: Definitions

In this section we propose a rigorous characterization of the Polar framework for the CVA technique. First of all, observe that in the Polar representation, all the change vectors of a given scene are included in a magnitude-direction domain MD defined as (see Fig. 2.1):

[0,ρ ] and [0,2 )maxMD ρ ϑ π= ∈ ∈ (2.4)

where ρmax is the maximum value assumed by the magnitude on the considered image, i.e.,

2 21, 2,ρ max ( ) ( )max D DX X= + . (2.5)

According to the given definition of the magnitude-direction domain MD, in order to establish a clear framework for CVA, we propose to identify different regions in MD for pointing out the information present in SCVs. From the definition in (2.4) and fol-lowing indications in [16], we expect that unchanged pixels have magnitude close to zero (often not exactly zero due to the pres-ence of noise components), while changed pixels have magnitude far from zero. Consequently it is possible to identify two different regions associated with: i) unchanged and ii) changed pixels. Thus the Polar domain can be split into two parts: i) circle Cn of no-changed pixels; and ii) annulus Ac of changed pixels. This can be done according to the optimal (in the sense of the theoretical Bayesian decision theory) threshold value T that separates pixels belonging to ωn from pixel belonging to Ωc (dark gray and light gray areas in Fig. 2.1, respectively).

Definition 1: the Circle of no-changed pixels Cn is defined as

πϑϑ 20 and 0: <≤<≤= Tρρ,Cn . (2.6)


39

Cn can be represented in the Polar domain as a circle with radius T. From this definition we can state that for the generic pixel (spa-tial position) (i,j), it holds that:

( ) ( )n ni, j i, j C∈ ω ⇔ ∈ (2.7)

or in other words:

( ) ( )ni, j ρ i, j T∈ ω ⇔ < . (2.8)

This means that all the unchanged pixels satisfy (2.7) [or equiva-lently (2.8)] and are included in Cn. Definition 2: the Annulus of changed pixels Ac is defined as:

: ρ and 0 2c maxA ρ, T ρϑ ϑ π= ≤ ≤ ≤ < . (2.9)

Ac can be represented in the Polar domain as a ring with inner ra-dius T and outer radius ρmax. From this definition we can state that for the generic spatial position (i,j), it holds that:

( ) Ω ( )c ci, j i, j A∈ ⇔ ∈ (2.10) or in other words:

( ) Ω ( ) ρc maxi, j T ρ i, j∈ ⇔ ≤ ≤ . (2.11)

This means that all the changed pixels satisfy (2.10) [or equiva-lently (2.11)] and are included in Ac.

According to the above definitions, the Polar domain can be described as the union of Ac and Cn, i.e.,

c nMD A C= ∪ . (2.12)

The previous definitions have been based on the values of the magnitude, independently on the direction variable. A further im-portant definition is related to sectors in the Polar domain, which are mainly related to the direction of the change vectors and therefore to the kinds of change occurred on the ground.

Definition 3: the Annular sector Sk of change ω kc ∈Ωc is defined as:

40

1 2 1 2, : and , 0 2k k k k kS ρ ρ Tϑ ϑ ϑ ϑ ϑ ϑ π= ≥ ≤ < ≤ < < . (2.13)

Sk can be represented in the Polar domain as a sector of change within the annulus of changed pixels [see (9)] and bounded from two angular thresholds

lkϑ and 2kϑ (see Fig. 2.1). We expect that

pixels that belong to the same kind of change are included in the same annular sector. In the Polar coordinate system, two angular coordinates identify two sectors: i) a convex sector (i.e. the small-est one), and ii) a concave sector (i.e. the largest one). As it is rea-sonable to expect that pixels belonging to the same change class have a low variance, generally the sector we are interested to is the convex one. It is worth noting that this condition is no longer satisfied if the convex sector covers the discontinuity between 0 and 2π In this case the variance of the changed pixels is high and the relation between the two angular coordinates is inverted, i.e.,

21 kk ϑϑ > ; thus, the definition of Sk becomes:

1 2

1 2

, : and 2 0 , 0 2

k k k

k k

S ρ ρ Tϑ ϑ ϑ π ϑ ϑϑ ϑ π

= ≥ ≤ < ∪ ≤ <≤ < <

. (2.14)

Fig. 2.1 depicts an example of annular sector as a hatched sector of annulus that overlaps region Ac between angular coordinates

lkϑ and 2kϑ .

In real applications, often the pixels with magnitude close to the optimal (in the sense of the theoretical Bayesian decision the-ory) threshold value T and with direction close to the two angular threshold values

lkϑ and 2kϑ can not be accurately labeled accord-

ing to a simple thresholding procedure due to the intrinsic uncer-tainty present in the data. In these cases, by taking into account that the spatial autocorrelation function of the images is not im-pulsive (i.e., pixels are spatially correlated4), it is possible to in-crease the reliability of the decision process according to a con-text-sensitive analysis of the investigated pixel [16]. This analysis 4 This is true under the reasonable assumption that the geometrical resolution of the

considered multispectral sensor is proper for the analyzed scene.


41

is aimed at exploiting the spatial correlation as an additional in-formation source in the decision process. In order to model and represent this uncertainty in the proposed framework, we can de-fine two additional regions: i) the annulus Au of uncertain pixels with respect to the magnitude; and ii) the annular sector rkuS of uncertain pixels with respect to change ω kc ∈Ωc and thus direc-tions

rkϑ (where r =1, 2).

Figure 2.1 Representation of the regions of interest for the CVA technique in the Polar coordinate system.

Definition 4: the Annulus Au of uncertain pixels is defined as:

: and 0 2uA ρ, T ρ Tϑ α α ϑ π= − ≤ ≤ + ≤ < (2.15)

where α is a parameter that defines the margin around T in which pixels cannot be easily identified as either changed or unchanged. Au can be represented in the Polar domain as a ring with inner ra-dius T-α and outer radius T+α (light gray annulus in Fig. 2.2). From this definition, we can state that:

( ) ( )ui, j A T ρ i, j Tα α∈ ⇔ − ≤ ≤ + . (2.16)

42

This means that all the uncertain pixels satisfying (2.16) are in-cluded in Au. The use of this definition depends on the specific data analysis strategy (if no contextual information is considered, it is assumed that α = 0 and consequently uA = ∅ ).

Definition 5: the Annular Sector rkuS of uncertain pixels of change ω kc ∈Ωc close to

rkϑ is defined as:

, : and , 0 2r r r r r rku k k k k kS ρ ρ Tϑ ϑ β ϑ ϑ β ϑ π= ≥ − ≤ < + ≤ < ,1 or 2r =

(2.17)

where rkβ is a parameter that defines the margin around

rkϑ in which pixels cannot be easily identified as belonging to ω kc (dark

Figure 2.2 Representation of the regions of uncertainty for the CVA technique in the Polar coordinate system.

gray annular sectors in Fig. 2.2). We expect that in general

21 kk ββ = (as for the annulus Au of uncertain pixels, if no contex-tual information is considered, it is assumed that

rkβ = 0 and con-

sequently rkuS = ∅ ).


43

In the following of the chapter, for simplicity, we will assume the absence of uncertainty, i.e, we will assume uA = ∅ and

rkuS = ∅ (r =1, 2).

2.3. Analysis of the Joint Conditional Distributions of Classes

The definition of the different regions of interest in the Polar domain allows a better representation of the change-detection problem and drives to the analysis of another important problem that concerns the expected distribution of classes of interest in the change-detection problem.

2.3.1. Class Distributions in the Cartesian Domain As known from the literature [17], the statistical distribution of

natural classes in images acquired by multispectral passive sen-sors can be considered approximately Gaussian. Thus, both mul-tidimensional random variables 1X and 2X can be modeled as a mixture of multidimensional Gaussian distributions in the Carte-sian domain. As DX is obtained subtracting 1X from 2X , its dis-tribution can be also reasonably represented as a mixture of mul-tidimensional Gaussian distributions, each of them associated with a class ωi , 1, , ,..., Ki n c n c cω ∈ = ω = ω ω ωΩ Ω :

1

| |

|

( ) (ω ) ( ω ) ( ) ( )

(ω ) ( ω ) (ω ) ( |ω )=

= +

= +∑ k k

n n c c

K

n n c ck

D D D

D D

X X X

X X

p P p P p

P p P p

Ω Ω (2.18)

where ( |ω )iDXp is a normal conditional density that models the distribution of the class iω in the multivariate difference image. As classes in XD can be approximated as jointly Gaussian distrib-uted, it is possible to show that all the components Xb,D, obtained subtracting corresponding spectral bands (b=1,2), are also a mix-ture of normally distributed random variables. This consideration and the assumption in (2.18) are the starting point for analyzing

44

the statistical distributions of the no-change class and of the K classes of change in the Polar domain.

2.3.2. Class Distributions in the Polar Domain From (2.18), it can be seen that the analytical expression of

class distributions in the Polar domain can be obtained by com-puting the joint conditional probability density functions of the magnitude and direction of SCVs [see (2.3)] of the 2-dimensional random variable XD. A simplifying hypothesis is to consider fea-tures X1,D and X2,D as independent (see section 2.7 for a detailed discussion on this hypothesis). Under this assumption, the distri-bution of the class ωi ( Ω∈ωi ) in a Cartesian coordinate system can be written as the product of the two marginal densities

( |ω )ib,DXp of the class ωi (b=1,2), i.e.,

2 21, 1 2, 22 2

1 2 1 2 ( ) ( )1( ) exp 2 22

μ μσ σπσ σ

⎡ ⎤− −⎢ ⎥− −⎢ ⎥⎣ ⎦

ω = D ,i D ,iD i

,i ,i ,i ,i

X Xp X | (2.19)

where ,b iμ and ,b iσ are the mean value and the standard deviation, respectively, of the Gaussian distributed marginal density of class ωi over the b-th considered feature (b=1,2). Applying the trans-formation from Cartesian to Polar coordinate system, the joint conditional distribution can be written as:

2 21, 2,

2 21, 2,

1, 2,

( cos ) ( sin )exp 2 2( | ) 2

ρ ϑ μ ρ ϑ μσ σ

ρ ϑ πσ σ

− −⎡ ⎤− −⎢ ⎥⎣ ⎦ω =

i i

i ii

i ip , . (2.20)

According to this general equation (which is the starting point for the statistical analysis reported in the next section) we can define the quantities typically used for evaluating the performance of change-detection algorithms (i.e., false alarms and missed alarms) in the context of the proposed framework. Let us define the fol-lowing decision regions: i) the region of changed pixels (Rc) that corresponds to the union

of all identified non-overlapping annular sectors Sk (k = 1,…,


45

K): ∪K

kkc SR

1== ;

ii) the region of no-changed pixels (Rn) that corresponds to the

union of circle of no-change Cn and the region 1

K

c kk

A S=

−∪

complementary to the region of changed pixels with respect to

Ac, i.e. ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−==∪∪K

kkcnn SACR

1

.

In ideal situations no pixels will fall in region 1

K

c kk

A S=

−∪ ,

whereas in real situations (when noise affects the data) we may have patterns in the annulus of changed pixels that do not belong to any of the sectors of changed pixels (these patterns are usually few and relatively isolated).

Given the aforementioned decision regions and the joint con-ditional distributions for the classes of change and no-change in (2.20), it is possible to analytically define the false and missed alarms.

False alarms occur when unchanged pixels are identified as changed. The probability of this kind of error Pf can be written as the integral of the joint conditional probability density function given the class of no-change over the region of changed pixels, i.e.

( | ) ρ ϑ ρ ϑ= ω∫c

f n

R

P p , d d . (2.21)

Missed alarms occur when changed pixels are identified as un-changed. The probability of this kind of error Pm can be written as the sum of the K integrals (one for each class of change kcω ) of the joint conditional probability density function given the class

kcω of change over the region associated to unchanged pixels, i.e.

1

( | ) ρ ϑ ρ ϑ=

= ω∫∑ k

n

K

m c

Rk

P p , d d . (2.22)

46

2.4. Analysis of the Marginal Conditional Distributions of Magnitude and Direction

The joint conditional probability in (2.20) is too general to be efficiently used in solving change-detection problems. A more suitable way to approach the problem is to compute the marginal conditional densities of the magnitude ρ and the direction ϑ . Starting from (2.20), these two densities can be computed for each class ωi by integrating (2.20) over the range of ϑ and ρ, re-spectively.

Let us first consider the marginal conditional density of the magnitude ( | )ip ρ ω . Integrating (2.20) over the range of ϑ leads to the following equation:

2,1,2 21, 2,

22 2

0

1, 2,

( cos ) ( sin )exp d2 2

( )2

ii

i i

ii i

ρ

p ρ |

πρ ϑ μ ρ ϑ μ ϑ

σ σ

πσ σ

⎡ ⎤− −− −⎢ ⎥⎢ ⎥⎣ ⎦

ω =∫

. (2.23)

This integral can not be expressed in a closed form, but it can be reduced to an infinite series of Bessel functions. By following [18], it is possible to show that ( )ωip ρ | can be written as:

2 22

1, 2, 0( ) ( )

cos 2 arctan , 0

( ) exp( ) ( 1)pi p p p

i i p=I P I Q R

Rp Q

ρp ρ | V

ρ

σ σ

∞

ε +

⎫⎛ ⎞ ≥⎬⎜ ⎟⎝ ⎠⎭

ω = − −∑(2.24)

where Ip(z) is the p-th order modified Bessel function of the first kind defined as:

2

1I ( ) exp( cos( ) ) 2

C

p

C

z z u jpu duπ

π

+

= − +∫ (2.25)

where C is a constant, j is the imaginary unit, and D, P, Q, R and εp are defined as follows:


47

2 2 2 2 21, 2, 2, 1, 2

2 2 2 21, 2, 1, 2,2 2 4i i i i

i i i iV μ μ ρ σ σ ρ

σ σ σ σ+ −= + + , 2 2

2, 1, 22 21, 2,4

σ σ ρσ σ

−= i i

i iP ,

1,21,

μ ρσ

= i

iQ , 2,

22,

μ ρσ

= i

iR , 1 for 0;

2 for 0;ppp

=⎧ε = ⎨ ≠⎩

.

(2.26)

The marginal conditional density of the direction ( )ϑ ωip | can be obtained by integrating (2.20) over the range of ρ. The integral can be written in a closed form. It is possible to prove that after some handling we obtain:

( )

2 2 2 222, 1, 1, 2,

2 22 2 2 3 1, 2,1, 2,

22 22, 1, 1, 2,

2 2 2 2 21, 2, 1, 2,

2, 12 22, 1, 1, 2,

(1 tan ( ))( ) exp24 ( tan ( ) )

tan( )2 exp

2 ( tan ( ) )

( tan( ) ) 1 erf

i i i ii

i ii i

i i i i

i i i i

ii i i i

μ μp |

μ μ

μμ μ

σ σϑϑσ σπ σ ϑ σ

σ ϑ σπ

σ σ σ ϑ σ

σσ ϑ σ

⎧ ⎛ ⎞++ω = −⎨ ⎜ ⎟+ ⎝ ⎠⎩

⎡ ⎛ ⎞+⎢ ⎜ ⎟−+⎢ ⎜ ⎟

⎝ ⎠⎣

+ +

2 2, 1, 2,

2 2 21, 2, 1, 2,

2 2 21, 2, 1, 2,

tan( )2( tan ( ) )

2 ( tan ( ) ) , [0,2 )

i i i

i i i i

i i i i

μϑ σσ σ σ ϑ σ

σ σ σ ϑ σ ϑ π

⎡ ⎤⎛ ⎞+⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥+⎝ ⎠⎣ ⎦

⎤+ + ∈⎦

(2.27)

Figs. 2.3 and 2.4 show examples of the behaviors of the mag-nitude and direction marginal conditional densities versus the mean values ( 1,iμ , 2,iμ ) and the standard deviations ( 1,iσ , 2,iσ ), re-spectively, of the class ωi characterized by a Gaussian distribu-tion in the Cartesian coordinate system. It is worth noting that the periodicity of the direction distribution depends on the tangent function; in real applications the proper maximum should be se-lected according to the data distribution.

As can be seen, (2.24) and (2.27) represent two complex mathematical expressions. In real applications, usually additional hypotheses can be made in order to simplify the analytical ex-pressions of the probability density functions. In the change-detection problem, different assumptions can be formulated for the classes of changed and unchanged pixels. In the following, the

48

cases related to the two classes of interest will be addressed sepa-rately and in greater detail.

(a)

(b)

Figure 2.3 Examples of conditional distributions of the magnitude: (a) with respect to different values of iμ2, ( iμ1, = 5, i1,σ = i2,σ =10); and (b) with re-

spect to different values of i2,σ ( iμ1, = iμ2, = 5 and i1,σ =10).


49

(a)

(b)

Figure 2.4 Examples of conditional distributions of the direction: (a) with respect to different values of 2,iμ ( 1,iμ = 5, i1,σ = i2,σ = 10) and in the particular case of ( 1,iμ = 2,iμ =0 that leads to the Uniform distribution; and (b) with respect to different values of i2,σ ( 1,iμ = 2,iμ = 5 and i1,σ =10).

2.4.1. Statistical Models for the Class of Unchanged Pixels As stated in section 2.3.2, we assume that images X1 and X2

have been coregistered [19],[20] and that possible differences in

50

the light and atmospheric conditions at the two times have been corrected [21]5. Under these hypotheses, we can reasonably as-sume that in unchanged areas natural classes do not significantly change their distributions between the two acquisition dates. This simplifies the computation of distributions in the Polar domain as we can write:

1, 2, 0ω ω≅ ≈n nμ μ (2.28)

1, 2,σ σ σω ω ω≅ =n n n. (2.29)

Substituting both expressions (2.28) and (2.29) into (2.23) and solving the integral, we get for the magnitude random variable the following probability density function:

2

2 2( ) exp

2σ σω ω

⎛ ⎞ω = −⎜ ⎟

⎝ ⎠n n

nρ ρp ρ | , 0≥ρ (2.30)

which is commonly known as the Rayleigh distribution. Concerning the statistical distribution of the direction variable

for the class of unchanged pixels, it can be obtained substituting (2.28) and (2.29) into (2.27) i.e.,

1( ) , [0,2 )2np |ϑ ϑ ππ

ω = ∈ (2.31)

This means that the statistical distribution of the direction is Uni-form within [0,2 )π .

2.4.2. Statistical Models for the Classes of Changed Pixels The analytical study of the distribution of the generic class ω kc ,

kc cω ∈Ω , (for simplicity of notation in the following ω kc will be in-dicated as ωk ), of changed pixels is more complex than the one carried out for the class of unchanged pixels. In this case, assump-tion (2.28) is no further valid, as changes in land-cover types modify the mean values of the natural classes in different ways in

5 This assumption will be discussed in section 2.4.3.


51

different spectral channels (this depends on the kind of change). This leads to the following condition:

1 2, , 0k kμ μω ω≠ ≠ . (2.32)

It is worth noting that if 1, 2,k kμ μω ω= the analysis of the distribu-tion is simplified. In order to further simplify the computation of the magnitude and direction statistical distributions, we can as-sume that:

1 2,,σ σ σk k kω ω ω≈ = . (2.33)

In some applications this assumption is reasonable, but its va-lidity should be verified for any specific case considered6. Thus, rewriting (2.23) according to (2.32) and (2.33) and solving the in-tegral, it is possible to show that the random variable representing the magnitude is Ricean distributed, with probability density function given by:

2 2

02 2 2

( ) exp I2

k k

k k k

kρ ρ M ρMp ρ |

σ σ σω ω

ω ω ω

⎛ ⎞ ⎛ ⎞+ω = −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

, 0≥ρ (2.34)

where I0(.) is the modified zeroth-order Bessel function of the first kind [see (2.24)] and ω kM the non-centrality parameter of the class of change kω :

2 21, 2,k k kM μ μω ω ω= + . (2.35)

It is worth noting that as ω kM becomes much larger than the standard deviation σωk , then the Ricean distribution tends to be-come Gaussian.

Concerning the density of the direction of the class of changed pixels ωk , it is possible to prove that, in the aforementioned as-

6 If the assumption is not verified, the general equations (2.24) and (2.27) should be

used for modeling the statistical distributions of magnitude and direction, respectively, or a proper pre-processing should be applied to the data before using the simplified model (see section 2.4.3).

52

sumptions, (2.27) can be simplified leading to the following Non-uniform distribution:

( ) ( )

2 2 2 22, 1, 2, 1,

2 2

22, 1, 2, 1,

2 2

tan( )1( ) exp 22 2 2 (1 tan ( ))

tan( ) tan( )exp 1 erf

2 (1 tan ( )) 2(1 tan ( ))

k k k k

k k

k k k k

k k

kμ μ μ μp | -

- μ μ - μ μ

ω

ϑϑ πσ σ π ϑ

ϑ ϑσ ϑ σ ϑ

ω ω ω ω

ω

ω ω ω ω

ω ω

⎧+ +⎛ ⎞⎪ω = +⎨⎜ ⎟ +⎝ ⎠⎪⎩⎫⎛ ⎞ ⎡ ⎤⎛ ⎞+ + ⎪⎜ ⎟ ⎢ ⎥+ ⎜ ⎟ ⎬⎜ ⎟+⎜ ⎟ +⎢ ⎥⎪⎝ ⎠⎣ ⎦⎝ ⎠ ⎭

[0,2 )ϑ π∈

(2.36)

2.4.3. Discussion In the previous sub-sections, we analyzed the statistical mod-

els more suitable to represent class distributions in the Polar do-main in the general case and in some simplifying assumptions. Since the use of simplified models is of great importance for the development of effective and adequately complex automatic change-detection techniques, here we report a critical discussion on the assumptions considered for modeling the distributions of the classes of changed and unchanged pixels. In addition, we ana-lyze practical implications of the theoretical analysis, in order to suggest criteria for driving the definition of proper pre-processing techniques for an effective data representation. Table 2.1 reports a summary of the theoretical statistical distributions derived (under simplifying assumptions) in sections 2.4.1 and 2.4.2 for magni-tude and direction of change and no-change classes.

TABLE 2.1

SUMMARY OF THE THEORETICAL MARGINAL CONDITIONAL DISTRIBUTIONS OF MAG-NITUDE AND DIRECTION FOR THE CHANGE AND NO-CHANGE CLASSES UNDER SIMPLI-

FYING ASSUMPTIONS.

Conditional distribution Class Magnitude (ρ) Direction ( ϑ )

Unchanged pixels ( ωn ) Rayleigh Uniform Changed pixels ( ωk ) Rice Non-Uniform

First of all, it is important to point out that a hypothesis at the

basis of the theoretical analysis reported in the previous sub-


53

sections consists in assuming independence among features de-scribing SCVs in the Cartesian domain. The validity of this as-sumption depends on the considered images and applications, as well as on the investigated spectral channels. Significant devia-tions from this assumption affect the precision of the analytical distributions derived for describing the behaviors of changed and unchanged pixels. Nonetheless, if for a generic data set the aforementioned assumption is not reasonable, it is possible to transform data from the original feature space to a transformed domain, in which features can be approximately modeled as un-correlated. This can be obtained by applying a principal compo-nent transformation (PCT) to the features characterizing the SCVs [22]. In this way, at the cost of an additional transformation ap-plied to the data, it is possible to properly adopt the analytical models described in sections 2.4.1 and 2.4.2 in the development of change-detection techniques7.

The aforementioned assumption is at the basis of the presented theoretical analysis. All the other assumptions (discussed in the following) allow only to simplifying the statistical distributions with respect to the general models in (2.24) and (2.27) which can be included in automatic techniques for operational change-detection algorithms, but are rather complex. For this reason, in the following we analyze the simplifying assumptions in greater detail and discuss possible pre-processing procedures aimed at transforming data so that these assumptions hold.

An important hypothesis that deserves to be discussed con-cerns the assumption that different features in the Cartesian SCV domain have similar standard deviations. The validity of the as-sumption in the original feature space depends on the considered images and applications, as well as on the investigated spectral channels. However, as for the assumption of the independence, if

7 It is worth noting that the PCT guarantees independence of features on the basis of the

global distributions of patterns in the feature space. This means that after transforma-tion the feature independence on the classes of changed and unchanged pixels can be assumed only in an approximate way.

54

this approximation is not acceptable for the considered data set, it is possible to transform the original feature space according to a procedure of diagonalization and whitening [22] and to apply change-detection algorithms to the transformed space (as the ap-plication of this procedure modifies the relation between the cor-relation terms of spectral channels, it should be applied with cau-tion)8.

A further relevant assumption to be analyzed for the class of unchanged pixels consists in the hypothesis that the mean vector components of the SCVs are equal to zero. This assumption is verified if the images are radiometrically corrected, so that the mean vectors are the same at the two dates (this condition can be always satisfied according to proper pre-processing strategies). Under this assumption we obtain that the magnitude has a Rayleigh distribution and the direction has a Uniform distribution. However, in some practical cases images are not radiometrically corrected and pre-processing procedures for matching the light conditions are neglected. According to the presented theoretical analysis, this may result in two main very critical effects: i) a pos-sible increase of the overlapping of the classes of unchanged and changed pixels in the magnitude domain; ii) a strong deviation of the conditional distribution of the direction of unchanged pixels from the expected Uniform model. The first effect is due to the fact that, although differences in light conditions result in a bias common to all classes in the Cartesian domain, when the non-linear magnitude operator is applied, the bias may result in an in-crease of overlapping between classes (this behavior will be shown in the experimental analysis reported in Section 2.5). The second effect results from the observation that if the mean-value components of the SCVs are different from zero, the direction distribution of the class of unchanged pixels is no longer Uniform, but assumes a completely different behavior, which should be

8 As stated for PCT also whitening produces effects on the basis of the global distribu-

tions of patterns in the feature space. This means that after transformation the standard deviation of the classes can be considered similar only in an approximate way.


55

modeled with equation (2.36) (see Fig. 2.4). This has a dramatic impact on the data processing strategy, as it completely changes the distribution of the direction with respect to what expected in the ideal case. These observations confirm the importance of the radiometric correction step in the CVA technique.

Finally, another important implication derived from the theo-retical analysis concerns the behavior of the distributions of the direction for the unchanged and changed classes, which are Uni-form and Non-uniform, respectively. This means that it is possible to exploit the direction information (and in particular the modes associated to distribution for each changed class) for reducing the effects of the residual sources of noise present in the pre-processed multitemporal images (e.g. the registration noise that appears outside the change modes can be easily removed, as it will be shown in the experimental analysis reported in section 2.5.1). This confirms from a theoretical point of view the analysis carried out in [4], where the direction information was used for identifying, modeling and reducing registration noise.

In order to illustrate the use of the proposed CVA framework and to assess its effectiveness, in the next two sections we con-sidere two different real multitemporal data sets: i) a single-change data set; and ii) a double change data set.

2.5. Experimental Results: Single-Change Case

2.5.1. Data Set Description and Experiment Design The first data set is made up of two multispectral images ac-

quired by the Thematic Mapper (TM) multispectral sensor of the Landsat 5 satellite on the Island of Sardinia (Italy) in September 1995 (t1) and July 1996 (t2). Both images have a spatial resolution of 30 [m]×30 [m]. The area selected for the experiments is a sec-tion (412×300 pixels) of the two scenes including Lake Mulargia. As an example of the images used in the experiments, Figs. 2.5 (a) and (b) show channel 4 of the September and July images, re-spectively.

56

Between the two acquisition dates only one kind of change oc-curred in the investigated area, which is related to the extension of the lake surface (the water volume of the Lake Mulargia in-creased producing an enlargement of the lake surface). The multitemporal images were coregistered and radiometrically cor-rected. A reference map of the analyzed site was defined accord-ing to a detailed visual analysis of both the available multitempo-ral images and the difference image. The obtained reference map contains 7480 changed pixels and 116120 unchanged pixels (see Fig. 2.5 (c)). The extracted information was used for both com-puting the parameters of the statistical distributions for the classes of interest and evaluating the performances (in terms of false and missed alarms) of the change-detection process carried out by us-ing the proposed statistical models.

(a)

(b)


57

(c)

Figure 2.5 Images of the Lake Mulargia (Italy) used in the experiments. (a) Channel

4 of the Landsat-5 TM image acquired in September 1995; (b) Channel 4 of the Landsat-5 TM image acquired in July 1996; (c) available reference map of changed areas.

The considered change-detection problem is relatively simple

and thus it is suitable for a proper understanding of the properties and potentialities of the proposed framework. In this particular single-change problem, we define ωω

1 cc ==cΩ . In the experi-ments, we considered only the two spectral channels 4 and 7 of the TM, i.e. the near and the middle infrared, as they are the most reliable for detecting changed areas. For simplicity of notation, in the following these channels will be referred with subscripts 1 and 2, respectively.

In order to assess the effectiveness of the proposed framework, three different experiments have been carried out.

In the first experiment, a qualitative analysis of the true distri-butions of data in the Polar domain versus different pre-processing applied to the images is carried out. This experiment is aimed at pointing out the effects of the pre-processing procedures on both the data distributions and the precision of the models in-troduced in section 2.4 for data representation.

The second experiment is aimed at validating the accuracy of the theoretical models of distributions presented in section 2.4 in fitting the true data distributions for both the magnitude and the direction, under the simplifying assumptions introduced in sec-

58

tions 2.4.1 and 2.4.2. Furthermore, the goodness-to-fit of the Rayleigh and Rice distributions adopted for the magnitude of the change and no-change classes, respectively, is compared with the goodness-to-fit of the widely used Gaussian model. Here, the well known Kolmogorov-Smirnov (KS) test is used for establish-ing whether a statistical model fits or not the true distribution [23]. The KS statistical test determines if two sets of data are drawn from the same statistical distribution. The test is based on the comparison between the cumulative distribution functions of the true data Sn(x)9 (or empirical distribution function) and the expected one F(x) (i.e., the cumulative distribution of the density function adopted for modeling the data) [23]. The KS test com-pares the cumulative distributions of a difference operator com-puting the so called KS-statistic Dn:

)()(sup xSxFD nx

n −= (2.37)

It is worth noting that Dn is a random variable, whose distribution does not depend upon F(x), i.e. the KS test is non-parametric and distribution free. The output of the KS-test consists in the accep-tance of the assumption that the true data distribution follows the selected model if α

nn DD ≤ with a high probability PKS; else, the hypothesis is rejected and the two distributions are considered dif-ferent. α

nD is the critical value that depends on both the desired confidence level α and the number of samples n used for estimat-ing the empirical distribution function (numerical values of α

nD for different combination of α and n are well known tabulated values [23]).

The third and last experiment is aimed at establishing the pos-sible improvements that can be obtained on the accuracy of the change-detection process (in terms of false and missed alarms, as well as total errors) by adopting the derived theoretical statistical models (for approximating the magnitude distributions of change

9 x are the values for which both the cumulative densities are known.


59

and no-change pixels) rather than the widely used Gaussian model. In addition, an analysis on the impact of a poor pre-processing phase on the change-detection accuracy is also re-ported.

2.5.2. Qualitative Analysis of the Class Distributions in the Polar Domain

The aim of the first experiment is to qualitatively show the ef-fects of an inaccurate pre-processing phase (in terms of radiomet-ric differences and/or misregistration noise) on the statistical dis-tributions of magnitude and direction in the Polar coordinate system. In order to accomplish this analysis, we study the statisti-cal distributions of SCVs obtained by applying the CVA tech-nique to multitemporal images in three different cases: i) radi-ometrically corrected and coregistered images; ii) coregistered images without radiometric corrections; and iii) radiometrically corrected images with a poor coregistration (a residual shift of about 2 pixels on ground control points was accepted).

As expected from the theoretical analysis, in all cases it is pos-sible to identify two clusters in the Polar domain. In the case of corrected images (Fig. 2.6 (a)), the first cluster is centered in the origin of the polar plot and shows high occurrences (red color) close to zero and a Uniform distribution with respect to the direc-tion domain. This cluster is associated to the unchanged SCVs. The second cluster shows a preferred direction and is located rela-tively far from the origin. This cluster is related to the SCVs asso-ciated with changed pixels. In this case, it is quite easy from a qualitative viewpoint to identify the decision boundary (threshold value on the magnitude) between the circle Cn of no-changed pix-els and the annulus Ac of changed pixels. Furthermore, also the sector S of the changed pixels is clearly visible (see Fig. 2.6 (a)).

The situation is significantly different in the second case, i.e. if no radiometric corrections are applied to the original images. Ra-diometric differences between the two acquisitions (see Fig. 2.6 (b)) have a dramatic impact on the distribution of the no-change class. As one can see, the cluster of unchanged pixels is no longer

60

centered in zero; thus, the direction distribution is no further Uni-form but assumes values in a subset of the domain, which is de-fined by the difference of the mean values of unchanged pixels at the two dates in the two considered spectral bands. In greater de-tail, in this condition, the no-change class distribution with non-zero mean can be approximated with the model described in sec-tion 2.4.2 for the class of changed pixels. This behavior points out that the use of the Uniform model for the approximation of the distribution of the direction of the class of unchanged pixels in the data analysis phase when images are not radiometrically corrected is not acceptable. Furthermore, by analyzing Fig. 2.6 (b), it is possible to observe that the mean value of the magnitude of the unchanged pixels increases (with respect to the case of radiomet-rically corrected images), while the mean value of the magnitude of the changed pixels decreases. This means that if only the mag-nitude is used for the change detection (like in many real applica-

(a)


61

(b)

(c)

Figure 2.6 Histograms in the Polar coordinate system obtained after applying CVA

to: (a) multitemporal radiometrically corrected and coregistered images; (b) coregistered multitemporal images without radiometric corrections; and (c) multitemporal radiometrically corrected images with a signifi-cant residual registration noise (single-change case).

tions) the classes result more overlapped. This effect, which is due to the non-linearity of the magnitude operator, involves a

62

higher change-detection error with respect to the case of radi-ometrically corrected data. In other words, the absence of radio-metric corrections does not result in a bias contribution common to both classes, but may decrease significantly the separability be-tween them in the magnitude domain.

In the third case, image misregistration generates in the histo-gram plotted in the Polar domain: i) more spread SCV distribu-tions; ii) the presence of unchanged SCVs that are out of Cn and assume values in the entire direction domain. The spread incre-ment is related to the non-perfect correspondence between multitemporal pixels, which leads to an increase of the variances of classes. The presence of pixels outside Cn and S is mainly due to the effects induced from border regions and details, which lead to the comparison of pixels belonging to completely different classes. These pixels have high magnitude values but direction that may differ from those of true changed pixels (Fig. 2.6 (c)). This behavior points out a very important guideline for practical applications, i.e. in situations where the residual misregistration between images can not be neglected, the use of the direction variable in addition to the magnitude one can reduce false alarms due to registration noise.

On the basis of the aforementioned analysis, it is clear that the Polar representation results in a useful qualitative tool for easily understanding the effectiveness of the pre-processing applied to the data.

2.5.3. Quantitative Analysis of the Accuracy of the Statistical Models of Class Distributions in the Polar Domain

This experiment aims at a quantitative validation of the ana-lytical models defined for approximating the statistical distribu-tions of the magnitude and direction of the classes of changed and no-changed pixels. The validation is carried out according to the KS test. In these trials only the radiometrically corrected and co-registered images were considered.

In order to perform the validation of the derived statistical models, the true mean values and standard deviations of the


63

change and no-change distributions were computed from XD in the Cartesian coordinate system on the basis of the available ref-erence map. The obtained values are summarized in Tab. 2.2. In addition, for the magnitude of the change and no-change classes a comparison between the goodness-to-fit of Rice or Rayleigh model, respectively, and the commonly used Gaussian model is performed. In the following, the analysis of the results obtained on the two classes are considered separately.

2.5.3.1 Statistical Models for the Class of No-Changed Pixels In order to adopt statistical models in (2.30) and (2.31) for the

magnitude and the direction of unchanged SCVs, respectively, it should be verified if the hypotheses in (2.28) and (2.29) hold. By observing numerical values of standard deviations ,σ ωnb in Tab. 2.2, it is reasonable to conclude that they are similar to each other and can be approximated to the mean of the standard deviations (which is 9.49) thus satisfying (2.29). For the mean values no ap-proximations should be introduced as (2.28) is verified (thanks to the use of the radiometrically corrected images).

TABLE 2.2

MEAN VALUES AND STANDARD DEVIATIONS FOR THE CLASS OF NO-CHANGED AND CHANGED PIXELS IN THE CARTESIAN COORDINATE SYSTEM (SINGLE-CHANGE CASE)

b ,ωnbμ ,σ ωnb cbμ ω,

cb ωσ ,

1 (TM4) 0 10.26 58.94 8.90 2 (TM7) 0 8.73 43.47 10.67

Let us first consider the magnitude variable. In Fig. 2.7 it is

possible to see that the Rayleigh model approximates with good accuracy the distribution of the unchanged pixels (extracted from the reference map). In greater detail, this model fits better the data than the Gaussian model. This is confirmed by the KS test that results in a significantly higher PKS value for the Rayleigh model than for the Gaussian one (0.6396 vs. 4102 −⋅ ).

64

Figure 2.7 Comparison between the behavior of the distribution of the magnitude of the unchanged pixels and its approximations obtained with Gaussian and Rayleigh models (single-change case).

Figure 2.8 Comparison between the behavior of the distribution of the direction of the unchanged pixels and its approximation obtained with the uniform model (single-change case).

Let us now consider the behaviors of the distributions in the

direction dimension. The KS test states that the SCV directions are uniformly distributed with a PKS value equal to 0.9939. This reasonable result is confirmed also by a qualitative visual com-


65

parison between the true data distribution and the Uniform distri-bution (Fig. 2.8).

2.5.3.2 Statistical Models for the Class of Changed Pixels In order to adopt statistical models in (2.34) and (2.36) for the

magnitude and the direction of changed SCVs, respectively, it should be verified if the hypothesis in (2.33) hold. Similarly to the no-change class, from numerical values in Tab. 2.2 it is possible to observe that it is reasonable to approximate the standard devia-tion values ,σ ωcb to the mean of the standard deviations, i.e. 9.77. This condition satisfies (2.33).

Figure 2.9 Comparison between the behavior of the distribution of the magnitude of the changed pixels and its approximations obtained with Gaussian and Rice models (single-change case).

From Fig. 2.9 it is possible to see that the Rice model fits well

the data in general, and only slightly better than the Gaussian model. This is confirmed by the KS test that results in a slightly higher PKS value for the Rice model than for the Gaussian one (0.9993 vs. 0.9961). The small difference in the two statistical models for this data set is due to the fact that the non-centrality parameter (2.35) is much larger than the standard deviation, thus the Ricean distribution tends to become Gaussian.

66

The KS test states that the SCV direction is distributed accord-ing to (2.36) with a PKS value equal to 0.3306. The relatively small value of PKS is due to the presence of SCVs whose direction differs from the expected one (see Fig. 2.10), as SCV direction is highly sensitive to noise components. Such outliers can be related to the presence of residual misregistration noise.

Figure 2.10 Comparison between the behavior of the distribution of the direction of the changed pixels and its approximation obtained with the nonuniform model (single-change case).

2.5.4. Analysis of the Effectiveness of the Proposed Frame-work for Solving Change-Detection Problems

This experimental part has two goals: i) the first is to evaluate the impact of radiometric corrections on the performances of CVA; and ii) the second is to assess the improvement of the change-detection accuracy obtained by adopting the proposed sta-tistical models rather than the Gaussian one for the change and no change classes in the magnitude domain.

In order to evaluate the impact of the radiometric corrections on the performances of the CVA technique, we have compared the accuracies yielded by thresholding the magnitude variable in the case of: i) radiometrically corrected and coregistered images; and ii) coregistered images without radiometric corrections. To


67

this end, the threshold values were defined according to a super-vised manual trial-and-error procedure (MTEP), i.e. the mini-mum-error threshold was derived by performing a non-automatic evaluation of the overall change-detection errors versus all the possible values of the decision threshold; and then the threshold value that yielded the minimum overall error was chosen. From the qualitative analysis carried out in subsection 2.5.1, we expect that the change-detection accuracy is lower when no radiometric corrections are applied. As can be seen from Tab. 2.3, the MTEP procedure applied to the magnitude of the original data set re-sulted in 1803 errors, while we obtained only 704 errors when thresholding was applied to the magnitude after a very simple ra-diometric correction procedure which adjusted the mean value of the images. The overall error is more than halved. In greater de-tail, after rediometrically correcting the multitemporal images, both missed and false alarms decreased significantly from 529 to 369 pixels and from 1274 to 335 pixels, respectively.

TABLE 2.3

OVERALL ERROR, FALSE ALARMS AND MISSED ALARMS (IN NUMBER OF PIXELS) AND THRESHOLD VALUE RESULTING FROM THE MTEP APPLIED TO THE COREGISTERED IMAGES WITH AND WITHOUT RADIOMETRIC CORRECTIONS (SINGLE-CHANGE CASE)

Radiometric cor-rections

False alarms

Missed alarms

Overall errors

Threshold value (T)

None 529 1274 1803 47 Mean adjustment 369 335 704 51

In order to asses the effectiveness of the proposed statistical mod-els in solving change-detection problems, we considered only the coregistered and radiometrically corrected multitemporal data set. Here, the MTEP results have been compared with the perform-ances obtained by solving the change-detection problem accord-ing to the Bayes decision rule (BDR) [22] under two different as-sumptions on statistical distributions: i) the proposed statistical models (i.e. Rayleigh model for the class of unchanged pixels and Rice model for the class of changed pixels); and ii) the widely used Guassian model for both classes.

68

TABLE 2.4 OVERALL ERROR, FALSE ALARMS AND MISSED ALARMS RESULTING FROM THE SE-

LECTION OF THE DECISION THRESHOLD VALUES CARRIED OUT BY USING MTEP, AND BDR WITH THE PROPOSED STATISTICAL MODELS AND THE STANDARD GAUSSIAN

STATISTICAL MODEL (SINGLE-CHANGE CASE)

False alarms

Missed alarms

Overall errors

Threshold value (T)

MTEP 369 335 704 51 BDR proposed models 855 101 956 43 BDR Gaussian model 1086 57 1143 40

As expected, thanks to the capability of the Rayleigh and Rice

density functions to better model the true data distributions (see subsection 2.5.2), the proposed models allow to obtain a lower amount of total errors with respect to the model based on the Gaussian distribution (956 vs. 1143). This is due to the fact that using the proposed model, the obtained threshold value (i.e., 43) is much closer to the optimal one (i.e., 51) than the threshold computed with the Gaussian model (i.e., 40). It is worth noting that although significant, the difference of threshold values be-tween the Gaussian and the proposed models is relatively small. This depends on the fact that on the considered data set the Rice distribution is close to the Gaussian one, as the non-centrality pa-rameter is much larger then the standard deviation. We expect that higher improvements can be obtained in more general cases.

2.6. Experimental Results: Double-Change Data Set

2.6.1. Data Set Description and Experiment Design The second data set is made up of the same two multispectral

images acquired on the Island of Sardinia (Italy) in September 1995 (t1) and July 1996 (t2) described in section 2.5.1 in which a second kind of change was introduced. In order to simulate the presence of the new change, a data set made up of two multispec-tral images acquired by the Landsat-5 TM multispectral sensor on the Island of Elba (Italy) in August 1994 (t1) and September 1994 (t2) was considered [16]. Between these two acquisitions a wild-fire destroyed a large part of the vegetation in the north-west part


69

of the island. On the basis of the available ground truth, the area affected from the change was isolated on spectral channels 4 and 7 of the TM images of both the August and September acquisi-

(a)

(b)

Figure 2.11 Simulated double-change data set. (a) Channel 4 of the simulated image

at t2; (b) reference map of changed areas (burned area in light gray color, lake enlargement in black color).

tions. The selected area was inserted in the lower-left part of the spectral channels 4 and 7 of the September and July images of the Sardinia Island. It is worth noting that in order to obtain a realistic representation of the statistics of the change, both radiances at t1 and t2 of the Elba data set were inserted in the Sardinia data set. In this way we obtained a data set that properly represent the proper-ties of the different kinds of changes considered. The reference

70

map of this data set was built by modifying the reference map of the Sardinia data set accordingly to the introduced changes. As an example of the resulting data set, Figs. 2.11 (a) and (b) show the channel 4 of the simulated image at t2 and the double-change ref-erence map, respectively. The reference map has 7480 pixels be-longing to the changed class

1ωc (which is associated with the change in water level in the lake, black color), 2414 pixels be-longing to the changed class

2ωc (which is associated with the burned area, light gray color), and 113706 unchanged pixels (white color).

The experiments for this data set were carried out only on the co-registered and radiometrically corrected pair of images in or-der to evaluate the effectiveness of the proposed theoretical framework for analyzing and extracting SCV information about different kinds of change. Three different experiments were car-ried out: i) a qualitative analysis of the distribution of the classes in the Polar domain; ii) a validation of the accuracy of the theo-retical models in fitting the true data distributions using the KS-test for the change class

2ωc (we refer the reader to section 2.5 for the analysis of magnitude and phase distributions of the classes of unchanged pixels and of changed pixels associated with the water level in the lake); and iii) an evaluation of the accuracy of the change-detection process (in terms of confusion matrix and Kappa coefficient) obtained by adopting the derived theoretical statistical models for both magnitude and direction distributions.

2.6.2. Qualitative and Quantitative Analysis of the Class Dis-tributions in the Polar Domain

As expected from the theoretical analysis, the presence of a second kind of change resulted in the appearance of an additional cluster in the Polar domain (Fig. 2.12). Thus the number of clus-ters is now three. As in the data set with a single change, the clus-ter associated with the unchanged SCVs is centered in the origin of the polar plot and shows high occurrences (red color) close to zero and a Uniform distribution with respect to the direction vari-


71

able. Both the clusters related to the SCVs associated with changed pixels are located relatively far from the origin and show a quite similar magnitude but different preferred directions. These differences are due to the different radiometric variations induced from the two kinds of changes on the considered spectral chan-nels.

Figure 2.12 Histograms in the Polar coordinate system obtained after applying CVA

to multitemporal radiometrically corrected and coregistered images (double-change case).

As in section 2.5.2, hypothesis in (2.33) should hold for adopting statistical models in (2.34) and (2.36) for the mag-nitude and the direction of changed SCVs, respectively. From numerical values in Tab. 2.5 it is possible to observe that also for the new kind of change it is reasonable to ap-proximate the standard deviation values

2, cbσ ω to the mean of the standard deviations, i.e. 10.83. This condition satisfies (2.33).

72

TABLE 2.5 MEAN VALUES AND STANDARD DEVIATIONS FOR THE CLASS OF CHANGED PIXELS

2ωc

IN THE CARTESIAN COORDINATE SYSTEM (SINGLE-CHANGE CASE)

b 2, cbμ ω

2, cbσ ω

1 (TM4) 55.34 11.87 2 (TM7) -11.77 9.79

Figure 2.13 Comparison between the behavior of the distribution of the magnitude of the changed pixels of class 2ωc and its approximations obtained with Gaussian and Rice models (single-change case).

The effectiveness of the theoretical model in fitting the true

data distribution is easy to understand in a qualitative way by ob-serving Fig. 2.13, where it is possible to see that the Rice model fits well the data in general, and slightly better than the Gaussian model. This is confirmed also by the KS test that results in a slightly higher PKS value for the Rice model than for the Gaussian one (i.e. 0.9903 vs. 0.9461). As for the class of change associated with the enlargement of the lake surface, the reason of the small difference for this class is due to the fact that the non-centrality parameter (2.35) is much larger than the standard deviation, and thus the Ricean distribution tends to become Gaussian.


73

Figure 2.14 Comparison between the behavior of the distribution of the direction of the changed pixels of class 2ωc and its approximation obtained with the nonuniform model (single-change case).

Analogously, from Fig. 2.14 it is possible to conclude that the

true direction distribution of SCVs of class 2ωc is very close to

the general model in (2.35). The KS test confirmed this observa-tion resulting in a PKS value equal to 0.9683.

2.6.3. Analysis of the Effectiveness of the Proposed Frame-work for Solving Change-Detection Problems

Finally, in order to assess the effectiveness of the proposed framework for solving change-detection problems, we compared the results yielded by the proposed statistical models for both the magnitude and the phase distributions with the results obtained applying a supervised MTEP. In order to distinguish the classes of unchanged pixels and the two classes of changed pixels, it is necessary to identify: i) the threshold value T that separates the circle Cn of no-changed pixels from the annulus Ac of changed pixels (T is identified by considering the two kinds of changes as

74

a single class10); ii) the two angular threshold values l1ϑ and 21ϑ that bound the annular sector S1 of changed pixels associated with the enlargement of the lake ( 1ωc ); and iii) the two angular threshold values l2ϑ and 22ϑ that bound the annular sector S2 of changed pixels associated with the burned area ( 2ωc ).

In this case the MTEP was applied in two sequential steps. The first step considers only the magnitude and identifies, among all possible values, the threshold value T that separates the class of unchanged pixels from the two classes of changed pixels (con-sidered as a single class in the magnitude domain) with the mini-mum overall error. The second step considers also the direction and identifies, given the value of T, the four angular thresholds that maximize the Kappa coefficient of the final change-detection map (in this case the two kinds of changes are separated from the no-change class and also from each other).

TABLE 2.6

THRESHOLD VALUE T AND ANGULAR THRESHOLD VALUES l1ϑ ,

21ϑ ,l2ϑ AND

22ϑ OB-

TAINED BY ADOPTING THE MTEP AND THE BDR WITH THE PROPOSED STATISTICAL MODELS (DOUBLE-CHANGE-CASE)

Change-detection procedure T ϑ l1 ϑ 21 ϑ l2 ϑ 22 K

MTEP 45 13.17° 45.84° 323.87° 12.02° 0.9272 BDR 40 13.17° 57.30° 323.30° 13.17° 0.9270

Also the solution of the change-detection problem by adopting

the proposed statistical models for the magnitude and the direc-tion distributions was obtained with a two-step procedure. The first step identifies the threshold value T applying the BDR under the hypothesis that the class of unchanged pixels is Rayleigh dis-tributed and the class of changed pixels is given by the sum of two Rice distributions. The second step detects the angular

10 It is worth noting that it is possible to optimize the change detection results by select-

ing a different threshold value in the magnitude domain for each annular sector (i.e., for each kind of change present in the considered scene).


75

threshold values l1ϑ , 21ϑ , l2ϑ and 22ϑ by applying the BDR un-der the assumption that the direction distribution of unchanged pixels is Uniform in [0,2π), and that both direction distributions of classes 1ωc and 2ωc follow (2.36).

TABLE 2.7

CONFUSION MATRICES FOR THE CHANGE-DETECTION MAPS OBTAINED WITH (A) THE MTEP AND (B) THE BDR WITH THE PROPOSED STATISTICAL MODELS (DOUBLE-

CHANGE CASE)

True Class

ωn 1ωc 2ωc

ωn 113172 294 338

1ωc 499 7020 8

Est

imat

ed

Cla

ss

2ωc 35 166 2068

True Class

ωn 1ωc 2ωc

ωn 112807 114 120

1ωc 798 7120 13

Est

imat

ed

Cla

ss

2ωc 101 246 2281

(a) (b)

As can be seen from Tab. 2.6, also in this case the threshold value T selected on the basis of the proposed statistical models (i.e., 40) is similar to the threshold value obtained with the man-ual trial-and-error procedure (i.e., 45). Furthermore, also in the direction domain the threshold selection procedure based on the proposed statistical models resulted in a pair of threshold values for each annular sector (i.e., l1ϑ =13.17° and 21ϑ =57.30° for S1, and l2ϑ =323.30° and 22ϑ =13.17° for S2) very similar to the opti-mal ones (i.e., l1ϑ =13.17° and 21ϑ =45.84° for S1, and

l2ϑ =323.87° and 22ϑ =12.02° for S2). The similarity of the thresh-old values resulted in almost the same value of the Kappa coeffi-cient of accuracy for both the change-detection procedures (i.e., 0.9372 for the MTEP and 0.9370 for the BDR). These good re-sults are further confirmed by the analysis of the confusion matri-ces (see Tab. 2.7).

76

2.7. Discussion and Conclusions In this chapter, a Polar theoretical framework for unsupervised

change detection based on the change vector analysis (CVA) technique has been presented. The main motivation of this work relies on the observation that the CVA is a widely used technique for unsupervised change detection in multispectral and multitem-poral remote sensing images, but a precise theoretically frame-work concerning its definition and use has not proposed in the lit-erature (in many applications CVA in used without a proper understanding of the implications of the representation of the change information in the magnitude-direction domain). In this work, we aimed at filling this gap by introducing: i) a proper Po-lar framework for the representation and the analysis of multitemporal data in the context of the CVA technique; ii) a set of formal definitions (which are linked to the properties of the data) related to pattern representation in the Polar domain; iii) a theoretical analysis of the distributions of changed and unchanged pixels in the Polar domain; iv) a critical analysis of the theoretical study of distributions aimed at driving a proper exploitation of the information present in the Polar representation; v) two examples of use of the proposed framework in change-detection problems.

In the light of the aforementioned contributions, we expect that the main impact of this work in the remote sensing commu-nity can be focused on the following issues: i) possibility to use in all practical applications of the CVA tech-

nique (irrespectively of the specific change-detection problem considered) a uniform polar representation with proper formal definitions of the different regions of interest based on the proposed framework;

ii) better understanding of the statistical properties of SCVs in the Polar domain and of the impact of the simplifying assump-tions usually considered in the literature in the development of automatic data analysis algorithms;

iii) presentation of a solid background for the development of ad-vanced and accurate automatic algorithms for change detec-


77

tion, which properly takes into account the statistical proper-ties of data in the Polar domain;

iv) better understanding of the fundamental role played by a proper pre-processing step (e.g., radiometric corrections, co-registration, etc.) for driving a correct design and use of effi-cient automatic data processing algorithms. The presented analysis points out that some of the simplifying

assumptions usually adopted for representing data distributions in the Polar domain can become critical if a precise modeling of the change-detection problem is desired. Among the other properties discussed in the Section 2.4.3, we stress four observations: • the theoretical and experimental analyses confirm that it may

be critical solving the change-detection problems by represent-ing the magnitude of classes of unchanged and changed pixels with Gaussian distributions, rather than using the more accu-rate models described in this chapter (i.e. the Rayleigh distri-bution for unchanged pixels and the Rice distribution for changed pixels);

• radiometric corrections play a fundamental role in unsuper-vised change detection based on CVA: i) for increasing the separability between the classes of changed and unchanged pixels (by increasing the distance between the mean values of the two classes in the magnitude domain), and ii) for properly exploiting the direction information in the data processing phase (if the radiometric corrections are neglected, the direc-tion distribution of the class of unchanged pixels is completely different from the expected Uniform model, resulting in an important source of errors in the design of automatic data-processing techniques);

• the use of the direction information in the change-detection algorithms can be very important for reducing the false alarms induced from registration noise;

• the use of the direction information in the change-detection algorithms is very important for distinguishing different kind of changes.

78

The effectiveness of the proposed Polar framework and of the related statistical analysis, as well as the importance of their im-plications have been verified on two change-detection problems, by analyzing qualitatively and quantitatively the reliability of the simplifying assumptions considered in the theoretical analysis of data distributions and their impact on the precision of the models. The results obtained confirm that the theoretical models presented in this chapter are suitable for a proper representation of the con-sidered data sets when the CVA technique is adopted.

As a final remark, it is worth noting that in the proposed framework, according to the majority of the literature, we analyze separately the magnitude and direction variables in both the statis-tical-modeling phase and the threshold-selection process. Al-though this is a simplification from the viewpoint of the Bayesian decision theory (which seems reasonable for studying with a lim-ited complexity the statistics of classes), it results in a better un-derstanding of both the physical meaning of these variables and the different roles they play in the change-detection problem. An alternative strategy for a joint analysis of the magnitude and di-rection variables could be use clustering procedures.

As future developments of this work, we are: i) studying the reformulation of some threshold selection algorithms developed in the literature [15],[16] according to the distributions derived from the theoretical analysis reported here; ii) considering the properties of the direction information for: a) devising effective unsupervised change-detection algorithms capable to automati-cally identify different kinds of change in a generic multitemporal data set; b) better reducing the effects of the registration noise in the Polar domain; c) optimizing the framework and the procedure for threshold selection in the magnitude domain by considering different threshold values for different kinds of change.


79

Appendix In this appendix we provide the guidelines for extending the

proposed framework to the B-dimensional case (B>2). Let us consider the general case of CVA applied to B spectral

channels of the considered multitemporal images. As stated in sec. 2.3.1 for the two dimensional case, also in the B-dimensional case it is reasonable to represent XD as a mixture of multidimen-sional Gaussian distributions as it is obtained by subtracting the multidimensional random variables X1 and X2, both modeled with a mixture of multidimensional Gaussian distributions. Further-more, also in this case, we assume that features Xb,D (b=1,...,B) are statistically independent11. Under this assumption, the distribution of the class ωi ( Ω∈ωi ) in a Cartesian coordinate system can be written as the product of the B marginal densities ,D( )ωibp X | re-lated to the class ωi (b=1,...,B), i.e.,

( )

2, ,

212

1

( )1( ) exp22

μσπ σ =

=

⎡ ⎤⎢ ⎥−⎢ ⎥⎣ ⎦

−ω =∏

∑B

b D b iD i BB

b ,ibb ,i

b

Xp X | (2.38)

where ,b iμ and ,b iσ are the mean values and the standard devia-tions, respectively, of the Gaussian distributed marginal density of class ωi over the b-th considered feature (b=1,...,B). Equation in (2.38) can be written in Hyperspherical coordinates using (2.2) as follows:

( )

22

1 212

21

2 22 1

1, ,21 1

2 21 1

1( ) exp2

2

2 2

ρ ϑ μϕρ ϑ ϕ ϕπ σ σ

ϕ ϑ μ ϕ ϕ μ

σ σ

−

−=

=

− −

− −= =

− =

⎡ ⎛ ⎞⎛ ⎞⎢ ⎜ ⎟−⎜ ⎟ω = ⎜ ⎟⎢ ⎜ ⎟⎝ ⎠⎝ ⎠⎢−⎢⎣

⎤⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎥⎜ ⎟ ⎜ ⎟− −⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎥⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠ ⎥− −⎦

∏∏

∏ ∏∑

k

B

B ,ikB i BB k

b ,ib B ,i

B b

k B i b b iBk k

B ,i b ,ib

sinsinp , , ,..., |

ρ sin cos ρ sin cos

⎥

(2.39) 11 Discussion on this hypothesis (and on the pre-processing to be applied to data for ob-

taining it in an approximate way) is reported in section 2.4.3.

80

The marginal conditional densities of the random variables ρ, ϑ and 1ϕ , 2ϕ ,..., 2Bϕ − for each class ωi can be computed by proper integrations of (2.39). The general formulation of the inte-grals to be evaluated is given in the following:

2

1 2 1 2

0 0 0

( ) ( )π π π

ρ ρ ϑ ϕ ϕ ϕ ϕ ϑ− −

⎡ ⎤ω = ω⎢ ⎥…⎢ ⎥⎣ ⎦

∫ ∫ ∫ …i B i Bp | p , , ,..., | d d d (2.40)

1 2 1 2

0 0 0

( ) ( )π π

ϑ ρ ϑ ϕ ϕ ϕ ϕ ρ+∞

− −

⎡ ⎤ω = ω⎢ ⎥…⎢ ⎥⎣ ⎦

∫ ∫ ∫ …i B i Bp | p , , ,..., | d d d (2.41)

2

1 2

0 0 0 0

( ) ( )π π π

ϕ ρ ϑ ϕ ϕ ρ ϑ+∞

−

⎡ ⎤| ω = ω⎢ ⎥…⎢ ⎥⎣ ⎦

∫ ∫ ∫ ∫h i B ip p , , ,..., | d d dϕ (2.42)

; 1,..., -2 and ϕ= ≠kd d k= B k hϕ In the general case, the models to be adopted should be based

on the solution of the above integrals. These solutions can be simplified in some particular cases. In the following we report the simplified equations for a pair of important situations: analogous to those shown in subsections 2.4.1 and 2.4.2.

As stated in 2.4.1, it is reasonable to expect that the mean along each of the B spectral channels for the class of no-changed pixels is equal to zero (i.e., , 0nbμ ω ≅ , b=1,…,B). A significantly simplified equation can be obtained in the approximation that all the standard deviations are similar to each other (i.e.,

, n nbσ σω ω≅ , b=1,…,B). Under this assumption we can rewrite (2.40) and (2.41) as:

( )

-1 2

1 22 2

2( ) exp1 222

kk

B

kB

ρp ρ |B

ρσσ ω

ω

⎛ ⎞ω = −⎜ ⎟

⎛ ⎞ ⎝ ⎠Γ⎜ ⎟⎝ ⎠

, 0≥ρ

1( ) , [0, 2 )2np |ϑ ϑ ππ

ω = ∈

(2.43)


81

Considering changed pixels, it is possible to derive a signifi-cantly simplified equation for the distribution of the magnitude in the case in which the mean along each of the B dimensions is not equal to zero (i.e., , , 0, , 1,...,ω ω≠ ≠ =k kp qμ μ p q B with ≠p q ) and under the assumption that all the standard deviations are similar to each other (i.e., , k kbσ σω ω≅ , b=1,…,B). Under these hypothe-ses (2.40) can be rewritten as:

12 22

12 2 22( -2)

( ) exp I2

k k k

kk k k

B

k ΒρM ρ M ρMp ρ |

Mσ σ σω ω ω

ωω ω ω

⎛ ⎞ ⎛ ⎞+⎛ ⎞ω = −⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

,

0≥ρ

(2.44)

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motely-sensed data.” Int. J. Remote sensing, Vol. 10, No. 6, pp.989-1003, 1989.

[2] P.R. Coppin, I. Jonckheere and K. Nachaerts, “Digital change detection in ecosystem monitoring: A review,” Int. J. Remote Sens., Vol. 25, No. 9, pp. 1565-1596, May 2004.

[3] D. Lu, P. Mausel, E. Brondízio and E. Moran, “Change de-tection techniques,” Int. J. Remote Sens., Vol. 25, No. 12, pp. 2365-2407, Jun. 2004.

[4] L. Bruzzone and R. Cossu, “Adaptive approach to reducing registration noise effects,” IEEE Trans. Geosci. Rem. Sens., Vol. 41, No. 11, pp. 2455-2465, Nov. 2003.

[5] W.A. Malila, “Change vector analysis: an approach for de-tecting forest changes with Landsat,” Proc. LARS Machine Processing of Remotely Sensed Data Symposium, W. Lafay-ette, IN: Laboratory for the Application of Remote Sensing, pp. 326-336, 1980.

[6] J.L. Michalek, T.W. Wagner, J.J. Luczkovich and R.W. Stof-fle, “Multispectral change vector analysis for monitoring coastal marine environments,” Photogramm. Eng. Remote Sensing, Vol. 59, No. 3, pp. 381–384, 1993.

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[7] L.A. Virag and J.E. Colwell, “An improved procedure for analysis of change in Thematic Mapper image-pairs,” Proc. of the XXI Int. Symposium of Remote Sensing of the Envi-ronment, Ann Arbor, MI, pp. 1101-1110, 26-30 October 1987.

[8] J.R. Jensen, Introductory Digital Image Processing: A Re-mote Sensing Perspective, Second Edition, Prentice Hall, Upper Saddle River, New Jersey, 1996.

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[10] T.R. Allen and J.A. Kupfer, “Application of spherical statis-tics to change vector analysis of Landsat data: southern Ap-palachian spruce-fir forests,” Remote Sensing Environment, Vol. 74, pp. 482-493, 2000.

[11] J. Chen, P. Gong, C. He, R. Pu and P. Shi, “Land-use/land-cover change detection using improved change-vector analy-sis,” Photogramm. Eng. Remote Sensing, Vol. 69, No. 4, pp. 369–379, 2003.

[12] T. Warner, “Hyperspherical direction cosine change vector analysis,” Int. J. Remote Sensing, Vol. 26, No. 6, pp. 1201–1215, 2005.

[13] K. Nackarets, K. Vaesen, B. Muys and P. Coppin, “Com-parative performance of a modified change vector analysis in forest change detection,” Int. J. Remote Sensing, Vol. 26, No. 5, pp. 839–852, 2005.

[14] E.M. Pereira e A. W. Stezer, “Spectral characteristic of fire scars in Landsat-5 TM images of Amazonia”, Int. J. Remote Sensing, Vol. 14, No. 11, 1993.

[15] L. Bruzzone, D. Fernández Prieto, “A minimum-cost thresh-olding technique for unsupervised change detection”, Int. J. Remote Sensing, Vol. 21, No. 18, pp. 3539-3544, Dec. 2000.

[16] L. Bruzzone, D. Fernández Prieto, “Automatic analysis of the difference image for unsupervised change detection”,


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IEEE Trans. Geosci. Remote Sensing, Vol. 38, No. 3, pp.1170-1182, 2000.

[17] J.A. Richards and X. Jia, Remote Sensing Digital Image Analysis: an Introduction, Springer-Verlag, New York, 1999.

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[19] J.R.G. Townshend, C.O. Justice and C. Gurney, “The impact of misregistration on change detection,” IEEE Trans. Geosci. Remote Sensing, Vol. 30, pp. 1054–1060, Sept. 1992.

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85

Chapter 3

3. A Split-Based Approach to Unsuper-vised Change Detection in Large-Size Multitemporal Images

This chapter presents a split-based approach to automatic and unsupervised change detection in large-size multitemporal remote sensing images. Unlike standard methods presented in the litera-ture, the proposed approach can detect in a consistent and reli-able way changes in images of large size also when the extension of the changed area is small (and therefore the prior probability of the class of changed pixels is very small). The method is based on: i) a split of the large-size image into sub-images; ii) an adap-tive analysis of each sub-image; iii) an automatic split-based threshold-selection procedure. This general approach is used for defining a system for damage assessment in multitemporal SAR images. The proposed system has been developed for properly identifying different levels of damages induced by tsunamis along coastal areas. Experimental results obtained on multitemporal RADARSAT-1 SAR images of the Sumatra Island, Indonesia, con-firm the effectiveness of both the proposed split-based approach and the presented system for tsunamis damage assessment.

(This chapter is in press in the IEEE Transaction on Geo-

science and Remote Sensing Disaster Special Issue, 2007. Co-author: Lorenzo Bruzzone)

86

3.1. Introduction In the last years the frequency of natural disasters has shown a

rapid increase [1]-[4]. Examples of this trend are related to re-cently occurred floods, earthquakes, avalanches, hurricanes, forest fires and tsunamis. These dramatic events increased the interest of the politic and the scientific communities in the definition of methodologies capable to prevent them, to mitigate their effects and to perform a fast and accurate damage assessment. Satellite remote sensing images acquired on the same area at different times are a valuable tool for addressing the mentioned problems. The information present in these data can be useful for extracting important indications for risk assessment, emergency manage-ment and damage inventory. In this chapter, we focus the atten-tion on the problem of damage inventory.

In order to perform an effective damage inventory, it is impor-tant to develop proper change-detection techniques for the auto-matic analysis of multitemporal remote sensing images. In the lit-erature, many techniques have been proposed for change detection in both optical and SAR remote sensing data [5]-[24]. Often changes are identified by comparing pixel-by-pixel two im-ages acquired on the same geographical area at two different times. The comparison can be carried out according to a differ-ence operator (this is the typical case of multispectral images) or to a ratio/log-ratio operator (as usually done in SAR image), as well as with more complex strategies based on context-sensitive dissimilarity measures computed between statistical distributions [17]. The resulting difference/ratio image is then analyzed accord-ing to either automatic thresholding algorithms [9]-[13],[22],[23] or complex context-sensitive [8],[24] and multiscale algorithms [18] to generate the final change-detection map. For simplicity, let us focus the attention on thresholding algorithms, which are the most widely used in the applications (however the discussion can be easily generalized to context-sensitive and multiscale pro-cedures). Most of the thresholding algorithms derive automati-cally the change-detection map under the assumption that the prior probability of the class of changed pixels is sufficient to

CHAPTER 3 - A SPLIT-BASED APPROACH TO UNSUPERVISED CHANGE DETECTION IN LARGE-SIZE MULTITEMPORAL IMAGES: APPLICATION TO TSUNAMI DAMAGE ASSESSMENT

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properly model this class with a significant statistical mode in the histogram of the difference/ratio image. However, as the men-tioned kinds of damages typically affect local portions of wide areas (e.g., regions or countries), a proper damage assessment procedure requires the analysis of wide scenes and thus of large-size images. This results in a small value of the prior probability of the class of changed pixels, which may affect the capabilities of the thresholding techniques to detect a proper threshold value if working on the whole image.

In the image processing literature, local adaptive thresholding techniques have been proposed for characterizing the local prop-erties of images. In change detection problems, these techniques compute a threshold value for each pixel neighborhood on the ba-sis of local statistics and apply it either to the entire neighborhood or only to the central pixel [19],[25]. As these methods result in many isolated change pixels and holes in the middle of connected change components, post processing steps are usually adopted for reducing noise in the final change-detection map and making it consistent with the hypothesis that changes are made up of a sig-nificant number of connected pixels [19]. Alternative approaches, mainly proposed for threshold-based classification of large-size images, perform an independent analysis of overlapping image blocks that results in different threshold values for each consid-ered region [26]-[28]. However in remote sensing change-detection problems a pixel-based threshold selection in local neighborhoods or a simple split of a large-size images in several smaller sub-images and a successive separate analysis and thresh-olding of each split can be critical as: i) threshold values should be consistent in all sub-images/blocks for obtaining significant change-detection maps also from a quantitative viewpoint (a sin-gle threshold value should be used in the entire large-size image for obtaining consistency with the radiometric properties of the data); ii) possible threshold-selection errors on a split/block gen-erate inaccurate change-detection results for that sub-image; and iii) changes might be not present in some sub-images (and several thresholding algorithms used in remote sensing applications im-

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plicitly assume the presence of two distributions and are not able to detect situations of absence of changes).

In order to overcome the aforementioned problems, in this chapter we propose an unsupervised split-based approach (SBA) to change detection for large-size multitemporal images, which is suitable to handle both multispectral images acquired by passive sensors and SAR images acquired by active sensors. The pro-posed method automatically splits the computed difference (or ratio) image in a set of non-overlapping sub-images of user de-fined size. Then the sub-images are sorted out according to their probability to contain a significant amount of changed pixels. Af-terward, a subset of splits having a high probability to contain changes is selected and analyzed. Under the assumption that these splits represent reliable observations of the same phenomenon of change, it is expected that the threshold-selection procedure is re-liable on them, as they are characterized by the highest prior probabilities of the change class among all splits. In order to properly extract the change information by thresholding the whole scene, two different strategies can be used for combining information present in different sub-images. The first strategy is based on an independent split analysis, that consists in applying threshold selection separately to each split for deriving a set of threshold values (one for each sub-image). Hence simple combi-nation techniques can be applied to the obtained set of thresholds to select a robust, unique and consistent threshold value to be ap-plied to the entire image. The second strategy exploits a joint split analysis that consists in applying thresholding to the joint distri-bution of pixels obtained by merging all the splits having a high probability to contain changes.

The proposed general method is used for defining a system based on multitemporal SAR images for damage assessment in areas affected by a tsunami. The proposed system is tested on two images acquired by the SAR sensor of the RADARSAT-1 satel-lite over the Sumatra Island (Indonesia) in April 1998 and in January 2005. Between the two acquisitions a tsunami destroyed large parts of the coast. Experimental results show that the pro-


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posed technique produces accurate change-detection maps capa-ble to identify the major damages caused from the tsunami on the coast.

This chapter is organized into five sections. Section 3.2 de-scribes the proposed general split-based approach to change de-tection in large-size multitemporal images. Section 3.3 presents a system for tsunami damage assessment, which exploits the pro-posed split-based approach and multitemporal SAR images. Sec-tion 3.4 reports experimental results obtained on multitemporal SAR images of the Sumatra Island. Finally, Section 3.5 draws the conclusions of this chapter.

3.2. Proposed Split-Based Approach to Change Detec-tion in Large-Size Multitemporal Images

Let us consider two co-registered remote sensing images X1 and X2, of size P Q⋅ , acquired over the same area at different times t1 and t2

1. Let , n c= ω ωΩ be the set of classes of no-changed and changed pixels to be identified. As shown in Fig. 3.1, the architecture of the proposed split-based approach (SBA) is based on three main blocks aimed at: i) image comparison; ii) split of the large-size image in N sub-images and selection of the L ( L N≤ ) splits having the highest probabilities to include changes; and iii) split-based threshold selection. In the following these blocks are described in greater detail.

3.2.1. Image Comparison The first step of the most widely used change-detection tech-

niques presented in the literature is based on a pixel-by-pixel (or parcel-by-parcel [8]) comparison between the two considered im-

1 In this chapter only the case of pairs of images is discussed. It is worth noting that the

proposed approach can be applied to a multitemporal sequence made up of more than two images by analyzing separately couples of images.

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ages, which is carried out according to a proper operator [14]-[18],[20],[21].

Figure 3.1 Block scheme of the proposed split-based approach to change detection in large-size multitemporal images.

When dealing with multispectral images, each spatial position

in X1 and X2 can be represented by an n-dimensional vector, whose components are associated with the radiances measured in different spectral channels. The most widely used comparison op-erator with this kind of images is the difference applied to the n-dimensional feature vectors, which allows to consider in the change-detection process all the available spectral information. Generally, the difference image XD is computed as the magnitude of the difference vectors. This technique is known as Change Vector Analysis (CVA) [5],[9] and has been successfully used in many different application domains.

When dealing with SAR images, either the difference or the ratio operator can be used [12]-[16]. However, the difference op-erator leads to an image that has a statistical distribution which depends on both the relative change of backscattering between the two acquisition dates and the reference intensity value. This re-sults in different statistical behaviors of changed pixels in image

Image split

Change-detection Map

Split-based analysisLarge

image t1 Image comparison

Large difference (or ratio) image

Adaptive split selection

1

N

Split-based threshold selection

TThresholdingLarge

image t2

1

N


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portions that show different absolute backscattering values. For avoiding this problem, comparison in SAR images is typically carried out by a ratio operator, which reduces multiplicative dis-tortion effects of noise common to the two considered images due to speckle and makes the statistical distribution of the resulting image dependent only on the relative changes between the two acquisitions. Usually the ratio image is expressed in a logarithmic scale to enhance low intensity pixels [14]-[16],[18] (and to obtain a more symmetrical distribution of the classes of changed and no-changed pixels) resulting in the log-ratio image XLR.

It is worth noting that instead of comparing the values of each single pixel, one may compare the probability density functions evaluated in a neighborhood of the considered spatial position in the two multitemporal images, according to proper dissimilarity measures [17]. In alternative, it is possible to derive multitempo-ral parcels [8] and to apply comparison at a parcel level (after the extraction of proper parcel-based features).

3.2.2. Image Split and Adaptive Split Selection Let XC be the image (of size P Q⋅ ) obtained after comparison

of multitemporal data. The most widely used unsupervised ap-proach to change detection is to apply a threshold-selection algo-rithm to XC and to generate the change-detection map accordingly to the derived threshold value. Usually the threshold-selection al-gorithms assume that the class of changed pixels can be associ-ated with a reliable statistical mode in the histogram of XC. This assumption is critical in large size images, as typically the phe-nomenon that involves changes only affects a small portion of the scene. This results in a very small prior probability of the class of change and thus in an almost indistinct mode in the histogram, which may involve a failure of threshold-selection algorithms. In order to overcome this problem, we propose to split the image XC in a set of sub-images. The image splitting procedure takes as in-put the large-size image XC and sub-divides it in a set of N sub-images CiX , i=1, ..., N, of user defined size ( p q⋅ ) (see Fig. 3.2). The choice of the values of p and q depends on the geometric

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resolution of the sensor and on the expected extension of change occurred in the investigated area. The basic requirement is that the amount of changes in a sub-set of splits should be statistically significant for making the threshold-selection procedure reliable and precise (empirically we can assume that a 10% of changed pixels is sufficient for guaranteeing high accuracy with proper

Q

p

q

CiX

P

CX Figure 3.2 Example of splitting a large image of size P Q⋅ in N splits of size p q⋅ .

threshold-selection algorithms [21]). An estimation of the split size (and thus of N) can be obtained by relating the above con-cepts with the size of the whole image. According to the hypothe-sis that changed pixels have a very small prior probability with respect to unchanged pixels, the most of the generated sub-images (splits) CiX have a high probability to contain either no changes or a non-significant amount of changed pixels. We expect that only few of them contain a number of changed pixels sufficient for characterizing this class in a statistically significant way. Un-der this realistic assumption, in most of the sub-images standard threshold-selection techniques may not identify proper threshold values as: i) most of them implicitly assume the presence of changes, thus when there are no changes they identify meaning-less threshold values; ii) they assume that the change class has a sufficiently high prior probability to result in a statistically sig-


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nificant mode in the histogram. In order to avoid such kind of problems, the set of sub-images with the highest probability to contain changes is identified. This task is carried out by analyzing the global statistical behaviors of the computed sub-images. Let

CiP be the probability that the sub-image CiX includes changed pixels. We reasonably expect that when considering a difference (or ratio) operator in the comparison, CiP is a function of the standard deviation iσ of sub-image CiX (which is used as index for changes also in [19],[26],[27])2, i.e.,

( )iC iP f σ= (3.1)

where f(.) is a monotonic function that increases by increasing the value of iσ . According to this definition, irrespectively of the analytical form of f(.), the set PC of sub-images ordered according to the probability of including changes can be derived as:

C C +1| , =1,..., i i i i Nσ σ= ≥P X (3.2)

The desired set C C⊆'P P of splits with the highest probabilities to contain changes is defined by selecting the first L elements of CP , i.e.:

1 2C C C C 1 2, , ..., | ... , L L L Nσ σ σ= ≥ ≥ ≥ ≤'P X X X (3.3)

3.2.3. Split-Based Threshold Selection Sub-images in C

'P can be analyzed according to different strategies in order to identify a threshold value reliable for the whole large-size image and consistent with the radiometric prop-erties of the data. Two main approaches can be distinguished: i) an independent split analysis strategy based on the combination of reliable split-based threshold values; ii) a joint split analysis strat-

2 An alternative measure to the standard deviation is the coefficient of variation, which

becomes useful when the noise of sub-images can be modeled as multiplicative or a residual multiplicative component is present in the splits [18].

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egy based on the combination of splits distributions and threshold selection.

The independent split analysis strategy is based on a separate analysis of the L sub-images included in C

'P and on a combination of decisions taken on each sub-image. The first step of this ap-proach is to compute a set 1,..., LT T=T of threshold values (one for each considered split in C

'P ) according to any of the thresholding procedures proposed in the literature (e.g. General-ized Kittler and Illingworth algorithm [10],[12],[13], Generalized EM-based algorithm [11],[20],[21]). In order to compute the final threshold value T to be applied to the whole image, different combination strategies can be adopted: i) compute the mean of threshold values in T (Mean-SBA); ii) compute the median of threshold values in T (Med-SBA). The mean is the simplest mathematical operator that can be adopted for estimating the threshold value T . Although from a statistical point of view the mean operator produces a reliable result, it has the drawback that in the presence of few samples it is slightly sensitive to outliers and may find an inconsistent threshold value if for few sub-images in C

'P unreliable threshold values are computed. This may be a critical problem, as in real applications it may happen that the threshold-selection algorithm does not provide reliable results on a split3. This problem can be overcome adopting the median operator instead of the mean one.

The joint split analysis strategy to threshold selection is alter-native to the independent one. It performs a simultaneous analysis of the selected splits (J-SBA) and then directly derives the final value of the decision threshold. The main idea exploited in this procedure is to jointly characterize the populations of changed and unchanged pixels using all splits in C

'P and to apply threshold 3 It is worth noting that, even if robust threshold-selection procedures are used (i.e. pro-

cedures for which the probability to detect a wrong threshold value is very small if the prior probability of changed pixels is not too small), it may happen that an imprecise value is selected on a split.


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selection to this joint distribution. The first step of this procedure is to define a new random variable given by the union of the radi-ances of all the L selected sub-images candidate to contain changes, i.e.,

C C C C1

' , i i

L

i=

= ∈∪ 'PX X X (3.4)

In this way the distribution of C'X properly represents the change-detection problems modeled in all the L splits, guarantee-ing a reasonable prior probability for the class of changed pixels. Therefore the threshold value T can be derived by applying threshold selection to C'X . On the one hand, this allows one the selection of a reliable threshold value without any combination of split-based threshold values. On the other hand, possible non sta-tionarity of distributions of classes of changed and no-changed pixels in different splits may affect the reliability of the statistical models used for representing class distributions in thresholding algorithms. This may decrease the accuracy of the threshold-selection procedure.

Irrespectively of the threshold-selection strategy considered, the final change-detection map XM is computed by applying the estimated threshold T to the large-size image XC.

3.3. A Novel Split-Based System for Tsunami Damage Assessment

In this section the general technique presented above for unsu-pervised change detection in large-size multitemporal images is exploited for designing an automatic system for tsunami damage assessment in multitemporal SAR images. Additional blocks with respect to the base scheme of Fig. 3.1 are necessary to handle this complex problem. In the following, after a proper problem de-scription, we present the architecture of the proposed system.

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3.3.1. Dataset and Problem Description The problem of damage assessment after a tsunami was stud-

ied and addressed by using two intensity images acquired by the SAR sensor of the RADARSAT-1 satellite over the north part of the Sumatra Island, Indonesia. The available data have a pixel spacing of 25 m in both azimuth and range directions. A tsunami strongly affected this area on 26th December 2004. After this date, different kinds of sensors acquired many images over the site in-terested by the natural disaster [29]. For this reason, it was possi-ble to have an image acquired after few days from the tsunami (January 2005). Unfortunately, the image in archive acquired by RADARSAT-1 previous to December 2004 was taken on April 1998. The time distance between the two multitemporal images is due to the need, given the acquisition after the tsunami, to find in the archives an image before the tsunami event with the same ac-quisition parameters, i.e. incidence angle, ascending/descending orbit and polarization [30].

In order to properly study and characterize the considered problem, a preliminary analysis of the investigated area has been carried out by: i) a visual comparison of high-resolution optical images acquired before and after the tsunami; ii) an analysis of the literature. From this analysis, it appears that the tsunami im-pact varied according to the shape and slope of the ocean floor, the presence or absence of reefs, mangroves and onshore forests, the orientation and the slope of the coastline, and the underlying rock and soil types. Image analysis shows that some areas have been highly modified by the tsunami. Estuary and wetland sites have apparently been scoured out and drainage patterns changed. Other sites show evidence of subsidence or drainage changes leading to potential new wetland areas [31]. As stated in [30], with the considered SAR images it is possible to map: eroded coasts, reefs and foreshores that have become exposed, areas where vegetation has disappeared or has been severely damaged, destroyed piers, quaysides and embankments and instantaneous extend of inundated areas.


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In accordance with the preliminary analysis, in this work we decided to investigate the change-detection problem according to two different objectives: i) identifying only changes associated to deep modifications of the environment (like coast erosion, beaches removal, estuary destruction and areas still flooded at ac-quisition date after tsunami), we refer to these damages as changes of level 1; and ii) identifying in a separate way changes of level 1 and changes associated to less severe modification of the environment (like areas in which vegetation was swept away and buildings were destroyed), we refer to these damages as changes of level 2.

3.3.2. Proposed System for Tsunami Damage Assessment The architecture of the proposed system (see Fig. 3.3) is made

up of 3 main parts: i) image pre-processing and comparison; ii) sea identification and masking; and iii) generation of the change-detection map according to the proposed adaptive split-based ap-proach.

Figure 3.3 Block scheme of the proposed system for tsunami damage assessment. First of all, the multitemporal images should be registered in

order to obtain alignment between pixels corresponding to the

Image Filtering

Large Log-ratio Image

Sea mask

Split-based analysis

Masked large Log-Ratio Image

Sea Identification

Image Comparison

Co-registration Sea-masking

SAR Large Image t2

Pre-processing

SAR Large Image t1

Change-detection Map

Thresholding T

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same area on the ground. This process was carried out according to a standard co-registration algorithm for SAR images, which is based on the maximization of cross-correlation between images in a given number of selected windows. After co-registration, the part common to both the acquisitions is selected to define a multitemporal pair of images having a size of 8662x8192 pixels. It is worth noting that we are clearly in presence of a large-size pair of SAR images.

Due to the active and coherent nature of the SAR signal, both intensity images are affected by multiplicative speckle noise, which may degrade the performances of change-detection tech-niques. In order to reduce noisy speckle components in the con-sidered images, while preserving sufficient spatial details, adap-tive de-speckling filters can be used. Many filtering techniques have been published in the literature (e.g. the Frost [32], Lee [33], Kuan [34], Gamma Map [35],[36]). These filters can be applied with different window sizes (or iteratively) in order to obtain the desired trade-off between signal-to-noise ratio and detail preser-vation.

After pre-processing, multitemporal images are compared pixel-by-pixel by means of a log-ratio operator [12],[18].

As expected, according to the considered application, both multitemporal images include large portions of sea. The log-ratio image on the sea has an undesirable behavior that depends on the variability of the conditions at the two acquisition dates (e.g. dif-ferent weather conditions, presence or absence of waves), which strongly affect the values of the backscattering coefficient. This instability may induce many false alarms. It is worth noting that the use of the difference operator instead of the log-ratio operator could reduce the component to the instability in the sea area due to the small values of the backscattering coefficient. Nevertheless, it has been demonstrated theoretically and experimentally [12]-[16] that the log-ratio operator results in both better statistical properties of the changed and no-changed pixels and in more ac-curate change-detection maps. In order to solve this problem, in the proposed system we introduce a block aimed at sea identifica-


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tion. A simple automatic unsupervised approach is adopted for detecting sea pixels and filtering them from the change-detection process. Sea or coastline detection in SAR images is a widely in-vestigated topic in the literature [37]-[39]. As we are interested in removing the seaside from the change-detection process, we focus the attention on sea identification rather than coastline detection. In [38] a simple approach is proposed for supervised seaside iden-tification, which is based on two steps: i) texture feature extrac-tion; and ii) supervised classification. The method is based on the observation that the coherent nature of the SAR signal makes the behavior of the texture due to the speckle on the sea strongly dif-ferent from that of the texture on the land. In particular, the sea shows a more homogeneous speckle texture than land areas [38] (which are characterized from the presence of various types of land covers) [37]. We propose a similar, yet unsupervised, ap-proach. As in [38], a texture measure is computed based on the analysis of the co-occurrence matrix; then an automatic threshold-ing algorithm is used for separating the sea from the land. Here the Kittler and Illingworth (KI) thresholding technique proposed in [12] has been adopted, which is based on the minimization of a biased estimation of the error probability under the assumption that the histogram can be modeled according to a mixture of two Generalized Gaussian distributions. The described procedure is applied to the image acquired before the tsunami in order to pro-duce a conservative sea map and to allow a proper identification of the coast erosion due to the tsunami. It is worth noting that for taking into account the effects of the window size used for com-puting the texture feature, a margin between the computed mask and the adopted one was imposed. This is not critical because the behavior of the sea along the coast is stable and does not affect the log-ratio image.

Once the log-ratio image has been masked (Fig. 3.4), it is ana-lyzed according to the split-based approach proposed in section 3.3. Concerning the threshold-selection algorithm, we adopted also in this step the Kittler and Illingworth technique extended to the Generalized Gaussian model proposed in [13]. This choice

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has been done as: i) this algorithm proved accurate on change-detection in intensity SAR images [13]; ii) unlike other algo-rithms presented in the literature, it can automatically detect sin-gle or double threshold values and can also identify situations in which there are no changes in the analyzed images [13].

3.4. Experimental Results In this section experimental results obtained on the Sumatra Is-

land dataset presented in section 3.3.1 are shown and analyzed.

3.4.1. Design of Experiments In order to reduce speckle noise components, we applied to the

considered images different de-speckling filter (i.e., refined Lee, Frost, Gamma Map). We obtained the best results with the Gamma Map filter. Fig. 3.4 shows the log-ratio image obtained by comparing the two intensity images filtered with a Gamma Map filter (window size 5x5, 3 iterations)4. This image has been used for all the experiments described in this section.

As expected, after comparison the seaside is strongly unstable due to the high variability of backscattering coefficient in ex-tended water surfaces. Thus the image acquired on April 1998 was analyzed for extracting the mask of sea pixels. In this particu-lar case, we thresholded the entropy measure computed form the co-occurrence matrix (size of the moving window 7x7 pixels, in-terpixel distance 1, direction 45°) after re-quantization on 32 lev-els. After removing sea pixels from the log-ratio image, un-masked pixels were quantized to integers in the range [0,255]. Fig. 3.4 shows the log-ratio image with masked sea pixels (re-ported in light gray color). This full image was subdivided in 272 splits of size 509x512 pixels (see dashed lines in Fig. 3.4). Among them, 123 splits were considered unreliable from a statis-tical point of view as including more than 85% of masked pixels (i.e., sea pixels) and thus removed from the split-based threshold- 4 The optimal window size and the number of iterations of the filter were selected ac-

cording to the procedure presented in [16].

CH

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Figure 3.4

Log-ratio im

age after sea masking. W

hite squares in dashed line identify all the computed splits, w

hile white continuous squares the six splits w

ith the highest probabilities to contain changed pixels (black color corresponds to the m

inimum

of the log-ratio image, w

hereas white color corresponds to the m

aximum

).

14 Km


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iσ

CiX

5

10

15

20

0 15 30 45 60 75 90 105 120 135 150

Figure 3.5 Diagram of the standard deviation values iσ of the considered N splits

C Ci ∈ PX sorted in descending order.

selection process. The remaining 149 sub-images were further analyzed for identifying splits with the highest probability to con-tain changed pixels (see section 3.2.2). Fig. 3.5 shows the behav-ior of the standard deviation values of the considered sub-images sorted in descending order. It is possible to see that between the first six sub-images and all the others there is a significant differ-ence of standard deviation values. Thus, these sub-images (see Fig. 3.6) were selected for performing threshold selection. It is worth noting that, as expected, all the selected sub-images are lo-cated along the coast (see splits pointed out with white squares in Fig. 3.4) where the highest amount of changes occurred. It is worth noting that a preliminary visual analysis of the histogram of the log-ratio image (and of a sub-set of splits) points out that, on the one hand, the classes of no-change and change of level 1 are associated with two modes that are reasonably well separated; on the other hand, the mode of the change of level 2 is strongly over-lapped to the other two distributions.

Different trials were carried out for assessing quantitatively and qualitatively the effectiveness of the proposed system. Two different set-ups were considered according to the objectives de-scribed in section 3.3.1. The two sets of experiments are treated

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separately in order to properly point out the effectiveness of the proposed system in problems with different complexity.

For both experimental set-ups the results obtained with the proposed split-based change-detection approach are compared with those obtained by applying: i) the automatic thresholding al-gorithm to the whole large-size log-ratio image; ii) the automatic thresholding algorithm to each split independently; iii) the opti-mal manual trial-and-error thresholding procedure (MTEP) to

1CX 2CX

3CX

4CX


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5CX

6CX Figure 3.6 Log-ratio image of the six splits with the highest standard deviation se-

lected according to the proposed split-based change-detection procedure. each split1. It is worth noting that the proposed split-based ap-proach may lead to a non-integer threshold value. In the follow-ing, as values in the log-ratio image for simplicity are quantized with integers in the range [0, 255], all identified threshold values are approximated with the nearest integer.

In order to perform a quantitative accuracy assessment, two test sites were selected among the 149 splits having less than 85% of sea pixels. The two test sites were accurately identified for modeling regions of the image with different properties, i.e.: i) split “A” shows a high prior probability of changed pixels; and ii) split “B” shows a small prior probability of changed pixels. It is worth noting that according to the properties required for split “A”, it is one of the sub-images also used for threshold selection (i.e., 5CX ). However, we expect that this does not introduce a sig-nificant bias in the validation procedure.

1 The MTEP identifies the threshold by analyzing all possible threshold values and se-

lecting the one resulting in the minimum overall change-detection error compared to the reference map.

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(a) (b)

Figure 3.7 Test-site associated with split “A”. (a) Log-ratio image, and (b) reference

map.

(a) (b)

Figure 3.8 Test-site associated with split “B”. (a) Log-ratio image, and (b) reference map.

For both sub-images, a reference map was defined manually

according to an accurate visual inspection of both the considered SAR images and a pair of very high geometrical resolution im-ages available for the study area. The reference map of split “A” contains 98487 unchanged pixels, 14802 pixels associated with


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the change of level 1, and 20826 pixels associated with the change of level 2. The reference map for split “B” contains 82958 unchanged pixels, 1043 pixels associated with the change of level 1, and 1554 pixel associated with the change of level 2. Figures 3.7 and 3.8 show the log-ratio images and the reference maps (where changes of level 1 are depicted in dark color and changes of level 2 are reported in dark gray) of splits “A” and “B”, respec-tively. In all experiments, our goal is to obtain a change-detection map as similar as possible to the reference maps yielded accord-ing to the aforementioned time consuming manual process.

3.4.2. Change-Detection Results: Single-Change Identification The first set of trials is aimed at identifying only the change of

level 1. In this set-up, we neglect the presence of the class of changes of level 2. This assumption does significantly affect the reliability of the thresholding algorithm which can be applied with a reasonable approximation as the distribution of changes of level 2 is strongly overlapped to the others.

TABLE 3.1

THRESHOLD VALUES FOR THE SIX SPLITS HAVING THE HIGHEST PROBABILITIES TO CONTAIN CHANGED PIXELS (SINGLE-THRESHOLD EXPERIMENT)

Considered split CiX 1CX

2CX 3CX 4CX 5CX

6CX

Threshold value Ti 150 156 166 153 160 147

Table 3.1 shows the threshold values obtained by applying the

KI algorithm independently to the considered splits. As one can see, due to the non-stationarity of the statistical properties of the classes of interest in the spatial domain of the image and to dif-ferent approximations of the thresholding algorithm in different splits, slightly different threshold values (ranging from 147 to 166) were obtained.

Results obtained on each split were used for computing the fi-nal threshold value with the proposed Med-SBA and Mean-SBA strategies. As one can see from Table 3.2, both strategies resulted in a threshold value (i.e., 155) which is close to the optimal

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threshold obtained manually (153 for split “A” and 157 for split “B”). Thus the overall error on split “A” (i.e., 3459) and “B” (i.e. 553) for both the Med-SBA and the Mean-SBA shows small dif-ferences with the overall error obtained by the MTEP on the two splits, respectively. Results obtained with the J-SBA are slightly better than those obtained with the Med-SBA and the Mean-SBA on both splits, as the threshold value (i.e., 154) is closer to the op-timal one (i.e., 153).

TABLE 3.2

THRESHOLD VALUES T , FALSE ALARMS, MISSED ALARMS AND OVERALL ERRORS OBTAINED WITH: THE SPLIT-BASED APPROACH AND THE THREE PROPOSED COMBI-

NATION STRATEGIES; THE THRESHOLDING ALGORITHM APPLIED TO THE WHOLE IM-AGE; THE THRESHOLDING ALGORITHM APPLIED TO SPLIT “A” AND “B”; AND THE

OPTIMAL-MANUAL TRIAL-AND-ERROR PROCEDURE

Threshold-selection technique T False

alarms Missed alarms

Overall errors

Med-SBA 155 1032 2427 3459 Mean-SBA 155 1032 2427 3459

J-SBA 154 1259 2109 3368 Large-size image thresholding 166 158 5750 5908

Split “A” thresholding 160 397 3974 4371 Split

“A

”

MTEP 153 1535 1821 3356 Med-SBA 155 321 232 553

Mean-SBA 155 321 232 553 J-SBA 154 362 187 549

Large-size image thresholding 166 64 608 672 Split “B” thresholding - - - - Sp

lit “

B”

MTEP 157 240 301 541

From Table 3.2 it can be also concluded that all the proposed

split-based approaches performed better than the change-detection analysis applied separately to splits “A” and “B”. In greater de-tail, one can observe that on split “A”, despite the relative high ratio between the prior probability of change and no-change classes, the computed threshold value (i.e., 160) resulted in a higher overall error (i.e., 4371) than the proposed approach. The situation is more critical when considering split “B”. Depending on the very small ratio between the prior probability of the classes


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of changed and no-changed pixels, in this split the threshold-selection algorithm did not identify any threshold value (it recog-nized a situation where there are no changes). The proposed split-based approach performed also better than a direct analysis of the whole large-size log-ratio image which pro-duces the worst results, due to the small prior probability of changed pixels with respect to the unchanged ones. It is worth noting that in other experiments (not reported in this chapter for space constraints) with different de-speckling filters applied for the pre-processing of original images, the procedure of threshold selection applied to the whole image was not able to identify any decision threshold, while the proposed approach still provided satisfactory results.

(a) (b)

Figure 3.9 Change-detection maps obtained on split “A” with (a) the MTEP and (b)

the proposed J-SBA. Besides numerical evaluation carried out on the selected test

sites (splits “A” and “B”) also a qualitative evaluation of the change-detection maps obtained on both splits with the proposed system was performed (see Figures 3.9 and 3.10). Furthermore, a qualitative analysis of the global change-detection map obtained with the SBA was performed (this map is not reported as too large). Both analyses confirmed the effectiveness of the proposed

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split-based approach, which produced satisfactory change-detection maps. It is worth noting that, in order to completely ex-ploit the prior information available on this specific application, the global change-detection map can be obtained by applying thresholding only to splits along the coast (i.e. splits that contain sea pixels), as in tsunami damage-assessment we expect that changes are concentrated only along the coast.

The above-reported quantitative and qualitative results prove the effectiveness of the proposed approach and its validity at an operational level for the automatic detection of changes of level 1.

(a) (b)

Figure 3.10 Change-detection maps obtained on split “B” with (a) the MTEP and (b)

the proposed Mean- or Med-SBA.

3.4.3. Change-Detection Results: Double-Change Identifica-tion

The second experimental set-up is aimed at assessing the ef-fectiveness of the proposed approach in identifying both the changes of level 1 and level 2. The detection of changes of level 2 is much more difficult than only the detection of changes of level 1 as: i) the statistical distribution of the related class is highly overlapped to that of the class of no-change and partially over-lapped to that of the class of change of level 1 (see Fig. 3.11); ii)


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not all the splits in the image (also among the six sub-images se-lected for deriving the threshold value according to the proposed SBA) include areas associated to change of level 2. This makes much more critical the task of the automatic threshold-selection algorithm, which in the case of double-threshold selection is in-trinsically less robust than in the case of single-threshold selec-tion. This last consideration is confirmed from the results reported in Table 3.3, which shows the values of the two thresholds de-tected for the six selected splits. As one can observe, the KI algo-rithm can identify the presence of two threshold values (and

0

0.02

0.04

80 100 120 140 160 180 200 220Gray-level value

PDF

Figure 3.11 Probability density function (PDF) of split “A” (black dashed line); and

distributions of classes of no-change (light gray line on the left side), change of level 1 (dark gray distribution in the middle) and change of level 2 (light gray line on the right side) evaluated according to the refer-ence map.

TABLE 3.3 THRESHOLD VALUES FOR THE SIX SPLITS HAVING THE HIGHEST PROBABILITIES TO

CONTAIN CHANGED PIXELS (DOUBLE-THRESHOLD EXPERIMENT)

Considered split CiX 1CX

2CX 3CX 4CX 5CX

6CX

Threshold value Ti,1 150 156 166 153 160 147 Threshold value Ti,2 127 - - 136 138 -

therefore of two kinds of changes) only in three splits, while for the remaining sub-images only one threshold value is detected. It follows that the proposed combination strategies for estimating

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the final threshold values were applied to: i) all the six selected splits when estimating the threshold value associated with changes of level 1 (T1,i); and ii) only the three splits when estimat-ing the threshold value separating changes of level 2 (T2,i). As can be seen from Table 3.4, all the three proposed split-based approaches are able to properly identify the two threshold values, which are very close to the threshold values obtained with the op-timal MTEP for both split “A” and “B”. In particular, for split “A” the lowest overall error was obtained with the Med-SBA, which resulted in 10846 errors with threshold values 155 and 133. These values are the closest one (among those derived by the pro-posed combination strategies) to the optimal result obtained with the MTEP, which identified the pair of threshold values 152 and 133, involving 10631 errors. Considering split “B”, the best re-sults were achieved with the Mean-SBA, which identified thresh-old values 155 and 136 resulting in 3012 overall errors. This error is very close to the one yielded with the MTEP (see Table 3.4).

TABLE 3.4

THRESHOLD VALUES 1T AND 2T , AND OVERALL ERRORS OBTAINED WITH: THE PRO-POSED SPLIT-BASED APPROACH; THE THRESHOLDING ALGORITHM APPLIED TO THE WHOLE IMAGE; THE THRESHOLDING ALGORITHM APPLIED TO SPLIT “A” AND “B”;

AND THE OPTIMAL MANUAL TRIAL-AND-ERROR PROCEDURE

Threshold-selection technique 1T 2T Overall errors

Med-SBA 155 133 10846 Mean-SBA 155 136 12054

J-SBA 154 131 12737 Large-size image thresholding 166 - -

Split “A” thresholding 160 138 15245 Split

“A

”

MTEP 152 133 10631 Med-SBA 155 133 3832

Mean-SBA 155 136 3012 J-SBA 154 131 4808

Large-size image thresholding 166 - - Split “B” thresholding - - - Sp

lit “

B”

MTEP 151 136 2938


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Since we have three classes, a more detailed analysis of results can be performed by considering the confusion matrices. Here, for space constraints, only the confusion matrices associated with the change-detection maps obtained with the MTEP for both split “A” and “B” and with the Med-SBA for split “A” and the Mean-SBA for split “B” are reported (see Tables 3.5 and 3.6). All the other confusion matrices show a similar trend. By analyzing Ta-bles 3.5 and 3.6, one can observe that for both splits the highest number of errors is associated with the class of changes of level 2, which is significantly confused with both the other classes. This behavior was expected on the basis of the complexity of the prob-lem as the information on changes of level 2 present in the origi-nal SAR images is intrinsically ambiguous. However, these re-sults are common to both the proposed SBA and the optimal MTEP; therefore, we can conclude that also in this second set-up the proposed approach produced satisfactory results.

TABLE 3.5 CONFUSION MATRICES FOR THE CHANGE-DETECTION MAPS OBTAINED ON THE SPLIT “A” WITH (A) THE PAIR OF THRESHOLD VALUES DERIVED WITH THE MTEP PROCE-DURE; (B) THE PAIR OF THRESHOLD VALUES OBTAINED WITH THE PROPOSED MED-

SBA

True Class No-

changeChangelevel 1

Changelevel 2

No- change 92729 41 1902

Change level 1 434 13270 1439

Est

imat

ed C

lass

Change level 2 5324 1491 17485

True Class No-

changeChangelevel 1

Changelevel 2

No- change 92729 41 1902

Changelevel 1 273 12375 759

Est

imat

ed C

lass

Changelevel 2 5485 2386 18165

(a) (b) Also in this case, all the proposed split-based approaches per-

formed better than either analyzing the whole large-size log-ratio image or independently the single splits “A” and “B”. In greater

114

detail, as expected, the small prior probability of the change of level 2 and the overlapping between its distribution and those of the other classes, resulted in the impossibility to detect the value of 2T by applying the threshold-selection algorithm to the whole large-size log-ratio image. Concerning the change-detection analysis performed independently on split “A”, the obtained error is significantly higher than the overall errors obtained with the proposed approach. It is worth noting that independent threshold selection performed on split “B” completely failed to identify any threshold value, while the proposed Med-SBA, Mean-SBA, and J-SBA resulted in threshold values close to the optimal ones.

TABLE 3.6 CONFUSION MATRICES FOR THE CHANGE-DETECTION MAPS OBTAINED ON THE SPLIT “B” WITH (A) THE PAIR OF THRESHOLD VALUES DERIVED WITH THE MTEP PROCE-

DURE; (B) THE PAIR OF THRESHOLD VALUES OBTAINED WITH THE PROPOSED MEAN-SBA

True Class No-

changeChangelevel 1

Changelevel 2

No- change 80614 16 357

Change level 1 429 933 127

Est

imat

ed C

lass

Change level 2 1915 94 1070

True Class No-

changeChangelevel 1

Changelevel 2

No- change 80614 16 357


Est

imat

ed C

lass


(a) (b) Also for this set-up a qualitative evaluation of the change-

detection maps obtained with the proposed system on splits “A” and “B” (see Figures 3.12 and 3.13), and on the whole large-size image was carried out. This assessment confirmed the effective-ness of the proposed approach, which despite the complexity of the change-detection problem inherent changes of level 2, pro-duced good quality change-detection maps. It is worth noting that also in this case we exploited the available prior information in


115

the change-detection process, i.e. we applied the proposed ap-proach only to splits that are along the coast.

(a) (b)

Figure 3.12 Change-detection maps obtained on split “A” with (a) the MTEP and (b)

the proposed Med-SBA.

(a) (b)

Figure 3.13 Change-detection maps obtained on split “B” with (a) the MTEP and (b) the proposed Mean-SBA.

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3.5. Discussion and Conclusions In this chapter, an unsupervised and automatic approach to

change detection in large-size multitemporal images has been proposed. The proposed approach automatically splits the consid-ered difference (or ratio) image in a set of sub-images (splits) of user defined size, which are sorted out according to their prob-ability to contain a significant amount of changed pixels. The sub-images having the highest probabilities to contain changed pixels are analyzed in order to derive the decision threshold for generat-ing the change-detection map. To this purpose, two different techniques have been proposed: i) an independent split analysis strategy, which detects the decision threshold on each split and then combine the results for obtaining the final value of the threshold according to simple (yet effective) combination strate-gies (Mean-SBA and Med-SBA); ii) a joint split analysis strategy that directly detects the value of the final decision threshold by analyzing the joint distribution of the splits having a high prob-ability to contain changed areas (J-SBA). On the one hand, the joint split analysis strategy has the advantage to jointly model the distributions of changed and unchanged classes by considering different portions of the images. On the other hand, it has the dis-advantage that if the distributions of classes are slightly different in different splits extracted from the large-size image (i.e., the dis-tributions are non-stationary in the scene), the decision threshold derived according to model-based thresholding approaches (e.g., Kittler and Illingworth technique, Bayes technique based on the EM algorithm) may be not accurate (due to a poor fitting of the joint distribution of classes to the model adopted for threshold se-lection). The independent split analysis strategy overcomes this disadvantage, properly applying the thresholding algorithm sepa-rately to each split (by reducing the problem of possible non-stationarity in the spatial domain). Among the two combination strategies, the method based on the average (Mean-SBA) is reli-able if all the splits convey proper information on the values of the decision threshold; the method based on the median value (Med-SBA) is more robust to outliers (possible splits in which the


117

thresholding algorithm provides poor estimation of the decision threshold values). It is worth noting that possible non-stationarity in the class distributions results in different values of the thresh-olds (and thus also affects the results provided by the independent split analysis strategy). However, this does not invalidate the models adopted for identifying the threshold values, but involves the need of fusing the results obtained on different splits.

The proposed approach has been used for designing a system for damage assessment in relation to the tsunami occurred in De-cember 2004 in Indonesia. To this purpose, a proper architecture that exploits the split-based change-detection system has been de-fined. Experimental results confirmed the effectiveness of the proposed approach, which detected in a automatic way the main damaged areas. In greater detail, all the three proposed change-detection strategies (i.e., the Mean-SBA, the Med-SBA and the J-SBA) identified in an automatic way threshold values for the de-tection of both changes of levels 1 and 2 that are very close to the optimal values that can be obtained manually. In addition, these strategies revealed significantly more accurate and robust than the approaches based on both the independent analysis of each split and the direct analysis of the whole large-size image.

It is worth noting that the detection of changes of level 1 is easier due to the good separability between the distribution of such class and that of the no-change class, whereas the strong overlapping between the distribution of the class of changes of level 2 and that of the no-changed pixels makes less reliable and accurate the identification of such kind of damages.

The experimental analysis pointed out that the proposed method requires a computational time comparable or smaller than traditional thresholding techniques. This is due to the fact that we split the analysis in sub-images, but the additional time intro-duced by the proposed method (split and combination) is negligi-ble with respect to the reduction of the time we obtain by focus-ing the threshold-selection algorithm only on a reduced number of pixels (those in the high standard deviation splits) instead of on all the pixels of the large-size image.

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As a final remark, it is important to observe that although the proposed split-based approach has been used for designing a sys-tem for the detection of damages caused from tsunami by using multitemporal SAR images, potentially it is general and can be considered for change detection in any pair of large-size multitemporal images. For this reason, as future developments of this work, we plan to extend the experimental investigation to other data sets and change-detection problems for better assessing the robustness of the approach in different scenarios.

Acknowledgments This work has been carried out in the framework of a scientific

collaboration with the Joint Research Center (JRC) of the Euro-pean Commission (Ispra (VA), Italy). The authors wish to thanks Dr. Daniele Erlich, Dr. Andrea Baraldi and Dr. Harm Greidanus for providing the RADARSAT-1 SAR image of Indonesia and for useful discussion on the developed system. The authors are also grateful to Sarmap s.a. for providing the SARscape® software used for image co-registration.

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Chapter 4

4. A Detail-Preserving Scale-Driven Ap-proach to Change Detection in Multitemporal SAR Images

This chapter presents a novel approach to change detection in multitemporal SAR images. The proposed approach exploits a wavelet-based multiscale decomposition of the log-ratio image (obtained by a comparison of the original multitemporal data) aimed at achieving different scales (levels) of representation of the change signal. Each scale is characterized by a different trade-off between speckle reduction and preservation of geomet-rical details. For each pixel, a subset of reliable scales is identi-fied on the basis of a local statistic measure applied to scale-dependent log-ratio images. The final change-detection result is obtained according to an adaptive scale-driven fusion algorithm. Experimental results obtained on multitemporal SAR images ac-quired by the ERS-1 satellite confirm the effectiveness of the pro-posed approach.

(This chapter was published on the IEEE Transaction on Geo-

science and Remote Sensing, 2005, Vol.43, No. 12, pp. 2963-2972, December 2005. Co-author: Lorenzo Bruzzone)

4.1. Introduction Change detection is a process that analyzes a pair of remote

sensing images acquired on the same geographical area at differ-

126

ent times in order to identify changes that may have occurred be-tween the considered acquisition dates. Change-detection tech-niques have been used successfully in many applications, such as environmental monitoring [1], study on land-use/land-cover dy-namics [2], analysis of forest or vegetation changes [3],[4], dam-age assessment [5], agricultural surveys [6], and analysis of urban changes [7],[8].

In recent years, several change-detection techniques have been proposed in the remote sensing literature for the analysis of im-ages acquired by passive sensors. Less attention has been devoted to change detection in Synthetic Aperture Radar (SAR) images. This is mainly due to the intrinsic complexity of SAR data, which require both an intensive pre-processing phase and the develop-ment of effective data analysis techniques capable of dealing with multiplicative speckle noise. Because of these two issues, end-users are less interested in SAR data for operational change-detection applications. However, despite the complexity of data processing, SAR sensors have important properties at the opera-tional level, since they are capable of acquiring data in all weather conditions and are not affected by cloud cover or different sunlight conditions (see [9] for greater details on the importance and the properties of SAR data in change detection).

In the literature, usually unsupervised change detection in SAR images is based on a 3-step procedure [9]: i) pre-processing; ii) pixel-by-pixel comparison of two images; and iii) image thresholding. The aim of pre-processing is to increase the SNR of the considered images (by reducing noisy speckle components), while preserving sufficient spatial details. Many adaptive filters for speckle reduction have been proposed, e.g. the Frost [10], Lee [11], Kuan [12], Gamma Map [13],[14], and Gamma WMAP [15] (i.e., the Gamma MAP filter applied in the wavelet domain) fil-ters. Despite their spatial adaptive characteristic, which tends to preserve the signal’s high frequency information, filter applica-tions often give the desired speckle reduction but also an unde-sired degradation of the geometrical details of the investigated scene. Pixel-by-pixel comparison is carried out according to a ra-

CHAPTER 4 - A DETAIL-PRESERVING SCALE-DRIVEN APPROACH TO CHANGE DETECTION IN MULTITEMPORAL SAR IMAGES

127

tio (or a log-ratio) operator in such a way as to take into account the multiplicative model of the speckle. The decision threshold can be selected either with a manual trial-and-error procedure (according to the desired trade-off between false and missed alarms) or with automatic techniques (e.g., by analyzing the sta-tistical distribution of the ratio image, by fixing the desired false alarm probability [4],[16], or following a Bayesian minimum er-ror decision rule [9]).

Depending on the kind of pre-processing applied to the multitemporal images, these techniques can achieve different trade-offs between detail preservation and accuracy in the repre-sentation of homogeneous areas in change-detection maps. But these are contrasting properties, in other words high accuracy in homogeneous areas usually requires an intensive de-speckling phase, which in turn degrades the geometrical details in the SAR images. This is due both to the filter’s smoothing effect and to the removal of the speckle’s informative components (which is re-lated to the coherence properties of the SAR signal).

In order to address the above limitations of standard methods, in this chapter we propose a scale-driven, adaptive approach to change detection in multitemporal SAR images. This is based: i) on a multiscale decomposition of the log-ratio image; ii) on a se-lection of the reliable scales for each pixel (i.e., the scales at which the considered pixel can be represented without border problems) according to an adaptive analysis of its local statistics; and iii) on a scale-driven combination of the selected scales. In greater detail, we propose to perform the scale-driven combina-tion by investigating three different strategies: a) fusion at the de-cision level by an “optimal” scale selection; b) fusion at the deci-sion level of all reliable scales; and c) fusion at the feature level of all reliable scales. The rationale of the proposed method is to exploit only high-resolution levels in the analysis of the expected edge (or detail) pixels and to use also low-resolution levels in the processing of pixels in homogeneous areas. The proposed method thus exhibits both a high sensitivity to geometrical details (e.g., the borders of changed areas are well preserved) and a high ro-

128

bustness to noisy speckle components in homogeneous areas. Ex-perimental results carried out on multitemporal ERS-1 images from Canada confirm the effectiveness of the proposed scale-driven approach.

The chapter is organized into five sections. The next section introduces the problem formulation and the basics of the proposed approach. Section 4.3 presents the proposed approach and focuses on its principal steps: i.e. i) multiresolution decomposition; ii) adaptive scale identification; and iii) scale-driven fusion. Experi-mental results obtained on real multitemporal SAR data are re-ported in section 4.4. Finally, conclusions are drawn in section 4.5.

4.2. Problem formulation and architecture of the pro-posed technique

Let us consider the two co-registered intensity SAR images, JjIiji,X 1 ≤≤≤≤= 1 ,1 ),( 1X and JjIiji,X 2 ≤≤≤≤= 1 ,1 ),( 2X ,

of size I×J, acquired over the same area at different times t1 and t2. Let uc ωω ,=Ω be the set of classes associated with changed and unchanged pixels. As shown in Fig. 4.1, the proposed ap-proach is made up of four blocks aimed at the following: i) image comparison; ii) multiresolution decomposition; iii) adaptive scale identification based on the local statistics computed at different resolution levels; and iv) generation of the final change-detection map according to an adaptive scale-driven fusion.

The first step of the proposed change-detection technique con-sists of a pixel-by-pixel image comparison. According to the lit-erature [9],[17]-[19], the comparison is carried out by a ratio op-erator to reduce the effects of speckle in the resulting image and for the measured signal to be independent of the absolute inten-sity value of the considered pixel in the multitemporal images [18],[19]. Let XR (where the subscript R stands for ratio) be the obtained “ratio image”. To enhance low intensity pixels, the ratio image is usually expressed in a logarithmic scale, resulting in the log-ratio image XLR:


129

2LR R 2 1

1

log log log log= = = −X

X X X XX

(4.1)

where log stands for natural-logarithm. With this operation the distribution of the two classes of interest ( cω and uω ) in the ra-tio image can be made more symmetrical and the residual multi-plicative speckle noise can be transformed in an additive noise component [9]1.

Figure 4.1 General scheme of the proposed approach.

The second step of the proposed method aims at building a

multiscale representation of the change information in the consid-ered test site. The desired scale-dependent representation can be obtained by applying different methods to the data, e.g., Lapla-

1 It is worth noting that the residual multiplicative speckle noise is expected to be par-

ticularly high in portions of the ratio image associated with changed areas on the ground.

X1 SAR image (time t1)

X2 SAR image (time t2)

Image comparison(log-ratio)

LRX

Adaptive scale identification

Change-detection map (M)

Scale-driven fusion

Multiresolution decomposition

0LRX …. 1-N

LRX…. nLRX

…. ….

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cian/Gaussian pyramid decomposition [20], wavelet transform [21],[22], recursively upsampled bicubic filter [23], etc. Given the computational cost and the assumption of the additive noise model required by the above techniques, we chose to apply the multiresolution decomposition process to the log-ratio image XLR, instead of decomposing the two original images X1 and X2 sepa-rately. At the same time this allows a reduction in computational cost and satisfies the additive noise model hypothesis. The selec-tion of the most appropriate multiresolution technique is related to the statistical behaviors of XLR and will be discussed in the next section. The multiresolution decomposition step produces a set of images 0 1

MS LR LR LR−= n NX X XX , ..., , ..., , where the superscript n

( 1,.....,1,0 −= Nn ) indicates the resolution level. As we shall con-sider a dyadic decomposition process, the scale corresponding to each resolution level is given by 2n. In our notation, the output at resolution level 0 corresponds to the original image, i.e.,

0LRLR ≡X X . For n ranging from 0 to N-1, the obtained images are

distinguished by different trade-offs between spatial-detail pres-ervation and speckle reduction. In particular, images with a low value of n are strongly affected by speckle, but they are character-ized by a large amount of geometrical detail, whereas images identified by a high value of n show significant speckle reduction and contain degraded geometrical details (high frequencies are smoothed out).

In the third step, local and global statistics are evaluated for each pixel at different resolution levels. At each resolution level and for each spatial position, by comparing the local and global statistical behaviors it is possible to identify adaptively whether the considered scale is reliable for the analyzed pixel.

The selected scales are used to drive the fourth step, which consists of the generation of the change-detection map according to a scale-driven fusion. In this chapter, three different scale-driven combination strategies are proposed and investigated. Two perform fusion at the decision level, while the third performs it at the feature level. Fusion at the decision level can either be based on “optimal” scale selection or on the use of all reliable scales;


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fusion at the feature level is carried out by analyzing all reliable scales.

4.3. Proposed adaptive scale-driven change detection technique

In this section, we focus on the novel aspects of the proposed change-detection approach. In particular, we present in detail the techniques for the following: i) obtaining a multiresolution de-composition of the log-ratio image; ii) adaptively identifying the scales to be considered in the analysis of each pixel; and iii) pro-ducing the final change-detection map according to a scale-driven fusion strategy.

4.3.1. Multiresolution decomposition of the log-ratio image As mentioned in the previous section, our aim is to handle the

information at different scales (resolution levels) in order to im-prove both geometrical detail preservation and accuracy in homo-geneous areas in the final change-detection map. Images included in the set XMS are computed by adopting a multiresolution de-composition process of the log-ratio image XLR. In the SAR litera-ture [15],[24]-[28], image multiresolution representation has been applied extensively to image de-noising. Here, a decomposition based on the two-dimensional discrete stationary wavelet trans-form (2D-SWT) has been adopted, as in our image analysis framework it has a few advantages (as described in the following) over the standard discrete wavelet transform (DWT) [29]. As the log-ratio operation transforms the SAR signal multiplicative model into an additive noise model, SWT can be applied to XLR without any additional processing. By applying SWT to the log-ratio image instead of working separately on the two images X1 and X2 the computational time of the proposed change-detection technique can be halved. 2D-SWT applies appropriate level-dependent high and low pass filters with impulse response (.)nh and (.)nl , ( 1,.....,1,0 −= Nn ), respectively, to the considered sig-nal at each resolution level. A one-step wavelet decomposition is

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based on both level-dependent high and low pass filtering, first along rows and then along columns in order to produce four dif-ferent images at the next scale. After each convolution step, unlike DWT, SWT avoids down-sampling the filtered signals. Thus, according to the scheme in Fig. 4.2, the image XLR is de-composed into four images of the same size as the original. In particular, decomposition produces: i) a lower resolution version

1LLLRX of image XLR, which is called the approximation sub-band,

and contains low spatial frequencies both in the horizontal and the vertical direction at resolution level 1; and ii) three high-frequency images 1LH

LRX , 1HLLRX and 1HH

LRX , which correspond to the horizontal, vertical, and diagonal detail sub-bands at resolution level 1, respectively. Note that, superscripts LL, LH, HL, and HH specify the order in which high (H) and low (L) pass filters have been applied to obtain the considered sub-band.

Figure 4.2 Block scheme of the stationary wavelet decomposition of the log-ratio

image XLR. Multiresolution decomposition is obtained by recursively ap-

plying the described procedure to the approximation sub-band LLLR

nX obtained at each scale n2 . Thus, the outputs at a generic resolution level n can be expressed analytically as follows:

Columnwise Rowwise

l0(.)

h0(.)

h0(.)

l0(.)

h0(.)

l0(.)

1LL LRX

1 LHLRX

1 HLLRX

1 HHLRX

LRX


133

( ) [ ] [ ]

( ) [ ] [ ]

( ) [ ] [ ]

( ) [ ] [ ]

1 1LL 1 LL

LRLR0 0

1 1LH 1 LL

LRLR0 0

1 1HL 1 LL

LRLR0 0

1HH 1 LL

LRLR0 0

( ) ( , )

( ) ( , )

( ) ( , )

( ) ( , )

− −+

= =

− −+

= =

− −+

= =

−+

= =

= + +

= + +

= + +

= + +

∑∑

∑∑

∑∑

∑

n n

n n

n n

n

D Dn n n n

p q

D Dn n n n

p q

D Dn n n n

p q

D Dn n n n

p q

i, j l p l q i p j q

i, j l p h q i p j q

i, j h p l q i p j q

i, j h p h q i p j q

X X

X X

X X

X X1−

∑n

(4.2)

where nD is the length of the wavelet filters at resolution level n. At each decomposition step, the length of the impulse response of both high and low pass filters is upsampled by a factor 2. Thus, filter coefficients for computing sub-bands at resolution level n +1 can be obtained by applying a dilation operation to the filter coefficients used to compute level n. In particular, 1-2n zeros are inserted between the filter coefficients used to compute sub-bands at the lower resolution level [29]. This allows a reduction in the bandwidth of the filters by a factor two between subsequent reso-lution levels.

Filter coefficients of the first decomposition step for n = 0 de-pend on the selected wavelet family and on the length of the cho-sen wavelet filter. According to an analysis of the literature [26],[30], we selected the Daubechies wavelet family and set the filter length to 8. Daubechies of order 4 low-pass filter prototype impulse response is given by the following coefficient set:

0.230378, 0.714847, 0.630881, -0.0279838,-0.187035, 0.0308414, 0.0328830, -0.0105974

The finite impulse response of the high-pass filter for the decom-position step is obtained by satisfying the properties of the quad-rature mirror filters. This is done by reversing the order of the low-pass decomposition filter coefficient and by changing the sign of the even indexed coefficients [31].

In order to adopt the proposed multiresolution fusion strate-gies, one should return to the original image domain. This is done

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by applying the two-dimensional inverse stationary wavelet trans-form (2D-ISWT) at each computed resolution level independ-ently. For further detail about the stationary wavelet transform, the reader is referred to [29].

In order to obtain the desired image set XMS (where each im-age contains information at a different resolution level), for each resolution level a one step inverse stationary wavelet transform is applied in the reconstruction phase as many times as in the de-composition phase. The reconstruction process can be performed by applying the 2D-ISWT: i) either to the approximation and thresholded detail sub-bands at the considered level (this is usu-ally done in wavelet-based speckle filters [27]); or ii) only to the approximation sub-bands at each resolution level2. Since the change-detection phase considers all the different levels, all the geometrical detail is in XMS even when detail coefficients at a par-ticular scale are neglected (in other words, the details removed at a certain resolution level are recovered at a higher level without removing them from the decision process). For this reason, in this chapter for simplicity we focus on the solution that only considers the approximation sub-bands in the reconstruction phase (it is worth noting that empirical experiments on real data have con-firmed that details sub-band elimination does not affect the change-detection accuracy provided by the proposed approach). Once all resolution levels have been brought back to the image domain, the desired multiscale sequence of images LR

nX ( 10,1,....., −= Nn ) is complete and each element in XMS has the same size as the original image.

It is important to point out that unlike DWT, SWT avoids decimating. Thus, this multiresolution decomposition strategy ‘fills in the gaps’ caused by the decimation step in the standard 2 It is worth noting that the approximation sub-band contains low frequencies in both

horizontal and vertical directions. It represents the input image at a coarser scale and contains most informative components, whereas detail sub-bands contain information related to high frequencies (i.e., both geometrical detail information and noise compo-nents) each in a preferred direction. According to this observation, it is easy to under-stand how proper thresholding of detail coefficients allows noise reduction [27].


135

wavelet transform [29]. In particular, the SWT decomposition preserves translation invariance and allows avoiding aliasing ef-fects during synthesis without providing high-frequency compo-nents.

4.3.2. Adaptive scale identification Based on the obtained set of multiscale images LR

nX ( 10,1,....., −= Nn ), we must identify reliable scales for each con-sidered spatial position in order to drive the next fusion stage with this information. By using this information we can obtain change-detection maps characterized by high accuracy in homogeneous and border areas.

Reliable scales are selected according to whether the consid-ered pixel belongs to a border or a homogeneous area at different scales. It is worth noting that the information at low resolution levels is not reliable for pixels belonging to the border area, be-cause at those scales details and edge information has been re-moved from the decomposition process. Thus, a generic scale is reliable for a given pixel, if the pixel at this scale is not in a bor-der region or if it does not represent a geometrical detail. To define whether a pixel belongs to a border or a homogeneous area at a given scale n, we propose to use a multiscale local coef-ficient of variation (LCVn), as typically done in adaptive speckle denoising algorithms [28],[32]. This allows to better handle any residual multiplicative noise that may still be present in the scale selection process after rationing3. As the coefficient of variation cannot be computed on the multiresolution log-ratio image se-quence, the analysis is applied to the multiresolution ratio image sequence, which can easily be obtained from the former by invert-ing the logarithm operation. Furthermore, it should be mentioned that by working on the multiresolution ratio sequence we can de-sign a homogeneity test capable of identifying border regions (or 3 An alternative choice could be to use the standard deviation computed on the log-ratio

image. However, in this way we would neglect possible residual effects of the multi-plicative noise component.

136

details) and no-border regions related to the presence of changes on the ground. This is different from applying the same test to the original images (which would result in identifying border and no-border regions with respect to the original scene but not with re-spect to the change signal).

The LCVn is defined as:

)()()(

ji,μji,σji,LCV n

nn = (4.3)

where )( ji,σ n and )( ji,μn are the local standard deviation and the local mean, respectively, computed for the spatial position (i,j) at resolution level n ( 10,1,....., −= Nn ), on a moving window of a user-defined size. A window size that is too small reduces the reliability of the local statistical parameters, while windows that are too large decrease in sensitivity to identify geometrical de-tails. Thus the selected size should be a trade-off between the above properties. Thanks to the normalization operation defined in (3), we can adapt the standard deviation to the multiplicative speckle model. This coefficient is a measure of the scene hetero-geneity [32]: low values correspond to homogeneous areas, while high values refer to heterogeneous areas (e.g. border areas and point targets). To separate the homogeneous from the heterogene-ous regions, a threshold value must be defined. In a homogeneous region the degree of homogeneity can be expressed in relation to the global coefficient of variation (CVn) of the considered image at resolution level n, which is defined as:

n

nn

μσCV = (4.4)

where nσ and nμ are the mean and the standard deviation com-puted over a homogeneous region at resolution level n, ( 1,.....,1,0 −= Nn ). Homogeneous regions at each scale can be de-fined as those regions that satisfy the following condition:

nn CVji,LCV ≤)( (4.5)


137

In greater detail, a resolution level r (r = 0,1,..., N-1) is said to be reliable for a given pixel if (5) is satisfied for all resolution levels t (t = 0,1,..., r). Thus, for the pixel (i,j), the set MS

ijRX of im-ages with reliable scale is defined as:

LR LR LR0

MS =ij ijR SnX X XX , ..., , ..., , with 1−≤ NSij (4.6)

where Sij is the level with the lowest resolution (identified by the highest value of n), such that the pixel can be represented without any border problems and therefore it satisfies the definition of re-liable scale showed in (5) (note that the value of Sij is pixel de-pendent).

It is worth noting that, if the scene contains different kinds of changes with different radiometry (e.g., with increasing and de-creasing radiometry), the above analysis should be applied to the normalized ratio image XNR (rather than to the standard ratio im-age XR) defined as:

1 2

2 1NR min ,= X XX X X

(4.7)

This makes the identification of border areas independent of the order with which the images are considered in the ratio, thus al-lowing all changed areas (independently of the related radiome-try) to play a similar role in the definition of border pixels.

4.3.3. Scale-driven fusion Once the set MS

ijRX has been defined for each spatial position, it is possible to derive the final change-detection map according to a proper scale-driven fusion strategy. In this chapter we propose and investigate three possible strategies: i) fusion at the decision level by an “optimal” scale selection (FDL-OSS); ii) fusion at the decision level on all reliable scales (i.e., scales included in MS

ijRX ) (FDL-ARS); and iii) fusion at the feature level on all reliable scales (FFL-ARS).

For each pixel, the fusion at the decision level by an “optimal” scale selection (FDL-OSS) strategy only considers the reliable

138

level with the lowest resolution, i.e., the “optimal” resolution level ijS . The rationale of this strategy is that the reliable level with the lowest resolution presents an “optimal” trade-off be-tween speckle reduction and detail preservation for the considered pixel. In greater detail, each scale-dependent image in the set XMS is analyzed independently in order to discriminate between the two classes cω and uω associated with change and no-change classes, respectively. The desired partitioning for the generic scale n can be obtained by thresholding LR

nX . It is worth noting that since the threshold value is scale dependent, given the set of im-ages 0 1

MS LR LR LR−= n NX X XX , ..., , ..., , we should determine (either

automatically [9],[33],[34] or manually) a set of threshold values 1−= Nn0 T ..., ,T..., ,T T . Regardless of the threshold-selection

method adopted, a sequence of change-detection maps 0 1

MS−= n NM M MM , ..., , ..., is obtained from the images in

0 1MS LR LR LR

−= n NX X XX , ..., , ..., . A generic pixel M(i,j) in the final change-detection map M is assigned to the class it belongs to in the map MS( )∈ijSM M computed at its optimal selected scale Sij, i.e.,

( ) ( ) uc,k ,ωji,Mωji,M kk =∈⇔∈ withijS and

1−≤ NSij (4.8)

The accuracy of the resulting change-detection map depends both on the accuracy of the maps in the multiresolution sequence and on the effectiveness of the procedure adopted to select the optimal resolution level. Both aspects are affected by the amount of resid-ual noise in LR

ijSX . To make the decision process more robust to noise, we pro-

pose an alternative approach that considers all reliable change-detection maps (with respect to the scale of the pixel) and applies a fusion at decision level rule (FDL-ARS). For each pixel, the set

0MSM ( , ) ( , ) ( , ) ( , )= ijSR nM M Mi j i j i j i j , ..., , ..., of the related reliable


139

multiresolution labels is considered. Each label M n in MSMR can be seen as a decision of a member of a pool of experts. Thus the pixel is assigned to the class that obtains the highest number of votes. In actual fact, the final change-detection map M is com-puted by applying at each spatial position a majority voting rule to the set MSM ( )R i, j . The class that receives the largest number of votes

kV ( )ω i, j , k=c,u, represents the final decision for the con-

sidered input pattern, i.e.,

( ) ( )argmax ω

ω ∈ Ω∈ω ⇔ω = h

h

k kM i, j V i, j , k=c,u (4.9)

The main disadvantage of the FDL-ARS strategy is that it only considers the final classification of each pixel at different reliable scales. A better exploitation of the information in the multiresolu-tion sequence XMS can be obtained by considering a fusion at fea-ture level strategy (FFL-ARS). In order to accomplish the fusion process at different scales, a new set of images

0 -1,...., ,...,MS MS MS MS=

R n NX X XX is computed by averaging all possible se-

quential combinations of images in XMS, i.e.,

∑=+

=n

h

hLR

nMS

n 011 XX , with n=0,1,...,N-1 (4.10)

where the superscript n identifies the highest scale included in the average operation. When low values of n are considered, the im-age MS

nX contains a large amount both of geometrical details and of speckle components, whereas when n increases, the image

MSnX contains a smaller amount both of geometrical details and of

speckle components. A pixel in position (i,j) is assigned to the class obtained by applying a standard thresholding procedure to the image MS

ijSX , Sij ≤ N-1, computed by averaging on the reliable scales selected for that spatial position, i.e.,

140

( ) ( )( )

MS

MS

,

⎧⎪∈⎨⎪⎩

≤

>

ij ij

ij ij

u

c

S S

S S

ω if i, jM i, j

ω if i, j

T

T

X

X (4.11)

where ijST is the decision threshold optimized (either automati-cally [9],[33],[34] or manually) for the considered image MS

ijSX . The latter strategy is expected to be capable of exploiting also the information component in the speckle, as it considers all the high frequencies in the decision process. It is worth noting that in the FFL-ARS strategy, as the information present at a given scale r is also contained in all images LR

nX with n<r, in the fusion process the components characterizing the optimal scale Sij (and the scales closer to the optimal one) are implicitly associated with greater weights than those associated with other considered levels. This seems reasonable, given the importance of these components for the analyzed spatial position.

4.4. Experimental Results

4.4.1. Data set description The data set used in the experiments is made up of two SAR

images acquired by the ERS-1 Synthetic Aperture Radar (SAR) sensor (C-band and VV-polarization) in the province of Sas-katchewan (Canada) before (1st July) and after (14th October) the 1995 fire season. The two considered images are characterized by a geometrical resolution of 25 [m] in both directions and by a nominal number of looks equal to 5. The selected test site (see in Figs. 4.3 (a) and (b)) is a section (350x350 pixels) of the entire available scene. A fire caused by a lightning event destroyed a large portion of the vegetation in the considered area between the two aforementioned dates.


141

(a) (b)

(c)

Figure 4.3 Images of the Saskatchewan province, Canada, used in the experiments. (a) Image acquired from the ERS-1 SAR sensor in July 1995, (b) image acquired from the ERS-1 SAR sensor in October 1995, (c) analyzed log-ratio image.

The two multilook intensity images were geocoded using the Digital Elevation Model (DEM) GTOPO30; no speckle reduction algorithms were applied to the images. The log-ratio image was computed from the above data according to (1).

In order to be able to make a quantitative evaluation of the ef-fectiveness of the proposed approach, a reference map was de-fined manually (see Fig. 4.5, (b)). To this end, we used the avail-able ground-truth information provided by the Canadian Forest

142

Service (CFS) and by the fire agencies of the individual Canadian provinces. Ground truth information is coded in a vector format and includes information about fires (e.g., geographical coordi-nates, final size, cause, etc.) occurred from 1981 to 1995 and greater than 200 hectares in final size. CFS ground truth was used for a rough localization of the burned areas as it shows a medium geometrical resolution. An accurate identification of the bounda-ries of the burned areas was obtained from a detailed visual analysis of the two original 5-look intensity images (Figs. 4.3 (a) and (b)), the ratio image and the log-ratio image (Fig. 4.3 (c)) car-ried out accurately in cooperation with experts in SAR-image in-terpretation. In particular, different color composites of the above-mentioned images were used to highlight all the portions of the changed areas in the best possible way. It is worth noting that no de-speckling or wavelet based analysis was applied to the images exploited to generate the reference map for this process to be as independent as possible of the methods adopted in the proposed change-detection technique. In generating the reference map, the irregularities of the edges of the burned areas were faithfully re-produced in order to be able to make an accurate assessment of the effectiveness of the proposed change-detection approach. At the end of the process, the obtained reference map contained 101219 unchanged pixels and 21281 changed pixels. Our goal was to obtain, with the proposed automatic technique, a change-detection map as similar as possible to the reference map obtained according to the aforementioned time consuming manual process driven with ground truth information and by experts in SAR im-age interpretation.

4.4.2. Results Several experiments were carried out to assess the effective-

ness of the proposed change-detection technique (which is based on scale-driven fusion strategies) with respect to classical meth-ods (which are based on thresholding of the log-ratio image).

In all trials involving image thresholding, the optimal thresh-old value was obtained according to a manual trial-and-error pro-


143

cedure. In greater detail, (among all possible values) we selected for each image the threshold value that showed the minimum overall error in the change-detection map compared to the refer-ence map. Thanks to this it was possible to evaluate the optimal performance of the proposed methodology without any bias due to human operator subjectivity or to the fact that the selection was made by an automatic thresholding algorithm. However, any type of automatic threshold-selection technique can be used with this technique (see [9] for more details about automatic thresholding of the log-ratio image). As the described procedure is independ-ently optimized for each considered image, it leads to different threshold values in each case. Performance assessment was ac-complished both quantitatively (in terms of overall errors, false and missed alarms) and qualitatively (according to a visual com-parison of the produced change-detection maps with reference data).

In order to apply the three proposed scale-driven fusion strate-gies (see section 4.3), the log-ratio image was first decomposed into seven resolution levels by applying the Daubechies-4 wave-let transform. Each computed approximation sub-band was used to construct different scales, i.e., 1 7

MS LR LR ,..., =X X X (see Fig. 4.4). In order to avoid distortions introduced along image borders by the SWT, the multiresolution wavelet decomposition was applied to a log-ratio image larger than 350×350 pixels in the accuracy assessment phase. It is worth noting that the full-resolution origi-nal image 0

LR LR( )≡X X was discarded from the analyzed set, since it was affected by a strong speckle noise. In particular, em-pirical experiments pointed out that when 0

LRX is used on this data set the accuracy of the proposed change-detection technique gets degraded. Nevertheless, in the general case, resolution level 0 can also be considered and should not be discarded a priori. A num-ber of trials were carried out to identify the optimal window size to compute the local coefficient of variation ( nLCV ) used to

144

(a) (b)

(c) (d)

(e) (f)


145

(g)

Figure 4.4 Multiscale image sequence obtained by applying the wavelet decomposi-tion procedure to the log-ratio image 1 7

LR LRMS = X XX , ..., .

detect detail pixels (e.g., border) at different resolution levels. The optimal size (i.e., the one that gives the minimum overall error) was selected for all analyzed strategies (see Table 4.1).

Table 4.1 summarizes the quantitative results obtained with the different fusion strategies proposed. As can be seen from the analysis of the overall error, the FFL-ARS strategy gave the low-est error, i.e. 5557 pixels, while the FDL-ARS strategy gave 6223, and the FDL-OSS strategy 7603 (the highest overall error). As expected, by including all the reliable scales in the fusion phase it was possible to improve the change-detection accuracy compared to a single “optimal” scale. In greater detail, the FFL-ARS strategy gave the lowest false and missed alarms, decreasing their values by 1610 and 436 pixels, respectively, compared to the FDL-OSS strategy. This is because on the one hand the FDL-OSS procedure is penalized both by the change-detection accuracy at a single resolution level (which is significantly affected by noise when fine scales are considered) and by residual errors in identi-fying the optimal scale of a given pixel; on the other hand, be-cause the use of the entire subset of reliable scales allows a better exploitation of the information at the highest resolution levels of

146

the multiresolution sequence in the change-detection process. It is worth noting that FFL-ARS outperformed FDL-ARS also in terms of false (2181 vs. 2695) and missed (3376 vs. 3528) alarms. This is mainly due to its ability to better handle all the informa-tion in the scale-dependent images before the decision process. This leads to a more accurate recognition of critical pixels (i.e., pixels that are very close to the boundary between the changed and unchanged classes on the log-ratio image), that exploit the joint consideration of all the information present at the different scales in the decision process. For a better understanding of the results achieved, we made a visual analysis of the obtained change-detection maps. Fig. 4.5 (a) shows the change-detection map obtained with the FFL-ARS strategy (which proved to be the most accurate), while Fig. 4.5 (b) is the reference map. As can be seen, the considered strategy produced a change-detection map that was very similar to the reference map. In particular, the change-detection map obtained with the proposed approach shows good properties both in terms of detail preservation and in terms of high accuracy in homogeneous areas.

TABLE 4.1

OVERALL ERROR, FALSE ALARMS, AND MISSED ALARMS (IN NUMBER OF PIXELS AND PERCENTAGE) RESULTING FROM THE PROPOSED ADAPTIVE SCALE-DRIVEN FUSION

APPROACHES.

False Alarms Missed Alarms Overall Errors Fusion strategy Pixels % Pixels % Pixels %

LCV window size

FDL-OSS 3791 3.75% 3812 17.91% 7603 6.21% 23×23 FDL-ARS 2695 2.66% 3528 16.58% 6223 5.08% 7×7 FFL-ARS 2181 2.15% 3376 15.86% 5557 4.54% 5×5

In order to assess the effectiveness of the proposed scale-driven change-detection approach, the results obtained with the FFL-ARS strategy were compared with those obtained with a classical change-detection algorithm. In particular, we computed a change-detection map by an optimal (in the sense of minimum error) thresholding of the log-ratio image obtained after despeckling with the adaptive enhanced Lee filter [32]. The enhanced Lee fil-ter was applied to the two original images (since a multiplicative


147

speckle model is required). Several trials were carried out while varying the window size, in order to find the value that leads to the minimum overall error. The best result for the considered test site (see Table 4.2) was obtained with a 7×7 window size. The thresholding operation gave an overall error of 8053 pixels. This value is significantly higher than the overall error obtained with the FFL-ARS strategy (i.e., 5557). In addition the proposed scale-driven fusion technique also decreased both the false (2181 vs. 3725) and the missed alarms (3376 vs. 4328) compared to the considered classical procedure. From a visual analysis of Fig. 4.6 (a) and Figs. 4.5 (a) and (b), it is clear that the change-detection map obtained after the Lee-based despeckling procedure signifi-cantly reduces the geometrical detail content in the final change-detection map compared to that obtained with the FFL-ARS ap-proach. This is mainly due to the use of the filter, which not only results in a significant smoothing of the images but also strongly reduces the information component present in the speckle. Similar results and considerations both from a quantitative and qualitative point of view were obtained by filtering the image with the Gamma MAP filter (compare Tables 4.1 and 4.2).

(a) (b)

Figure 4.5 (a) Change-detection map obtained for the considered data set using the FFL-ARS strategy on all reliable scales; (b) reference map of the changed area used in the experiment.

148

To better understand the extent of the validity of the proposed scale-driven method, we also analyzed the effectiveness of classi-cal thresholding of the log-ratio image after denoising with a re-cently proposed more advanced despeckling procedure. In par-ticular, we investigated a discrete wavelet transform (DWT) based denoising [27],[35] technique (not used previously in change-detection problems). This technique achieves noise reduc-tion in three steps: i) image decomposition (DWT); ii) threshold-ing of wavelet coefficients; and iii) image reconstruction by in-verse wavelet transformation (IDWT) [27],[35]. It is worth noting that also this procedure is based on the multiscale decomposition of the images. We can therefore better evaluate the effectiveness of the scale-driven procedure in exploiting the multiscale infor-mation obtained with the DWT decomposition. Wavelet based denoising was applied to the log-ratio image since an additive speckle model is required. Several trials were carried out varying the wavelet-coefficient denoising algorithm while keeping the type of wavelet fixed, i.e., Daubechies-4 (the same used for multi-level decomposition). The best result (see Table 4.2) was obtained by a soft thresholding of the detail coefficients according to the universal threshold ( )JIlog2σT 2 ⋅= , where I×J is the image size and 2σ is the estimated noise variance [35]. The soft thresholding procedure sets detail coefficients that fall between T and -T to zero, and shrinks the module of coefficients that fall out of this interval by a factor T. The noise variance estimation was per-formed by computing the variance of the diagonal-detail sub-band at the first decomposition level. Given the above thresholding ap-proach, we selected the number of decomposition levels that re-sulted in the minimum change-detection overall error. This mini-mum was reached with a six-level wavelet decomposition. However, also in this case the obtained error (i.e., 7012 pixels) was significantly higher than the overall error obtained with the proposed approach based on the FFL-ARS strategy (i.e., 5557 pixels). Moreover, the presented method performed better also in terms of false and missed alarms, which were reduced from 4243


149

TABLE 4.2 OVERALL ERROR, FALSE ALARMS, AND MISSED ALARMS (IN NUMBER OF PIXELS AND

PERCENTAGE) RESULTING FROM CLASSICAL CHANGE-DETECTION APPROACHES.

False Alarms Missed Alarms Total Errors Applied filtering technique Pixels % Pixels % Pixels %

Filter win-dow size

Enhanced Lee filter 3725 3.68% 4328 20.34% 8053 6.57% 7x7

Gamma MAP filter 3511 3.47% 4539 21.33% 8050 6.57% 7x7

Wavelet denoising 2769 2.74% 4243 19.94% 7012 5.72% -

to 3376, and from 2769 to 2181, respectively (see Tables 4.1 and II). By analyzing Fig. 4.6 (b), 4.5 (a), and 4.5 (b), it can be seen that the change-detection map obtained by thresholding the log-ratio image after applying the DWT-based denoising algorithm preserves geometrical information well. Nevertheless, on observ-ing the map in greater detail, it can be concluded qualitatively that the spatial fidelity obtained with this procedure is lower than that obtained with the proposed approach. This is confirmed, for ex-ample, when we look at the right part of the burned area (circles

(a) (b)

Figure 4.6 Change-detection maps obtained for the considered data set by optimal

manual thresholding of the log-ratio image after the despeckling with (a) the Lee-enhanced filter, (b) the DWT-based technique.

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in Fig. 4.6 (b)), where some highly irregular areas saved from the fire are properly modeled by the proposed technique, but smoothed out by the procedure based on DWT denoising. This confirms the quantitative results and thus the effectiveness of the proposed approach in exploiting information from multilevel image decomposition

It is worth noting that the improvement in performance shown by the proposed approach was obtained without any additional computational burden compared to the thresholding procedure af-ter wavelet denoising. In particular, both methods require analysis and synthesis steps (though for different purposes). The main dif-ference between the two considered techniques is the scale-driven combination step, which does not increase the computational time required by the thresholding of detail coefficients according to the standard wavelet-based denoising procedure.

4.5. Discussion and conclusion In this chapter, a novel adaptive scale-driven approach to

change detection in multitemporal SAR images has been pro-posed. Unlike classical methods, this approach exploits informa-tion at different scales (obtained by a wavelet-based decomposi-tion of the log-ratio image) in order to improve the accuracy and geometric fidelity of the change-detection map.

Three different fusion strategies that exploit the subset of reli-able scales for each pixel have been proposed and tested: i) fusion at the decision level by an optimal scale selection (FDL-OSS); ii) fusion at the decision level of all reliable scales (FDL-ARS); and iii) fusion at the feature level of all reliable scales (FFL-ARS). As expected, a comparison among these strategies showed that fusion at the feature level led to better results than the other two proce-dures, in terms both of geometrical detail preservation and accu-racy in homogeneous areas. This is due to a better intrinsic capa-bility of this technique to exploit the information present in all the reliable scales for the analyzed spatial position, including the amount of information present in the speckle.

Experimental results confirmed the effectiveness of the pro-posed scale-driven approach with the FFL-ARS strategy on the


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considered data set. This approach outperformed a classical change-detection technique based on the thresholding of the log-ratio image after a proper despeckling based on the application of the enhanced Lee filter and also of the Gamma filter. In particu-lar, change detection after despeckling resulted in a higher overall error, more false alarms and missed alarms, and significantly lower geometrical fidelity. In order to further assess the validity of the proposed approach, the standard technique based on the thresholding of the log-ratio image was applied after a despeck-ling phase applied according to an advanced DWT-based denois-ing procedure (which has not been used previously in change-detection problems). The obtained results suggest that the pro-posed approach performs slightly better in terms of spatial fidelity and significantly increases the overall accuracy of the change-detection map. This confirms that on the considered data set and for solving change-detection problems, the scale-driven fusion strategy exploits the multiscale decomposition better than stan-dard denoising methods.

As a final remark, it is worth noting that all experimental re-sults were carried out applying an optimal manual trial-and-error threshold selection procedure, in order to avoid any bias related to the selected automatic procedure in assessing the effectiveness of both the proposed and standard techniques. Nevertheless, this step can be performed adopting automatic thresholding procedures [9],[36].

Future developments of this work are related to the application of the proposed adaptive scale-driven approach to change detec-tion in very high resolution SAR images. Furthermore, we plan to extend the use of the scale-driven technique to change detection in multiband and fully polarimetric SAR data.

Acknowledgment This work was supported by the Italian Ministry of Education,

University and Research. The authors are grateful to Dr. Fran-cesco Holecz and Dr. Paolo Pasquali (SARMAP s.a.®, Cascine di

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Barico, CH-6989 Purasca, Switzerland) for providing images of Canada and advice about ground truth.

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Chapter 5

5. A Multilevel Parcel-Based Approach to Change Detection in Very High Resolu-tion Multitemporal Images

In this chapter, we propose a novel parcel-based context-sensitive technique for unsupervised change detection in very high geometrical resolution images. In order to improve pixel-based change-detection performances, we propose to exploit the spatial-context information in the framework of a multilevel ap-proach. The proposed technique models the scene (and hence the changes occurred in the multitemporal data) at different resolu-tion levels, by defining multitemporal and multilevel “parcels” (i.e. small homogeneous regions shared by both original images). Change detection is achieved by applying a specific comparison algorithm to each pixel of the considered images, which properly analyzes the multilevel and multitemporal parcel-based context of the investigated spatial position. The adaptive nature of multitemporal parcels and their multilevel representation allow to properly model complex objects in the investigated scene as well as borders of the changed areas and change details. Experimen-tal results confirm the effectiveness of the proposed approach.

(This chapter was published in the Proceeding of the IEEE

2005 International Geoscience and Remote Sensing Symposium, (IGARSS '05), Seoul, Korea, 25-29 July, 2005. Co-author: Lorenzo Bruzzone)

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5.1. Introduction In the literature [1],[2] many techniques have been proposed

for change detection in medium resolution multispectral data. Most of them produce reliable change-detection maps by analyz-ing pixel-by-pixel two images acquired on the same area at differ-ent times. However, the availability of very high resolution data (e.g., images acquired by Quikbird and Ikonos satellites) results in a new set of possible applications, which require the generation of change-detection maps characterized by both a high geometri-cal precision and the capability of properly modeling the complex objects/areas present in the scene. Nonetheless, classical change-detection techniques result ineffective on very high resolution im-ages, as they often assume spatial independence among pixels, which is not a reasonable approximation in high geometrical reso-lution data. For this reason, it is necessary to develop advanced context-sensitive change-detection methods capable to properly exploit the specific properties of very high resolution images [3].

In order to address the above limitations of the standard tech-niques, in this chapter we present a novel unsupervised approach to change detection in very high resolution multitemporal images. The proposed approach exploits a multilevel context-based image modeling of multitemporal acquisitions aimed at representing each changed area at the proper resolution level. In particular, the scene (and hence the changes occurred in the multitemporal data) is modeled at different resolution levels, by defining multilevel and multitemporal “parcels”. A multitemporal parcel represents the local adaptive neighborhood of a pixel, and has the property to be homogeneous on both temporal images considered. It can be obtained according to the fusion of segmentation results obtained separately on the two images, by imposing an additional con-straint on the homogeneity in the temporal domain. Change detec-tion is achieved by applying a specific comparison algorithm to the considered images. In particular, comparison is performed in-volving feature vectors which properly represent the multilevel and multitemporal parcel-based context information of the inves-tigated spatial position. The adaptive nature of multitemporal par-

CHAPTER 5 - A MULTILEVEL PARCEL-BASED APPROACH TO CHANGE DETECTION IN VERY HIGH RESOLUTION MULTITEMPORAL IMAGES

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cels and their multiresolution representation allow to properly modeling complex objects in the investigated scene as well as borders of the changed areas and change-detection details. These properties allow one to obtain change-detection maps character-ized by high accuracy in both homogeneous and border areas as well as high fidelity in modeling the shapes of changed ob-jects/areas on the ground, thus outperforming standard pixel-based change-detection techniques.

The chapter is organized into four sections. The next section presents the proposed approach and focuses on its main steps: i.e. i) hierarchical multitemporal parcel generation; ii) multilevel par-cel-based feature extraction; and iii) feature comparison and change detection map generation. Preliminary experimental re-sults obtained on simulated very high resolution images are re-ported in section 5.3. Finally, conclusions are drawn in section 5.4.

5.2. Proposed Parcel-Based Change-Detection Tech-nique

Let us consider two co-registered very high-resolution multitem-poral and multispectral images, X1 and X2 (of size I×J), acquired over the same area at different times, t1 and t2, respectively. Let xh(i,j) be the spectral feature vector of the generic pixel at spatial position (i,j) at the acquisition date h (h=1,2). Let nc ωω=Ω , be the set of classes associated with changed and unchanged pixels, respectively. The proposed approach is composed of three main phases (see Fig. 5.1): i) generation of the hierarchical multitempo-ral parcel-based characterization of the spatial context of each pixel; ii) multilevel parcel-based feature extraction; iii) generation of the final change-detection map according to a proper context-based multilevel comparison algorithm. These phases are de-scribed in the following.

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Figure 5.1 General scheme of the proposed approach.

The rationale of the first phase is to adaptively generate a model of the spatial context of each pixel according to a multi-level strategy. Each resolution level is defined according to prede-fined spectral, spatial and temporal constraints. To adaptively characterize the spatial context of each pixel by taking into ac-count a hierarchical multiscale context representation, we propose to decompose the two images acquired over the area of interest from the pixel level to higher levels of representation of its spatial and temporal context. The hierarchical-multitemporal modeling allows one to capture and exploit the entire information present in the considered data set by working with adaptive multitemporal context/neighborhood systems at different levels. This task is based on the application of a segmentation technique (here a re-gion growing segmentation procedure has been considered) with a set of properly defined parameters, that take in account both spectral and spatial constraints. The segmentation process [4] is firstly independently applied to both the considered images in or-

X2 (time t2)

Hierarchical multitemporal parcel generation

Change-detection map

Multilevel parcel-based fea-ture extraction

Pixel … …lP

Feature comparison and change detection map generation

M1 M2

X1 (time t1)

LP


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der to obtain a multilevel representation of the spatial context of each pixel in the investigated scene. The multitemporal parcels are then obtained by imposing homogeneity in the temporal do-main at different scales according to a fusion of segmentation maps at corresponding scales. This procedure results in the defini-tion of a hierarchical parcel-based representation of the consid-ered scene. At each scale, pixels are characterized by adaptive multitemporal parcels of different sizes and shapes that at the same time satisfy homogeneity constraints in the spatial and tem-poral domains [2]. It is worth noting that, according to a specific constraint included in the algorithm, in the proposed method a multitemporal parcel related to a specific pixel at a given level is completely included in the multitemporal parcel of the same pixel at a higher level (i.e., a level with lower resolution).

The multilevel context-sensitive image characterization of both considered images is obtained according the following for-mal definition. Let Pl(X1,X2) be the set of parcels associated to X1 and X2 and let Ul(Z) be the homogeneity predicate in the spatial domain, where the superscript identifies the generic resolution level l (l=1,…,L). Varying the homogeneity predicate Ul accord-ing to l allows one defining the adaptive spatial context of the pixel at different scales. This homogeneity predicate is defined according to different spatial and spectral attributes at different levels (which should be properly selected on the basis of the spe-cific segmentation algorithm adopted). The multitemporal homo-geneity constraint is defined as a logical combination of the spa-tial homogeneity predicates applied to the two acquisitions. The parcel map at a generic level l is a partition Pl(X1,X2) in a set of N l regions l

sp (s = 1,2, …, N l) such that:

1. 1X==∪

lN

r

rX1

1 and 2X==∪

lN

r

rX1

2

where ( ) ( ) 2,1,,,, =∈= hpjijiX ls

rh hx ;

2. pixels in lsp (l=1, 2, ..., L) are connected;

3. ( ) ( ) ),...,2,1( AND 21lrlrl NrtrueXUtrueXU === ;

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4. ( ) ( ) falseXXUfalseXXU zrlzrl =∪=∪ 2211 OR , zr ≠ , where r

hX and zhX ( )2,1=h are adjacent.

Conditions (1) and (2) guarantee that all pixels in X1 and X2 at generic resolution level l are distributed into N l connected re-gions. Condition (3) determines the homogeneity properties of the parcels in both original images (i.e. the homogeneity in the tem-poral domain) and condition (4) expresses the maximality of each parcel. An additional constraint is added to guarantee a precise hierarchy between the context of a pixel defined at different lev-els, i.e.:

5. lk

N

1q

1lq pp

lk

==

−∪

where lkN is the number of objects at level l-1 that compose the

parcel lkp . Satisfying condition (5) means that the multitemporal

parcel of a pixel at level l-1 cannot be included in more than one parcel at level l. It is worth noting that level zero represents the pixel level, i.e. the pixel for which the context is hierarchical de-fined.

The second step of the proposed approach aims at characteriz-ing each pixel in X1 and X2 by exploiting the information included in the hierarchical parcel-based structure. In particular, the mean vectors (whose components are associated with the different spec-tral channels of the considered images) computed on the pixels included in the parcels at the considered resolution level l are ex-tracted for each acquisition date. Thus, for each pixel, we com-pute a multidimensional vector Mh(i, j) (h = 1,2) [which describes the pixels and, through the hierarchical tree, the spatial and tem-poral context (parcel) in which the pixel is included] defined as:

1M (i, j) (i, j), (i, j),..., (i, j),..., (i, j)= l Lh h h h hx μ μ μ (5.1)

where ),( jilhμ is the mean vector associated to the pixel at spatial

position (i,j) at time h and level l of the hierarchical tree. The feature vectors Mh(i, j) that characterize each pixel and

the related context information at different levels are given as in-


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put to the comparison and change-detection map generation mod-ule. According to the literature [1],[2] the comparison step is car-ried out extending the well known change vector analysis tech-nique (CVA) to our case. The output of the CVA is the so called difference image and contains information about possible changes occurred in the considered scene between the two acquisitions. As we apply the CVA directly to the multilevel context-sensitive fea-ture vectors M1(i,j) and M2(i,j), the obtained difference image contains information of changes at different resolution levels. The value MD(i,j) of the general pixel at spatial position (i,j) in the dif-ference image is given by:

2 1M ( ) ( ) ( )= −D i, j i, j i, jM M (5.2)

Finally, the change-detection map can be produced by threshold-ing the difference image according to either automatic or manual thresholding strategies [2].

5.3. Experimental Results In order to assess the effectiveness of the proposed approach,

different experiments were carried out on very high resolution multispectral and multitemporal remote-sensing images acquired by the Quikbird sensor on the Trentino area (Italy). In particular, we considered a portion 800×800 pixels of a multispectral image acquired in March 2004 (Fig. 5.2 (a)). Starting from this image (t1) a simulated data set has been generated. A second image (t2) has been derived by inserting different kinds of simulated changes at different resolution levels into the t1 image. Simulated changes have been accurately introduced in order to be as likely as possi-ble to real changes (see highlighted areas in Fig. 5.2). In particu-lar, buildings have been added or removed from the scene and land-cover variations have been simulated. Four versions of the simulated image at t2 were generated by adding different realiza-tions of zero-mean Gaussian noise to the aforementioned modi-fied image. Simulated images are distinguished by decreasing SNR values, i.e. 25, 20, 17, 15 dB respectively. Each pair

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(a)

(b)

Figure 5.2 (a) Original image (t1) and (b) simulated image for SNR = 17dB (t2). Cir-

cles highlight the simulated changes.


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composed of the t1 and one of the t2 images constitutes one differ-ent multitemporal data set (thus we obtain four different multitemporal data sets). The proposed multilevel context-sensitive change-detection technique has been applied to all data sets. In addition, for comparison, a standard pixel-based change-detection technique has been considered.

TABLE 5.1

CHANGE-DETECTION RESULTS (IN NUMBER OF PIXELS) OBTAINED BY USING THE STAN-DARD PIXEL-BASED APPROACH.

SNR [dB] False Alarms

Missed Alarms

Overall Error

25 52 1136 1188 20 87 2135 2222 17 299 2807 3106 15 293 3601 3894

Tables 5.1 and 5.2 summarize results obtained in the experi-

mental trials with the four different multitemporal data sets using the standard pixel-based change-detection approach and the pro-posed multilevel context-sensitive technique. As one can observe, for each selected SNR value, the proposed technique performs better then the standard one reducing the overall classification er-rors. In particular, as expected, for low values of SNR (i.e. 15 and 17 dB) both false and missed alarms decreased with the use of the multilevel spatial-context information. It is worth noting that the

TABLE 5.2 CHANGE-DETECTION RESULTS (IN NUMBER OF PIXELS) OBTAINED BY USING THE PRO-

POSED MULTILEVEL CONTEXT-SENSITIVE TECHNIQUE.

SNR [dB] False Alarms

Missed Alarms

Overall Error

25 54 1076 1130 20 155 1881 2036 17 252 2611 2863 15 189 3263 3452

performance improvement introduced by context modeling in-creases as the SNR becomes lower. In greater detail, with high SNR (i.e., 25 dB) we register a performance improvement of

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about 50 pixels, whereas when the SNR decreases to 15 dB the proposed technique reduces the overall errors of approximately 400 pixels.

Figure 5.3 Change-detection map obtained by applying the proposed multilevel

context-sensitive technique to the t2 image characterized by SNR = 17dB. Also qualitative results confirm the effectiveness of the pro-

posed technique. The change-detection maps obtained with the proposed methodology (Fig. 5.3) show higher accuracy in both homogeneous and border areas with respect to those obtained with the standard approach. This behavior is due to the proper ex-ploitation of the information at different resolution levels, which allows modeling each occurred change at the correct resolution level. Furthermore, the use of the context information permits to obtain high fidelity in modeling the shapes of changed ob-jects/areas on the ground and also to reduce noise effects (isolated false and missed alarms are removed) on the final change-detection map.


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5.4. Discussion and Conclusions In this chapter, a novel approach to change detection in very

high resolution multitemporal images has been presented. The approach is based on a parcel-based characterization of the con-sidered scene, which allows to adaptively modeling the context of each pixel according to a hierarchical multilevel representation. Such a representation considers both spatial and temporal homo-geneity constraints and is ruled by precise hierarchical relation-ships between each pixel in the multitemporal images and the re-gions that adaptively define the related context at different levels (scales). Each pixel is characterized by a feature vector, which is obtained computing the mean on the parcels at different scales. The final change-detection map is computed by extending the well known change vector analysis procedure to the multilevel parcel-based feature vectors computed on the two considered im-ages.

Quantitative and qualitative results on simulated very high resolution images point out that the proposed approach performs better than the standard pixel-based approach. In particular, when the SNR decreases the performance improvement introduced by the proposed method increases with respect to the standard pixel-based technique. This improvement can be observed both in the quantitative evaluation of the errors and in the qualitative analysis of the change-detection maps, which are characterized by high fidelity in both homogeneous and border regions.

As future developments of this work we plan: i) to extend the experimental analysis to the use of real multitemporal very high resolution images; ii) to better model the multilevel context-based information by means of more complex feature vectors (e.g., by characterizing the spatial context with the most reliable attributes for the specific level considered); iii) to introduce in the proposed methodology an adaptive level-selection module aimed at identi-fying for each considered spatial position the number of parcel levels that better represent the pixel behavior.

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References [1] C. Coppin, I. Jonckheere, K. Nackaerts, B. Muys, E. Lambin,

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[2] L. Bruzzone, D. Fernández Prieto, “Automatic analysis of the difference image for unsupervised change detection”, IEEE Trans. Geosci. Remote Sensing, Vol. 38, No. 3, 2000, pp.1170-1182.

[3] B. Desclee, P. Bogaert, P. Defourny, “Object-based method for automatic forest change detection”, Proc. IEEE Int. Geo-sci. Rem. Sens. Symp., IGARSS '04, Vol. 5, Anchorage, Alaska, 20-24 Sept. 2004, pp. 3383-3386.

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Chapter 6

6. Conclusions

In this thesis unsupervised change detection in multitemporal remote sensing images has been addressed by considering differ-ent issues related to this research topic. For each issue, a deep study of the literature was carried out and limitations of currently published methodologies were identified. Starting from this analysis, novel solutions were theoretically developed, imple-mented and applied to real multitemporal remote sensing data in order to verify their effectiveness. In greater detail, our attention was focused on the definition of automatic and unsupervised ap-proaches to change detection. The proposed approaches can be applied to different kinds of remote sensing images acquired by: i) passive sensors (i.e., multispectral optical images) and active sensors (i.e. SAR images); and ii) medium and very high geomet-rical resolution sensors.

Following the different properties of the aforementioned im-ages, we focused our attention on both single-scale (single-level) and multiscale (multilevel) approaches to change detection. In the following, the main conclusions on these techniques are given.

With respect to single-scale change-detection techniques, two novel contributions were proposed: i) a formal theoretical frame-work for CVA in the polar domain; and ii) a change-detection technique suitable for handling large-size remote sensing images.

The first contribution concerns the definition of a framework for describing the properties of spectral change vectors obtained applying the CVA technique. A theoretical analysis was carried out that resulted in a set of formal definitions and allowed to de-

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rive the statistical distributions of changed and unchanged pixels in the polar domain. The proposed framework represents an im-portant reference and a useful support for the development of novel change-detection techniques based on change vector analy-sis and for driving the pre-processing to be applied to multitem-poral data. Furthermore, it points out the importance of the direc-tion information, which can be exploited for: a) automatically identifying different kinds of changes; b) reducing the effects of the registration noise in the Polar domain; c) optimizing the pro-cedure for threshold selection in the magnitude domain.

Concerning the problem of change detection in large-size im-ages, it represents a topic of great importance in operational re-mote sensing as in many applications wide areas should be ana-lyzed where only a small amount of changes may be occurred. The approach proposed in the thesis automatically splits the con-sidered difference (or ratio) image in a set of sub-images of user defined size, which are sorted out according to their probability to contain a significant amount of changed pixels. The sub-images having the highest probabilities to contain changed pixels are ana-lyzed in order to derive the decision threshold for generating the change-detection map. To this purpose, two different techniques have been proposed: i) an independent split analysis strategy; and ii) a joint split analysis strategy. The joint split analysis strategy has the advantage to jointly model the distributions of changed and unchanged classes by considering different portions of the images, and the disadvantage that, if the distributions of classes are slightly different in different splits, the decision threshold de-rived according to model-based thresholding approaches may be not accurate. The independent split analysis strategy overcomes this drawback, properly applying the thresholding algorithm sepa-rately to each split. The proposed approach has been used for de-signing a system for damage assessment in relation to the tsunami occurred in December 2004 in Indonesia by using multitemporal SAR intensity images. On this data set the proposed split-based approach showed to be able to properly identify threshold values

CHAPTER 6 – CONCLUSIONS

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very close to the optimal ones obtained with a manual trial-and-error procedure.

Concerning multiscale change detection two main novel tech-niques were proposed: i) a scale-driven change detection method for multitemporal SAR images; and ii) a multilevel parcel-based change-detection algorithm for very high geometrical resolution images.

The problem of multilevel change detection in SAR images was addressed by presenting an approach based on a multiscale decomposition of the log-ratio image obtained by comparing multitemporal SAR images and on an adaptive fusion of the in-formation retrieved at different scales. Multiscale image represen-tation is obtained by means of a wavelet-based decomposition. The fusion step is performed by means of three different strate-gies that exploit the subset of reliable scales for each pixel: i) fu-sion at the decision level by an optimal scale selection; ii) fusion at the decision level of all reliable scales and iii) fusion at the fea-ture level of all reliable scales. The proposed technique shows two main advantages with respect to standard pixel-based tech-niques: i) it is robust to the presence of noisy components in ho-mogeneous areas; and ii) it is highly sensible to geometrical de-tails. The application of this technique to real multitemporal SAR data resulted in a change-detection map that is uniform in homo-geneous regions and that follows with a good fidelity the bounda-ries between change and no-change areas.

The problem of multilevel change detection in very high geo-metrical resolution images was addressed by presenting an ap-proach that exploits multiresolution spatial-context information. The approach is based on a parcel-based characterization of the considered scene, which allows to adaptively modeling the con-text of each pixel according to a hierarchical multilevel represen-tation. Such a representation considers both spatial and temporal homogeneity constraints and is ruled by precise hierarchical rela-tionships between each pixel in the multitemporal images and the regions that adaptively define the related context at different lev-els (scales). Each pixel is characterized by a feature vector, which

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is obtained computing the mean on the parcels at different scales. The final change-detection map is computed by extending the well known change vector analysis procedure to the multilevel parcel-based feature vectors computed on the two considered im-ages. The capability of parcels to adaptively model the complex shape of objects at different resolutions allowed to obtain change-detection maps where borders of the changed areas and change details are well represented. This improves the performance with respect to the standard pixel-based techniques.

All the change-detection techniques developed in this thesis proved to be effective with regard to their main objectives when applied to real remote sensing data. Each approach allowed im-proving the change-detection results obtained with standard methods presented in the literature. The reader can refer to the conclusions of each single chapter for further details on the per-formance and future developments of each single proposed method. From a general point of view, the research carried out in this thesis resulted in the definition of novel methodological and technical contributions in relation to some of the more critical problems present in unsupervised change detection literature. In addition, it resulted in the implementation of processing tools suitable to be adopted in real applications, as all approaches con-sidered involve low computational cost and can meet end-user re-quirements.

As future developments of the research work presented in this dissertation, the following directions will be considered: i) exten-sion of the proposed single-scale (single-level) approaches to a multiscale (multilevel) change-detection framework; and ii) opti-mization of the multiscale techniques in order to better exploit the multilevel spatial context-information.

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