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Unsupervised Segmentation of Synthetic Aperture Radar Sea Ice Imagery Using A NovelMarkov Random Field Model

David A. Clausi and Huawu DengDepartment of Systems Design Engineering

University of WaterlooWaterloo, Ontario, Canada N2L 3G1

Email: dclausi,h2deng@engmail.uwaterloo.caTelephone: (519) 888 - 4567 x2604 Fax: (519) 746-4791

Abstract— The operational segmentation of SAR sea iceimagery is a practical, challenging objective in the realmof applied pattern recognition. This research is in supportof operational activities at the Canadian Ice Services (CIS),a government agency that monitors all ice-infested regionsunder Canadian jurisdiction. This paper uses a fusion of toneand texture to segment SAR sea ice images in an unsupervisedmanner. A novel Markov random field (MRF) segmentationtechnique is employed and produces improved results overK-means and the traditional MRF implementation.

I. I NTRODUCTION

The research literature contains many examples of theapplication of pattern recognition techniques to remotesensing imagery. However, few of these examples directlysatisfy a defined operational need. This paper discussesan application of pattern recognition applied to remotesensing imagery with a demonstrated operational basis.This research is in support of the activities of the CanadianIce Service (CIS) (http://www.cis.ec.gc.ca/), a governmentagency that is responsible for the monitoring of all ice-infested waters of Canada.

Sea ice monitoring is critical for Canada, given its north-ern latitude coupled with extensive ocean-based coastalregions. These regions must be monitored to satisfy tacticalneeds with respect to ship navigation and ice breaker pri-orities and to satisfy environmental assessment needs withrespect to evaluating ice volumes, extents and types. Theonly means of producing timely information is through theuse of remotely sensed imagery. Also, given the uncertainweather conditions in coastal zone regions coupled with thedesire to capture imagery day or night, it is preferable touse synthetic aperture radar (SAR) for such an application.RADARSAT is a Canadian owned and operated satellitethat carries a SAR sensor. The sensor was designed withice reconnaissance as its primary target market. It usesa 5cm wavelength andHH polarization. Many differentmodes exist that encompass a variety of incidence anglesand pixel resolution. The SCANSAR mode is routinelyused at CIS at a resolution of50m. Operationally, this

data is2 × 2 block averaged which does not damage itsvisible interpretation.

An example of a SAR sea ice image and its correspond-ing ice map produced at CIS is presented in Fig. 1. Giventhat this SAR image is dimensioned to11, 152 × 17, 632(pixels), the details of the ice typing are not apparent.At full resolution, details are provided that allow the iceanalyst to create the ice map. The ice map indicates regionsof consistent ice types. An ”egg code” describes each ofthe regions identified in the SAR image. These egg codesare representative of a World Meteorological Organizationstandard (see http://www.natice.noaa.gov/egg.htm for de-tails) used in ice typing worldwide. The first row of theegg code represents the total ice concentration (in tenths),the second row represents the ice concentration for eachof the constitutive ice types, the third row indicates codesfor the particular ice type, and the fourth row representscodes for the floe size.

II. BACKGROUND

The objective of typical ice typing algorithms in the re-search literature is to identify solidified ice stages, namelyfirst year rough, first year smooth, and multiyear ice types.However, this is quite limited with respect to the true scopeof the operational requirements. For example, open watertakes on different forms depending on incidence angleand prevalent winds, making it very difficult to classify.Ice types in the early stages of development can mimiccharacteristics in later stages of development. SAR sea iceimagery is complex due to both sensor (eg. speckle noise,antenna gain patterns) and environmental (eg. ice typetransitions, prevailing weather conditions) characteristics.The ice analyst uses a variety of cues for determining theice types of a particular region, primarily tone, texture andfloe boundary shape.

The primary shortcoming of the ice maps as a sourceof information is that each egg code region only givesregional approximations of the ice concentrations. In otherwords, the ice map product does not provide information

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Fig. 1. RADARSAT SCANSAR sea ice image of the Gulf of St. Lawrence taken February 19, 1997 (dimensions 11,152× 17,632 pixels). Correspondingice map produced by Canadian Ice Services (CIS).

on a pixel-by-pixel basis. Given the vast geographical sizeof egg code regions, the concentrations do not providesufficient navigational information. For example, one mayknow that a particular egg code region has approximately20% multiyear ice, but there is no information to tell theship’s navigator where the multiyear is concentrated in aregion that typically extends for hundreds of kilometers.

The objective in this research is to use the egg codedata as input for performing pixel-by-pixel segmentationof thee associated SAR region. That is, for example, onewould know a priori the number of classes as well as thelabels for these classes. Although the egg codes provide anappropriate starting point for the segmentation, it is well-recognized that these offer only approximate estimates ofthe a priori probabilities.

III. SAR SEA ICE SEGMENTATION

A. Texture Features

Texture is a very important cue in the human visualsystem. Texture features have a demonstrated ability tosupport image segmentation in many areas and have alsodemonstrated potential for classifying sea ice types in SARimagery [1] [2] [3] [4]. Various texture methods are foundin the research literature to extract texture features [5].For SAR sea ice image classification, there is supportiveevidence that the gray level co-occurrence probability(GLCP) method [6] is an effective method to generateappropriate texture features [1] [2] [3] [7] [4].

Details of this algorithm are widely available anddescribed in the above references. With respect to thetesting performed here, we captured the probabilities [1] byquantizing to 64 grey levels, used a window size of7× 7,a pixel separation of 1, and standard orientations of 0, 45,90, and 135 degrees. Two statistics were applied to the

3probabilities to capture the texture features: contrast andentropy. This generates an 8-dimensional feature space.

Generally, the co-occurrence feature response can bemodelled by a Gaussian distribution function. Denote thefeature vector extracted from a random image (X = x) byF = f , whereF denotes a random variable andf is aninstance ofF . Y = y stands for a segmented result basedon the feature vectorF = f . That is,

p(fks |ys = m) =

1√2πσk

m2

exp

[− (fk

s − µkm)2

2σkm

2

], (1)

whereµkm andσk

m are the mean and standard deviation forthem-th class in thek-th feature component, andfk

s is thek-th feature component off at sites.

B. Classification

Standard pattern recognition methods for performingclustering or classification do not account for neighbourrelationships that are critical for solving a segmentationproblem. For example, the standard K-means [8] approachclusters based only on the feature space representation,completely ignoring the spatial interactions. That is, amodel that accounts for the high probability that adjacentpixels belong to the same class should be used.

A Markov random field (MRF) is recognized to be apowerful stochastic tool used to model the joint probabilitydistribution of the image pixels in terms of local spatialinteractions [9] [10] [11]. Using MRF models for imagesegmentation has a couple of advantages. First, the spatialrelationship can be seamlessly integrated into a segmen-tation procedure. Second, the MRF based segmentationmodel can be inferred in the Bayesian framework whichis able to utilize different types of image features.

IV. SEGMENTATION MODEL

According to the Bayes rule, the segmentation problemis formulated as:

P (Y = y|F = f) =p(F = f |Y = y)P (Y = y)

p(F = f). (2)

P (Y = y|F = f) is the posteriori probability ofY = yconditioned onF = f . p(F = f |Y = y) denotes theprobability distribution ofF = f conditioned onY = yand functions to fit the feature data, which is thus referredto as the feature modelling component.P (Y = y) is apriori probability ofY = y and is used to describe the labeldistribution of a segmented result only, which is normallyreferred to as the region labelling component.p(F = f) isthe probability distribution ofF = f . It will be assumedthat each component ofF = f be independent on the

other components with respect toY = y (conditionalindependence).

Suppose the energy form ofP (Y = y) is ER and thatof

∏Kk=1 [p(fk|Y = y)] is EF . A general energy formE

for P (Y = y|F = f) can be derived from the product ofP (Y = y) and

∏Kk=1 [p(fk|Y = y)] [10]:

E = ER + αEF , (3)

whereα is a weighting parameter used to determine howmuch ER and EF individually contribute to the entireenergyE. Its Gibbs form [11] isP (Y = y|F = f) =1Z exp

[− 1T E

], whereZ =

∑ΩY

exp[− 1

T E]

and ΩY isa set of all possible configurations ofY . Concrete formsfor each ofER andEF are required for practical segmenta-tion. Generally, for a segmentation task, the second orderpairwise MLL model is chosen and the potentials of allnon-pairwise cliques are defined to be zeros [11].

The intensity feature can be modelled using a Gammadistribution, allowing the energy formEF to be written as:

EF (x) =∑

s,Ys=m

l

µmxs − (l − 1) log xs + l log µm

(4)wherel is the number of looks. For the task of segmentingdifferent ice types, the GLCP features are used as the imagefeatures. Under the assumption of a Gaussian distribution,the energy formEF of the product of allp(fk

s |Ys = m)can be written as:

EF (f) =∑

s,Ys=m

K∑

k=1

[(fk

s − µkm)2

2(σkm)2

+ log(√

2πσkm)

],

(5)whereµm andσm represent the class mean and standarddeviation.

To implement the MRF model (Eq. (3)) requires estima-tion of three parameters:α (from Eq. (3)),µm, andσm (forall m). Traditionally, estimation ofµm and σm for eachclass requires training data. However, using an unsuper-vised environment, training data are not provided. Instead,the expectation-maximization (EM) algorithm [12] [13] isused to estimateµm andσm.

The difficulty is that there is no closed-form definitionfor α. A commonly used strategy [10] is to assign ana priori constant value by experience before executingthe EM algorithm. A root problem is that the traditionalMRF-based segmentation model is very easily trapped inlocal maxima due to the spatial homogeneity constraintimposed by the region labelling component. As a result,the feature modelling component might not be able to learnthe global parameters (i.e.µm and σm for each class).A new implementation scheme is proposed here to solvethis problem by making the weighting parameterα varyduring unsupervised segmentation. The introduction of the

4variable weighting parameter should not only enable thesegmentation procedure to learn the global parameters ofthe feature modelling component but also impose a spatialhomogeneity constraint on the label distribution (throughthe region labelling component). In this context, the param-eter may vary with respect to the annealing procedure. Thefollowing function is selected for the variable weightingparameterα:

α(t) = c1 ∗ γt + c2, 0 < γ < 1, (6)

whereγ, c1 and c2 are constants andt represents thetth

iteration. Experimentally, we have determined that settingγ = 0.95, c1 = 80 and c2 = 1/K (where K is thedimension of the feature space) are appropriate values fora variety of imagery. Using this function, the feature mod-elling component will first (whenα(t) is larger) dominatethe MRF model in order to learn its global parameters andthen (whenα(t) is close toc2) interact with the regionlabelling component to refine the segmented result. Thus,the energy of the MRF model can be rewritten as:

E = ER + α(t)EF (7)

V. EXPERIMENTAL RESULTS

The image shown in Fig. 2(a) is part of a C-band HHRADARSAT ScanSAR image (100m pixel spacing) in theBaffin Bay / Davis Strait region acquired on February 7,1998. This image consists of three types of sea ice: multi-year ice (bright floes), grey-white ice (running primarilyfrom top to bottom in the middle), and grey ice (observedon the left hand side and surrounding the multi-year floeson the right hand side). Visually, this image would be verydifficult to segment and even the manual segmentationsby trained human operators would have tremendous vari-ability (manual segmentation would also be a very timeconsuming exercise). Although tonal distinctions are notedvisually, the histogram is unimodal (not shown).

Segmentation using K-means (Fig. 2(b)) shows a seg-mentation that is not effective. Boundaries of unique re-gions are somewhat defined, however, the regions them-selves are “spotty” in their classification since local spatialinteractions are not accounted. Segmentation using theMRF model with constant weighting produces an inef-fective segmentation where the form of the ice regions isnot properly recognized (Fig. 2(c)). The only method thatproduces an acceptable segmentation is the MRF modelusing a variable weighting scheme (Fig. 2(d)). Here, themulti-year floes are consistent and the grey and grey-whiteregions show acceptable divisions. The application of theMRF model with the variable parameter using a fused(texture and intensity) is able to generate the most accurateresult.

VI. CONCLUSIONS

An unsupervised means of segmenting SAR sea iceegg code regions is proposed and successfully tested. Thevariable weighting MRF procedure is a more appropriatemethod for performing SAR sea ice segmentation thanusing K-means or the traditional MRF method.

ACKNOWLEDGMENTS

The authors are thankful to GEOIDE(http://www.geoide.ulaval.ca/) and CRYSYS (http://www.crysys.ca) for their financial support and CIS(http://www.cis.ec.gc.ca/) for providing the SARsea ice images (all RADARSAT imagesc©CSA –http://www.space.gc.ca).

REFERENCES

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(a) (b)

(c) (d)

Fig. 2. (a) Original RADARSAT image (631 × 595 pixels). Segmentation using (b) K-means, (c) MRF model with a constant weighting parameter(α = 8) and (d) MRF model with a variable weighting parameter (α(t) = 80 ∗ 0.95t + 1/9). All segmentations performed using intensity fused withGLCP texture features.