An Image-Based Endmember Bundle Extraction Algorithm Using ... · An Image-Based Endmember Bundle...

IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING, VOL. 8, NO. 6, JUNE 2015 2607

An Image-Based Endmember Bundle ExtractionAlgorithm Using Both Spatial and Spectral

InformationMingming Xu, Liangpei Zhang, Senior Member, IEEE, and Bo Du, Member, IEEE

Abstract—With the development of imaging technology, remotesensing images with a high spatial and spectral resolution havebecome available and have been used in various applicationssuch as the identification of materials and the estimation ofphysical parameters. Although many endmember extraction algo-rithms have been proposed for hyperspectral data sets whichextract/select the standard endmember spectrum for each exist-ing endmember class or scene component, there are still someproblems in endmember extraction which blur the discriminationbetween the different types of ground objects and lead to inac-curate endmember extraction. One problem is that the definitionof pure materials (or endmembers) can be subjective and appli-cation dependent. The other problem is that spectral variabilityis inevitable due to the different imaging conditions, especially ina hyperspectral image with a higher spatial resolution. In thispaper, to account for the spectral variability, each endmemberof a material is represented with a set or “bundle” of spec-tra, and an image-based endmember bundle extraction algorithmusing both spatial and spectral information is proposed. Thereare four steps in the proposed method of extracting endmem-ber bundles: 1) pixel purity index preprocessing; 2) homogeneityindex calculation; 3) region-based candidate endmember selec-tion; and 4) spectral clustering. Experiments with both syntheticand real hyperspectral data sets indicate that, by considering theendmember variability in the original hyperspectral data, the pro-posed method shows a significant improvement over the currentstate-of-the-art endmember bundle extraction methods.

Index Terms—Endmember bundles, endmember extraction,hyperspectral image, spectral variability.

I. INTRODUCTION

S PECTRAL mixture analysis (SMA) is a technique formodeling a reflectance spectrum as the combination of

a finite number of spectrally unique signatures of the pureground components, referred to as endmembers [1], [2]. Theappropriate extraction of endmembers is of great significance

Manuscript received May 22, 2014; revised October 28, 2014; acceptedNovember 10, 2014. Date of publication January 01, 2015; date of currentversion July 30, 2015. This work was supported in part by the National BasicResearch Program of China (973 Program) under Grant 2011CB707105 andGrant 2012CB719905, and in part by the National Natural Science Foundationof China under Grant 41431175 and Grant 61471274.

M. Xu and L. Zhang are with the Remote Sensing Group, StateKey Laboratory of Information Engineering in Surveying, Mapping, andRemote Sensing, Wuhan University, Wuhan 430079, China (e-mail: [email protected]; [email protected]).

B. Du is with the School of Computer Science, Wuhan University, Wuhan430072, China (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSTARS.2014.2373491

in hyperspectral image processing, providing the prior infor-mation of the pure materials for spectral unmixing [3], objectclassification [4], [5], and target detection [6]–[8]. In fact, end-members act as the basic unit to quantitatively explore the finespectral information of hyperspectral images.

In recent years, many different endmember extraction algo-rithms have been proposed [9]: 1) Pure-pixel-based algorithms:in the pure-pixel-based algorithms, it is assumed that there is atleast one pure pixel per endmember in the data. Representativealgorithms are the pixel purity index (PPI) [10], N-FINDR[11], the simplex growing algorithm (SGA) [12], vertex com-ponent analysis (VCA) [13], and iterative error analysis (IEA)[14]. 2) Nonpure pixel-based algorithms: these algorithms seekan endmember convex geometry with the minimum volume.They include iterative-constrained endmembers (ICE) [15],minimum volume-constrained nonnegative matrix factoriza-tion (MVC-NMF) [16], minimum volume simplex analysis(MVSA) [17], the convex analysis-based minimum volumeenclosing simplex (MVES) [18], and simplex identificationvia variable splitting and augmented Lagrangian (SISAL) [19].3) Statistical methods: the statistical methods perform betterin highly mixed images than the geometrical-based meth-ods, and are formulated as a statistical inference problem,usually adopting the Bayesian paradigm [2]; however, theyhave a higher computational complexity than the geometrical-based approaches. The statistical methods include independentcomponent analysis (ICA) [20] and the Bayesian approaches[21]–[23]. Recent studies have also constructed integratedframeworks in which both the spectral information and the spa-tial arrangement of the pixel vectors are taken into account[24], [25]. Typical methods include automatic morphologicalendmember extraction (AMEE) [26], spatial-spectral endmem-ber extraction (SSEE) [24], spatial preprocessing (SPP) usinga sliding window approach [27], region-based SPP (RBSPP)[25], and spatial-spectral preprocessing (SSPP) prior to end-member identification [28].

All the methods mentioned above are based on three differ-ent scenarios according to Bioucas-Dias et al. [2] (as shownin Fig. 1): 1) The data in Fig. 1(a) contain at least one purepixel per endmember; in other words, there is at least one spec-tral vector in each vertex of the data simplex. 2) The data inFig. 1(b) do not contain pure pixels, but contain enough spectralvectors on each facet. In this case, we can fit a minimum volumesimplex to the data. 3) The data in Fig. 1(c) are highly mixed,with no spectral vectors near the facets. In this case, minimum

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2608 IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING, VOL. 8, NO. 6, JUNE 2015

Fig. 1. Illustration of three mixed scenarios.

Fig. 2. Influence of spectral variability on unmixing.

volume algorithms would fail, and we need to resort to a sta-tistical framework. Strictly speaking, no pixel, however small itmight be, represents completely homogeneous characteristics.However, in fact, the definition of a pure material (or endmem-ber) can be subjective and application dependent [2]. In manyapplications, the actual situation may be as shown in Fig. 2.That is, it does not mean that no pure pixels exist, but that toomany pure pixels exist. As described in [29], the same imagecan contain different endmembers in different levels. In thecommonly used level for an image, objects of interest shouldoccupy a certain number of pixels, and it is almost impossi-ble that all the objects are less than one pixel, except for somespecial applications, such as subpixel target detection. This is abasic assumption in our algorithm. In the case shown in Fig. 2,spectral variability is inevitable under different conditions ofillumination and atmospheric conditions, due to the differentimaging conditions, especially in a hyperspectral image with ahigher spatial resolution [32]. Variation in endmember spectralsignatures is a fundamental issue in SMA as it leads to pooraccuracy in endmember fractions [30]–[32].

One approach to address spectral variability in a materialis the use of endmember sets (bundles) [33]. Bateson andCurtiss [34] proposed an approach for semiautomatic end-member selection from images. However, due to the spectralvariability, different users may generate different sets of end-members, given the same image. Bateson et al. [35] introducedthe concept of endmember bundles to incorporate the endmem-ber variability in SMA. Rather than using a single vector, anendmember is represented by a bundle of vectors in the spec-tral space. Roberts et al. [36] developed multiple endmemberSMA (MESMA) to map the subpixel proportion of Chaparralin the Santa Monica Mountains, California, where endmemberswere dynamically selected from a spectral library containing

Fig. 3. Illustration of the proposed method of endmember bundle extraction.

hundreds of reference endmembers. When the spectral signa-tures were allowed to vary from pixel to pixel, they found thatmost of the images could be simulated with a two-endmembermodel. Ju et al. [37] developed a mixture discriminant analysisalgorithm to infer land-cover fractions. They found that usingmixture discriminant analysis, which accounts for the intra-class variations, outperformed the traditional SMA in extractingsubpixel fractions of the vegetation types.

Endmember bundles extracted from an image can be appliedin many cases [38]–[42], but endmember bundle extractionalgorithms may not always be mature [43], [44]. Canham et al.[43] and Somers et al. [44] performed traditional endmem-ber extraction methods on a subset of the HSI, and performedspectral clustering as the final step. However, they did not con-sider the spatial information, which is also important for imageprocessing [26]–[28]. What is more, in these methods, end-members with high spectral contrast can be easily selected,whereas those with low spectral contrast are more problem-atic [24]. In this paper, an image-based endmember bundleextraction algorithm which takes the endmember variabilityand spatial information into account during the SMA is pro-posed. There are four steps in the proposed method of extractingendmember bundles (the flowchart is shown in Fig. 3). PPI pre-processing is used to reduce the computational complexity instep 2), which uses the spatial information. Region-based candi-date endmember selection can prevent the low spectral contrastmaterial being involved. The main innovative aspects include:1) the proposed method does not need a large number of randomprojections to find the representative PPI scores, and it does nothave the problem of the threshold T selection; 2) although thespatial information is considered, the computational complexity

XU et al.: IMAGE-BASED ENDMEMBER BUNDLE EXTRACTION ALGORITHM 2609

is far less than for the other methods which also considerthe spatial information; 3) the proposed method can performbetter in finding low spectral contrast material, which can beeasily ignored by the other methods; and 4) the number ofendmembers is not needed.

The rest of the paper is organized as follows. Section IIdescribes three state-of-the-art endmember bundle extractionalgorithms. The proposed algorithm is then presented inSection III. Section IV presents a comparison of the proposedmethod and the above-mentioned algorithms with both simu-lated and real data sets. Section V concludes the paper andintroduces the future research.

II. ENDMEMBER BUNDLE EXTRACTION

In this section, we introduce three state-of-the-art algorithmsthat can extract endmember bundles.

A. PPI Algorithm

The main idea behind the PPI algorithm is that endmembersshould be located at the spatial extremes of the data cloud inthe spectral space [10]. By projecting the data onto randomvectors, these extreme pixels will also have a higher proba-bility of appearing as extremes in the projections. The PPIalgorithm counts how many times a pixel has been identifiedas an extreme, and hence associates a score with each pixel.The pixels with the highest PPI scores are designated as end-members. While the PPI algorithm is simple to implement, itscomputational requirements are large. Since the data set is ofvery high dimensions, a large number of random projections arerequired to find the representative PPI scores. Furthermore, theendmember candidates returned by the PPI algorithm can differbetween runs due to the random nature of the projections, andoften show large correlations. The PPI algorithm then works inseveral steps.

1) Generate a set of K (a large number) random vectors{si}Ki=1 (skewers).

2) Project the data orthogonally onto these skewers, andfind the indices of the maximum and the minimum ofthese projections. Increase the corresponding PPI scoresby one, which count how many times a pixel is found asan extreme.

3) The endmember candidates are those points with a PPIscore larger than T (T is a threshold).

4) Postprocessing, e.g., clustering of endmembers orremoval of redundant endmembers. We consider clus-tering of endmembers in this paper, in order to achieveendmember bundles.

B. Spatially Adaptive Endmember Extraction (SAEE)

The spatially adaptive linear unmixing algorithm presentedhere uses local endmember selection, local abundance map gen-eration, and global endmember clustering (LLG) (as shown inFig. 4) [43]. In this paper, we focus on the endmember extrac-tion phase of the hyperspectral unmixing process. Therefore,

Fig. 4. Illustration of the LLG method.

Fig. 5. Illustration of endmember bundle extraction.

we just choose steps 1) and 3) in this method, termed the spa-tially adaptive endmember extraction (SAEE) method. In [43],the Max-D algorithm was used for endmember extraction andthe gram-matrix algorithm was used for dimensionality esti-mation, and these algorithms can be interchanged with otheralgorithms that perform the same task. Because the estimationof the number of endmembers and the identification of the spec-tra are performed on spatially local image tiles, a clusteringstep is required to determine which local endmembers shouldbe assigned to the same class. In this paper, we use the Max-Dand HySime algorithms.

C. Image-Based Endmember Bundle Extraction (EBE)

The basic idea of this endmember bundle extraction methodis to run the endmember extraction algorithm on randomlyselected subsets of the original hyperspectral image [44]. Afterendmembers are extracted from every subset, they are mergedto form sets of endmember spectra (bundles) from the differentground components. By using a k-means clustering algorithm,with the Euclidean distance as the similarity measure, the setsof spectra are then divided into separate endmember bundlesfor each ground component. An illustration of the approach ispresented in Fig. 5 [44].

III. SPATIAL AND SPECTRAL FEATURE-BASED

ENDMEMBER BUNDLE EXTRACTION

The proposed method consists of four steps: 1) PPI prepro-cessing; 2) homogeneity index (HI) calculation; 3) region-basedcandidate endmember selection; and 4) spectral clustering.

A. PPI Preprocessing

While the PPI algorithm is simple to implement, its com-putational burden is heavy. Since the data set has very highdimensions, a large number of random projections are requiredto find the representative PPI scores. The selection of thethreshold T poses another problem, since it is hard to fix Tbeforehand, and it can have a significant effect on the num-ber of endmembers returned by the algorithm. This step is a


coarse screening. In the PPI preprocessing: 1) the number ofrandom projections is less than in the general PPI algorithm and2) the threshold T is set to 0. The PPI preprocessing consists ofthree steps: 1) Generate a set of K (10 000 for simulation datawith four endmembers and 100 000 for real data with 10–15endmembers) random vectors. 2) Project the data orthogonallyonto this skewer, and find the indices of the maximum and theminimum of these projections. Increase the corresponding PPIscores by one, which count how many times a pixel is foundas an extreme. 3) The endmember candidates are those pointswith a PPI score larger than 0 (0 is a threshold). After the abovepreprocessing, a lot of candidate endmembers will be selected.

B. HI Calculation

As mentioned in these SSEE papers [26], [27], pure pixelsgenerally locate in spatially homogenous areas, whereas mixedpixels usually lie in transition areas or inhomogeneous areas.Based on this idea, the proposed method calculates the HI ofthe candidate endmembers from the spatial information. Wedefine the similarity of adjacent pixels as the HI. The HI isquantitatively measured by the similarity of the pixels insidethe neighborhoods, and several different similarity criterionscan be used [45], such as the spectral angle distance (SAD),Euclidean distance (ED) measure, spectral correlation mea-sure (SCM), and spectral information divergence (SID). In thispaper, we choose SID as the criterion. SID is a similarity cri-terion which assumes that x = (x1, . . . , xL) is a pixel withthe probability vector p = (p1, . . . , pL), and y = (y1, . . . , yL)is another pixel with the probability vector q = (q1, . . . , qL),

where pj = xj/L∑

l=1

xl and qj = yj/L∑

l=1

yl. The self-information

of x and y is defined as [42]

Il(x) = − log pl and Il(y) = − log ql. (1)

The SID is defined as [41]

SID(x,y) = D(x‖y) +D(y‖x) (2)

where

D(x‖y) =L∑

i=1

pl(Il(y)− Il(x)) =

L∑i=1

pl log

(plql

)(3)

and

D(y‖x) =L∑

i=1

ql(Il(x)− Il(y)) =L∑

i=1

ql log

(qlpl

). (4)

The HI is defined as

HI(i, j) = max(SID(x, xm,n)) (5)

where xm,n are the neighborhood pixels of pixel x.This step is to calculate the HI with a sliding neighborhood

window through the candidate endmembers. The size of thesliding window depends upon the sizes of the objects in theimage, and the degree of object crushing.

C. Region-Based Endmember Selection

A smaller HI means that it is more probable that the pixelsare pure ones. In this step, a threshold of the HI is needed forchoosing pure pixels. In different environments, or for differentmaterials, the degree of endmember variability will be differ-ent. For this reason, we partition the whole image, adaptivelychoose the different thresholds for different blocks, and obtainthe candidate endmember set with different thresholds in thedifferent blocks. The initial threshold is chosen according tothe statistical histogram of the HI values. We then adaptivelyadjust this threshold according to the proportion of the selectedcandidate endmembers. The size of a block is set based on theenvironmental complexity of the image. If the materials are dis-tributed widely and evenly, the size of the blocks can be a littlelarger, and vice versa. In our experiments, the percentage ofcandidate endmembers was no more than 2%–5% of the wholedata set, and this percentage could change depending on thespatial resolution of the hyperspectral image. Under the sameapplication requirements, the higher the spatial resolution, themore endmembers could be chosen. This step is summarized asfollows:

D. Spectral Clustering

Clustering aims at grouping the candidate endmembers in thefeature space. The clustering algorithm used in this paper is thek-means algorithm [46], and its goal is to determine a set ofc points, called centers, so as to minimize the distance fromeach pixel vector to its nearest center. Here, c is the numberof endmembers, which is estimated by HySime [47] using thefinal results. The initial centers are the most spectrally differ-ent pixels, which are determined with the orthogonal subspaceprojection (OSP) method [48]. The spectrum with the biggestnorm is chosen as the first initial center. U represents the ini-tial centers which have been determined. We then try to find therest of the initial centers which are the most different from thedetermined initial centers

s = argmax(P⊥U r) (6)

where P⊥U = I−UU#, U# =

(UTU

)−1UT is the pseudoin-

verse of U, and r represents the candidate endmembers.


At each stage, the algorithm moves every center point to thecentroid of the set of pixel vectors for which the center is thenearest neighbor according to the SID, and then updates theneighborhood by recomputing the SID from each pixel vectorto its nearest center. These steps are repeated until the algorithmconverges to a point that is a minimum for the distortion.

IV. EXPERIMENTS

This section describes the extensive experiments conductedon both simulated and real hyperspectral data, to allow a com-prehensive analysis of the proposed method compared withthree other endmember bundle extraction methods. Because allthe endmembers and the corresponding abundances in the sim-ulated image were known in advance, it was easy to preciselymanipulate the parameters.

The SAD metric, which is widely used in the study of hyper-spectral unmixing, was used to evaluate the unmixing results.The well-known SAD metric between the pixel a and b isgiven by

SAD(xa,xb) = cos−1

(xa · xb

‖xa‖ · ‖xb‖)

(7)

where ‖xa‖ and ‖xb‖ are the norms of xa and xb, respectively.The root-mean-square error (RMSE) was the other metric

used in the experiments. In the experiments on the syntheticdata set, the abundance maps were available, so the error inthe abundance maps of each class could be calculated. In theexperiments on the real data set, the RMSE between the orig-inal image and the reconstruction image was used since theabundance maps were not available.

In the following, we briefly describe the techniques selectedin this work for the comparative purposes, which consistedof PPI, SAEE, and an endmember bundle extraction method(hereinafter called EBE). In SAEE, the Max-D and HySimealgorithms were used in the experiments. In EBE, the endmem-ber extraction algorithm was OSP, which was proved to performwell in [44]. The whole image was divided into ten subsets inthe experiments, and the number of endmembers was set to ninein the real data experiments.

A. Synthetic Hyperspectral Image

In this experiment, we derived spectra from the DIRSIGspectral library [49], and used the spectral variations of fourmaterials (grass, muddy water, concrete, and asphalt) to gen-erate a simulated hyperspectral image of a size of 12 100,covering 398 bands. Each material in the DIRSIG library con-tains several hundred spectral variations of the same material.These variations were generated from experimentally measureddata and randomization of the experimentally measured sig-natures [43]. In the DIRSIG library, there are 300 variationsof grass, 300 variations of asphalt, 200 variations of muddywater, and 100 variations of concrete. Fig. 6 shows the spectraof the four materials. The synthetic image was generated usingthe linear mixture model (LMM), and by imposing the abun-dance sum-to-one constraint (ASC) on each simulated pixel.

Fig. 6. Four material spectra from the DIRSIG spectral library. (a) Muddy.(b) Grass. (c) Concrete. (d) Asphalt.

Fig. 7. Synthetic image with no noise (R: 0.4 µm, G: 0.5 µm, and B: 0.6 µm).

Fig. 8. RMSE matrix.

The synthetic image contains four groups of randomly selectedvariations of four spectra from the DIRSIG library. Each cir-cle in the synthetic image contains one of the four spectrawith an abundance value of 1.0, representing a pure signal. Theremaining image pixels are linear combinations of the four purespectra. In the middle parts of the image, the abundance of eachpixel is proportional to the distance from the four pure spectra.In the surrounding parts of the image, the abundance of eachpixel is randomly generated. The synthetic image with no noiseis shown in Fig. 7. White Gaussian noise was added into thesynthetic scenes with a 40-dB signal-to-noise ratio (SNR).

The following is an analysis of the spectra from the DIRSIGspectral library used in the experiments. We used the RMSE


Fig. 9. Statistical information for the RMSE matrix.

Fig. 10. HI histogram of the synthetic data set.

to indicate the spectral variability [50]. If spectrum A1 ismodeling spectrum B1, then the RMSE is defined as follows:

RMSE =

√(A1 − B1)T(A1 − B1)

M(8)

where M is the number of bands.In order to test the inter-class and intra-class similarity, we

used each spectrum in the DIRSIG spectral library to modelall the spectra in the DIRSIG spectral library, and we created a900× 900 RMSE matrix using (15) (as shown in Fig. 8). Theinter-class RMSE can be used to indicate the spectral variabil-ity within-class, and the intra-class RMSE can used to indicatethe confusion between classes. In other words, the statisticalcharacteristic of the RMSE can evaluate the likelihood of con-fusion between classes and the spectral variability within-class.Box charts for the RMSE matrix are shown in Fig. 9. FromFig. 9, we can see that: 1) the difference within-class is large,especially for grass and asphalt, and one single spectrum isnot enough to represent a single class; and 2) the differencebetween muddy water and asphalt is small, which increases thedifficulty of the image interpretation. These situations are com-mon in real images and lead to a poor accuracy in endmemberextraction and endmember fractions. Therefore, these spectraare very suitable for evaluation experiments.

Fig. 11. Endmember bundles of the proposed method.

Fig. 12. Statistical information of the SADs. (a) Muddy. (b) Grass.(c) Concrete. (d) Asphalt.

Fig. 13. RMSE between the abundance maps and reference abundance maps.

For the experiments, it should be pointed out that: 1) thethreshold in the PPI algorithm was set to the minimum valuethat could ensure that all four classes were involved in thespectra extracted; 2) the number of random vectors in the PPIalgorithm was far more than the number of random vectors in


Fig. 14. RMSE between the abundance maps and reference abundance maps,with different block sizes.

Fig. 15. RMSE between the abundance maps and reference abundance maps,with different thresholds.

Fig. 16. AVIRIS Cuprite subscene (50 bands).

the preprocessing, so that the PPI algorithm could obtain goodresults; and 3) in the proposed method, the block size was setto 55 and the threshold was set to 0.6, according to the HIhistogram (as shown in Fig. 10). Fig. 11 shows the extractedendmember bundles of the proposed method. The quantitativeevaluation metric was the SAD between each extracted end-member and the set of ground-truth spectral signatures in theDIRSIG spectral library. The lowest spectral angle representsthe best performance. Because a set of spectra (bundle) repre-sent one class in the experiments, a set of SADs were obtainedfor each class. The statistical information of the results is shownin Fig. 12. In Fig. 12, the numbers are the number of spectrafor each bundle. The RMSEs between the original images andreconstruction image are shown in Fig. 13. Iterative implemen-tation of SMA (ISMA) was used as the abundance estimationalgorithm in the experiments [51].

Fig. 17. HI histogram of the Cuprite data.

Fig. 18. USGS ground-truth map of Cuprite.

From the experimental results, we can see that: 1) althoughthe proposed method is based on the PPI algorithm, the SADsof the proposed method were much better than for the PPIalgorithm. Furthermore, the number of random vectors in theproposed method (10 000) was less than the number of ran-dom vectors in PPI (100 000). 2) The asphalt class was difficultto extract. Fig. 9 shows that the difference within the asphaltclass is large, and more spectra were needed to represent thisclass. However, the SAEE method could not extract the asphaltendmember, and the EBE method only extracted a single spec-trum for asphalt. In order to extract the asphalt endmember,the top 64 spectra with the highest scores were chosen for thePPI algorithm. 3) Some of the SADs for the proposed methodwere greater than those for EBE, but the number of endmem-bers extracted by the proposed method was more than that byEBE. 4) The proposed method extracted 99 spectra, and 90spectra were correct according to the reference abundance map.Although nine spectra were inaccurate, the maximum abun-dances of each of these extracted spectra were all greater than


Fig. 19. Endmember bundles of the proposed method (the reference spectra are represented by asterisks).

Fig. 20. Statistical information of the SADs.

0.8, and the larger the dominant abundances, the more difficultthey are to extract. 5) Fig. 12 shows that the SAD results ofthe PPI method were poor because of the pursuit of “extreme,”which results in it being easily affected by noise. Overall, theproposed method is effective in extracting endmember bun-dles. 6) Fig. 13 shows that the RMSE of the proposed methodbetween the abundance map and the reference abundance mapis the smallest among all the methods.

A sensitivity analysis of the results of the proposed algorithmto the two parameters, the block size and the threshold, is shownin Figs. 14 and 15. Fig. 14 shows the RMSE between the abun-dance maps and reference abundance maps, with different blocksizes, with the same threshold of 0.6. From Fig. 14, we can seethat when the block size is equal to 25, 35, and 55, the pro-posed method can obtain a better result. The ideal block sizeshould be a compromise. It should be large enough to obtainpure pixels in each of them, but too large blocks will lose theadvantage of the local analysis to extract variants of the end-members. Low spectral contrast material should be avoided in

Fig. 21. RMSE between the original images and reconstruction images.

a single block. Fig. 15 shows the RMSE between the abundancemaps and reference abundance maps, with different thresholds,with the same block size of 55. The HI histogram of the syn-thetic data is shown in Fig. 10. Even if the threshold is slightlyoverestimated, it would only result in more iterations becauseof the update rule t = 0.9 t, which means more computations.


Fig. 22. Abundance maps of the proposed approach (below) compared with the PPI method (above).

B. Real Hyperspectral Image

To evaluate the effectiveness of the endmember bundleextraction technique in a different analysis scenario, a realimage was used. This real data set covering the Cupritescene was captured by the Airborne Visible Infrared ImagingSpectrometer (AVIRIS) sensor in 1997, and is shown in Fig. 16.There are 50 bands in the data, with a size of 350× 400, cov-ering the wavelength range of 2.0−2.48µm. The data set hasbecome a popular benchmarking data set for algorithm eval-uation, due to the extensive ground-truth data available forthe scene from the USGS. Swayze and Clark [52] have alsoproduced a report about the ground truth of the area.

It should be pointed out that: 1) in the EBE method, thenumber of endmembers to be extracted was set to 12 accord-ing to previous studies [44]; 2) the threshold value in PPI wasset to 10, with 50 000 projections performed in total, while only10 000 projections were performed in the proposed method; and3) in the proposed method, the block size was set to 30 and thethreshold was set to 0.01, according to the HI histogram (asshown in Fig. 17). The reference spectra were from the USGSmineral spectral library. Based on Fig. 18, 11 kinds of classesand 78 spectra in the USGS library were chosen for quantitativeevaluation (the differences, such as between Alunite GDS83Na63 and Alunite GDS82 Na82, were ignored). Because thenumber of SADs is large, we just show the statistics of theSADs. Fig. 19 shows the spectra extracted by the proposedmethod and the reference spectra represented by asterisks (fromleft to right, from top to bottom: Alunite, Calcite, Halloysite,Jarosite, Kaolinite, Muscovite, Buddingtonite, and Unknownmaterial). Quantitative evaluations of the seven known mineralsare shown in Fig. 20. In Fig. 20, the numbers are the numberof spectra for each bundle. The RMSE between the originalimages and reconstruction images is shown in Fig. 21. ISMAwas used as the abundance estimation algorithm in the experi-ments [51]. Finally, Fig. 22 shows the abundance maps of theproposed approach compared with the PPI method, which wasthe second best method according to Fig. 21.

From the experimental results, we can see that the pro-posed method obtained the best results. The SAEE method onlyextracted five kinds of minerals, and the distribution of thesefive kinds of minerals was not balanced (more “Muscovite” andless other minerals). EBE and PPI could extract seven kindsof minerals. The proposed method could extract eight kinds of

minerals (as shown in Fig. 19). Fig. 20 shows that most of themean SADs of the proposed method were the smallest amongall the methods. From Fig. 21, we can see that the proposedmethod achieved the smallest RMSE.

V. CONCLUSION AND FUTURE RESEARCH

This paper has proposed an image-based endmember bundleextraction method using both spatial and spectral information.The proposed method consists of four steps: 1) PPI preprocess-ing; 2) HI calculation; 3) region-based candidate endmemberselection; and 4) spectral clustering.

The innovative aspects include: 1) we solve the problem ofrequiring a large number of random projections to find the rep-resentative PPI scores, and we also solve the problem of thethreshold T selection; 2) although the spatial information isconsidered, the computational complexity is far less than for theother methods which also consider spatial information; 3) theusual strategy of finding the extreme points can easily ignore thelow spectral contrast material (such as asphalt in the simulateddata experiments), and the proposed method can obtain betterresults under this situation; and 4) the number of endmembersis not needed.

The experimental results with synthetic and real hyperspec-tral data sets, in which the proposed method obtained balancedendmember bundles and the smallest errors, indicate that theproposed strategy shows significant improvements over thecurrent state-of-the-art endmember bundle extraction methods.Although the proposed method performs well, further study isneeded to determine the parameters (the threshold and the blocksize) automatically.

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Mingming Xu received B.S. degree in surveyingand mapping engineering from China University ofPetroleum, QingDao, China, in 2011. She is cur-rently pursuing the Ph.D. degree at the State KeyLaboratory of Information Engineering in Surveying,Mapping, and Remote Sensing (LIESMARS), WuhanUniversity, Wuhan, China.

Her research interests include spectral unmixinganalysis in hyperspectral remote sensing image.

Liangpei Zhang (M’06–SM’08) received the B.S.degree in physics from Hunan Normal University,Changsha, China, in 1982, the M.S. degree inoptics from Xi’an Institute of Optics and PrecisionMechanics, Chinese Academy of Sciences, Xi’an,China, in 1988, and the Ph.D. degree in photogram-metry and remote sensing from Wuhan University,Wuhan, China, in 1998.

He is currently the Head of the Remote SensingDivision, State Key Laboratory of InformationEngineering in Surveying, Mapping, and Remote

Sensing, Wuhan University. He is also a “Chang-Jiang Scholar” ChairProfessor appointed by the Ministry of Education of China. He is currentlya Principal Scientist for the China State Key Basic Research Project (2011–2016) appointed by the Ministry of National Science and Technology of Chinato lead the remote sensing program in China. He has authored/coauthored morethan 350 research papers. He is the holder of ten patents. His research interestsinclude hyperspectral remote sensing, high-resolution remote sensing, imageprocessing, and artificial intelligence.

Dr. Zhang is a Fellow of the IEE and an Executive Member (Board ofGovernors) of the China National Committee of International Geosphere–Biosphere Programme, Executive Member of the China Society of Imageand Graphics, etc. He regularly serves as a Co-Chair of the series SPIEConferences on Multispectral Image Processing and Pattern Recognition,Conference on Asia Remote Sensing, and many other conferences. Heedits several conference proceedings, issues, and geoinformatics sympo-siums. He also serves as an Associate Editor of the IEEE TRANSACTIONS

ON GEOSCIENCE AND REMOTE SENSING, INTERNATIONAL JOURNAL OF

AMBIENT COMPUTING AND INTELLIGENCE, INTERNATIONAL JOURNAL

OF IMAGE AND GRAPHICS, International Journal of Digital MultimediaBroadcasting, Journal of Geospatial Information Science, and Journal ofRemote Sensing.

Bo Du (M’10) received the B.S. degree from WuhanUniversity, Wuhan, China, in 2005, and the Ph.D.degree in photogrammetry and remote sensing fromthe State Key Laboratory of Information Engineeringin Surveying, Mapping, and Remote sensing, WuhanUniversity, Wuhan, China, in 2010.

He is currently an Associate Professor with theSchool of Computer Science, Wuhan University. Hisresearch interests include pattern recognition, hyper-spectral image processing, and signal processing.

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