METRIC LEARNING FOR HYPERSPECTRAL IMAGE SEGMENTATION

Brian D. Bue1, David R. Thompson2, Martha S. Gilmore3, Rebecca Castano2

1 Rice University, Electrical and Computer Engineering, 6100 Main St., Houston, TX, 770062 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, 91109

3 Wesleyan University, Earth and Environmental Sciences, Weslayan Station, Middletown, CT 06459

ABSTRACT

We present a metric learning approach to improve the performanceof unsupervised hyperspectral image segmentation. Unsupervisedspatial segmentation can assist both user visualization and auto-matic recognition of surface features. Analysts can use spatially-continuous segments to decrease noise levels and/or localize featureboundaries. However, existing segmentation methods use task-agnostic measures of similarity. Here we learn task-specific sim-ilarity measures from training data, improving segment fidelity toclasses of interest. Multiclass Linear Discriminant Analysis pro-duces a linear transform that optimally separates a labeled set oftraining classes. This defines a distance metric that generalizesto new scenes, enabling graph-based segmentations that empha-sizes key spectral features. We describe tests based on data fromthe Compact Reconnaissance Imaging Spectrometer (CRISM) inwhich learned metrics improve segment homogeneity with respectto mineralogical classes.

Index Terms— Segmentation, Metric Learning, CRISM

1. HYPERSPECTRAL IMAGE SEGMENTATION

Unsupervised hyperspectral image segmentations can reveal spatialtrends that show the physical structure of the scene to an analyst.They highlight borders and reveal areas of homogeneity and change.Segmentations are independently helpful for object recognition, andassist with automated production of symbolic maps. Additionally,a good segmentation can dramatically reduce the number of effec-tive spectra in an image, enabling analyses that would otherwise becomputationally prohibitive. In particular, using an oversegmenta-tion of the image instead of individual pixels can reduce noise andpotentially improve the results of statistical post-analysis.

Recent work in hyperspectral image segmentation include thewatershed transform [1], Markov Random Fields [2], and the Felzen-szwalb graph segmentation algorithm [3]. Generally speaking, thesetechniques cluster pixels based on spatial proximity and a measure ofspectral similarity. Existing hyperspectral segmentation approachesgenerally use task-agnostic distance measures that treat all channelsequally or weight them based on global statistical properties of thedataset. Such metrics are often confused by noise, instrument arti-facts, or spectral variations that are irrelevant to semantic categoriesof interest. Learning a task-specific similarity metric from labeleddata can ameliorate this problem. Methods to learn such metricsinclude Information Theoretic Metric Learning (ITML) [4], Neigh-bourhood Components Analysis (NCA) [5], and variants of Gener-alized Relevance Learning Vector Quantization (GRLVQ) [6].

This work aims to improve unsupervised segmentations bylearning a task-relevant measure of spectral similarity from expert-labeled training data. We employ a multiclass Linear Discriminant

Analysis (LDA) based approach to learn this measure. Learnedmeasures produce segmentations that are not only are more visuallycohesive, but also quantitatively more accurate in separating knownmaterials into disjoint segments, in comparison to segmentationsproduced using unweighted metrics. We evaluate this technique bycomparing a set of expert-labeled mineral class maps to the segmen-tation maps produced by learned metrics, and provide a results on acase study focusing on several well-analyzed CRISM images [7]

2. METRIC LEARNING FOR HYPERSPECTRAL IMAGESEGMENTATION

We use the Felzenszwalb segmentation algorithm for its simplicityand computational efficiency [3, 8]. This is an agglomerative clus-tering approach that joins pixels into groups based on a pairwisedistance d(xi,xj) between adjacent pixels xi and xj . The seg-mentation algorithm represents the image as an 8-connected grid ofnodes; each node corresponds to a single pixel. All pixels are ini-tially treated as separate segments and iteratively joined into largergroups. We weight edges between the nodes according to d(xi,xj);previous studies have used spectral angle distance and Euclidean(Euc) distance. The maximum internal edge weight of a segmentS, Int(S), is defined as the largest edge weight in its minimum span-ning tree, MST(S).

Int(S) = maxxi,xj

d(xi,xj) ∀ xi ∈ S, xj ∈ S, (xi,xj) ∈ MST(S)

The smallest edge weight that joins two neighboring segments Sa

and Sb (i.e. the most similar pixel pair on their border) defines thecross-segment distance:

Dif(Sa, Sb) = minxi,xj

d(xi,xj) ∀ xi ∈ Sa,xj ∈ Sb, (xi,xj) ∈ E

Two adjacent segments are merged when the cross-segment distanceis larger than the minimum of both internal weights, weighted by aconstant k and inversely proportional to a segment’s area |S|.

MInt(Sa, Sb) = min

(Int(Sa) +

k

|Sa|, Int(Sb) +

k

|Sb|

)(1)

Larger k values cause a preference for larger segments, but is not aminimum segment size – smaller segments are allowed when thereis a sufficiently large difference between spatially neighboring seg-ments. However, in some cases, a minimum segment size is de-sirable, so as a final step, we merge small segments below a user-defined threshold ≥ 1 with their spectrally-closest neighbors.

We augment the segmentation algorithm with a task-specificMahalanobis distance metric learned from training data. The(squared) Mahalanobis distance between samples {xi,xj} ∈ RD

is: dM(xi,xj) = (xi − xj)TM(xi − xj), where M = ATA is a

D ×D linear transformation matrix. We seek to learn the matrix Awhich best separates a set of samples belonging to C classes. Ourapproach employs multiclass linear discriminant analysis (LDA) tomaximize the ratio of between-class vs. within-class separation S:

S = (αTΣbα)(αTΣwα)−1 (2)Here, Σb and Σw are the between and within class scatter ma-trices, respectively. By selecting the top C − 1 eigenvectors ofΣw

−1Σb, we define a projection into a C − 1 dimensional sub-space that captures variability between features with respect to train-ing data [9]. To prevent Equation 2 from becoming ill-posed due toan insufficient number of training samples, we regularize Σw by aparameter γLDA ∈ [0, 1] (selected via cross-validation) according to:Σw = (1− γ)Σw + γI, where I is the identity matrix.

We also learn a Mahalanobis distance using Information The-oretic Metric Learning [4]. ITML calculates the matrix M bymaximizing the relative entropy between a multivariate Gaussianparametrized by a set of training samples, and another multivariateGaussian belonging to a known, well-behaved Mahalanobis distancefunction. This maximization is constrained such that similar classesremain nearby one another and dissimilar classes remain far apart inthe space defined by the learned metric. The ITML algorithm takesa parameter γITML which controls the tradeoff between satisfyingsimilarity/dissimilarity constraints and maximizing the divergencebetween the Gaussians. We use the code provided by the authors[10] to learn the metric and select γITML.

3. EVALUATING SEGMENTATION RESULTS WITHRESPECT TO CLASS KNOWLEDGE

We attempt a superpixel segmentation in which the image is conser-vatively oversegmented; that is, we accept that single surface fea-tures may be split into multiple segments, but try to ensure that eachindividual segment - or superpixel - has homogeneous mineralogy[8]. We compare superpixels produced using each metric to a setof expert-labeled classes defined by a planetary geologist. The ge-ologist identified the primary constituents in each of the images westudy, along with the image pixels containing the purest examplesof each mineral, and defined class maps for the materials using theENVI spectral angle mapper (SAM) function [11]. As a final step,the geologist examines the spectral angles for each class and definethresholds to filter out ambiguous or mixed materials. We excludethese pixels from the following performance evaluation.

Because we seek an oversegmentation of an image, each expert-labeled class will likely be split into multiple segments. However,when we use a learned metric to segment each image, we expect theresulting segments to be better separated with respect to the train-ing classes – i.e., pixels in each segment are more likely to belongto a single training class, rather than multiple classes – in compari-son to metrics which do not account for class relationships. We de-fine two measures to quantify the degree to which the resulting seg-ments partition distinct mineralogical classes. The first measure isthe conditional entropy of the class map given the segmentation map,H(class|seg). H(class|seg) quantifies the remaining uncertainty fora random variable – in our case, the distribution of material classes –given the value of another random variable – the partitions producedby segmentation algorithm. In the case of a perfect segmentationof the classes, H(class|seg) will be zero, as the segmentation per-fectly reconstructs the class map. Thus, we prefer smaller valuesof H(class|seg). Our second measure of segmentation quality, the“impurity ratio,” is the ratio of “impure” vs. “pure” segments withrespect to the class map. A “pure” segment consists of pixels be-longing to a single class, whereas an “impure” segment consists of

pixels belonging to multiple classes. Because segment size can biasthis score, we scale the impurity ratio for each segment by its size inpixels. As with H(class|seg), smaller impurity ratios are better.

We evaluate the quality of segmentations produced by each met-ric learning algorithm by segmenting spatially contiguous halves ofeach image. We sample 100 spectra from each class from the firsthalf of the image (subsequently referred to as the “train” image), anduse these points to train each metric learning algorithm. We then seg-ment the train image and the remaining half of the image (the “test”image), using the metrics produced by LDA, ITML and the (base-line) Euclidean distance. Both the distance metric and the internalbias k (Equation 1) alter the size – and subsequently the quantity –of the resulting superpixels. To objectively compare results betweenseveral metrics, we must compare segmentations that produce a sim-ilar number of superpixels. To achieve this balance, we segment eachimage using a range of k values in [10−3, 101] and provide overallstatistics for segmentations produced by each metric on that range.We chose this range because the number of superpixels produced byeach metric followed a similar trend for all of the images we stud-ied. We focus on segmentations that produce 200-1250 superpixels,as segmentations with few superpixels tend to inadequately capturemorphological characteristics of the imagery we study, while seg-mentations with large quantities of superpixels are more sensitive tonoise and insignificant differences in spectra. We ignore superpix-els consisting of less than 50 pixels, as they tend to be unstable andnoisy with respect to the training classes. Ignoring these small su-perpixels is done for evaluation purposes only, as it allows for a moreconsistent evaluation of the resulting segmentation maps.

4. CASE STUDY: CRISM IMAGERYWe examine three well-studied CRISM scenes: 3e12, 3fb9, and 863e(omitting the frt0000 catalog prefix). We use the Brown CRISMAnalysis Toolkit [12] to perform radiometric correction and atmo-spheric calibration, and remove noisy bands in the extreme shortand long wavelengths, leaving a total of 231 bands in the in the[1.06, 2.58] µm range for analysis. Our final preprocessing stepis to normalize each spectrum by its Euclidean norm, to compen-sate for linear illumination effects [13]. Figure 1 shows the normal-ized mean spectra of the most pure, expert-labeled material samplesfor the classes in each image we consider. See [8] for further de-tails regarding these images and their constituent material classes.Figures 2 and 3 give the H(class|seg) and impurity ratios, vs. thenumber of segments using each metric. LDA outperforms both theEuclidean metric and ITML, sometimes dramatically (e.g. on im-ages 863e and 3fb9). The Euclidean metric performs worst, whichis not surprising since it is more susceptible to noise that a learnedmetric will often suppress. ITML yields similar performance tothe Euclidean distance for training images 3e12 and 3fb9, which islikely because the quantity of training samples is small for these twoimages – which consist of two and three material classes, respec-tively. On image 863e, with training consisting of 5 material classes,ITML approaches the performances of LDA. This is also reflectedin the summary statistics per-image for each segmentation given inTable 1. Note that the performance improvements on testing dataover training data on the 863e image are due to the fact that thetest image contains a smaller number of Kaolinite (670) and Mont-morillionite (93) pixels than in the training image, which are easilyconfused with other training classes (e.g., Kaolinite vs. FeMg Smec-tice). Figure 4 shows a set of resulting segmentation maps for whichthe Euclidean and LDA/ITML-learned metrics produced a compara-ble number of segments. Visually, the LDA-based segmentation pro-duces segments that better match the underlying morphology of the

3e12

3fb9

863e

# segments (train) # segments (test)

Fig. 2. H(class|seg) values for Euc (green), LDA (yellow) andITML (magenta) segmentations vs. number of segments on train-ing (left) and testing (right) images.

3e12

3fb9

# segments (test)# segments (train)

863e

Fig. 3. Impurity ratios for Euc (green), LDA (yellow) and ITML(magenta) segmentations vs. number of segments on training (left)and testing (right) images.

FeMg Smectite

Fig. 1. Normalized mean spectra of samples from most pure mate-rial classes in images 3e12, 3fb9 and 863e. The “neutral” class inimage 863e is a mostly featureless, dark material which is spectrallydissimilar from each of the other material species. Due to varyingatmospheric and illumination conditions at capture time, and differ-ences caused by atmospheric calibration, spectra belonging to thesame material species may not have identical spectral representa-tions in different images - e.g., the olivine spectra in image 3e12 vs.those in 3fb9.

image data. The Euclidean-based segmentation, and to a lesser de-gree, the ITML-based segmentation, both suffer from column strip-ing artifacts as noisy bands are not well compensated for using thesemetrics. This is also reflected in the per-class purity percentagesgiven in Table 2. Both learned metrics outperform the baseline, withLDA improving over the Euclidean metric for material classes FeMg

H(class|seg)Image Euc LDA ITML3e12 0.0169 / 0.0676 0.0148 / 0.0588 0.0191 / 0.06553fb9 0.0884 / 0.378 0.0497 / 0.242 0.0972 / 0.354863e 0.0473 / 0.00403 0.0184 / 0.000584 0.031 / 0.00228

Impurity/PurityImage Euc LDA ITML3e12 0.018 / 0.0619 0.0116 / 0.0573 0.02 / 0.05963fb9 0.0661 / 0.296 0.0368 / 0.195 0.0745 / 0.294863e 0.0684 / 0.032 0.0398 / 0.0124 0.0611 / 0.0266

Table 1. Average H(class|seg) and impurity ratios for each imageand similarity metric. Green and red fonts indicate the best and worstperforming metrics, respectively.

Smectite, Montmorillonite and Nontronite. ITML gives comparableperformance to LDA for most materials, but the gains are not as sig-nificant for the Montmorillionite and Nontronite classes.

Class (# pixels) Euc LDA ITMLFeMg Smectite (6443) 26 49 48Kaolinite (4051) 98 99 99Montmorillonite (10901) 11 31 17Nontronite (4753) 37 52 40Neutral Region (115225) 97 99 98Average 53 66 60

Table 2. Average pure pixels / segment for Euclidean, LDA andITML-based segmentations of image 863e (Figure 4). Best andworst average per-class accuracy given in green and red font, re-spectively.

5. DISCUSSION AND FUTURE WORK

The superior performance of LDA over ITML on all three of ourimages is somewhat surprising, considering the simplicity of the

ITML (890 segments)Euc (819 segments) LDA (825 segments)863e Class Map

Class (# pixels) Euc LDA ITMLFeMg Smectite (6443) 26 49 48Kaolinite (4051) 98 99 99Montmorillonite (10901) 11 31 17Nontronite (4753) 37 52 40Neutral Region (115225) 97 99 98Average 53 66 60

Table 2. Pure pixels / segment for Euclidean, LDA and ITML-basedsegmentations of image 863e shown in Figure 4. Best and worstaverage per-class accuracy given in green and red font, respectively.

is to normalize each spectrum by its Euclidean norm, to compensatefor linear illumination effects. Figure 1 shows the mean spectra ofthe most pure material samples for the classes within each imagewe consider in this work. See [1] for further details regarding theseimages and their constituent material classes.

Figures 2 and 3 give the H(class|segment) and purity scores, re-spectively, vs. the number of segments produced by each metric.LDA outperforms both the baseline Euclidean metric and ITML, oc-casionally quite dramatically (e.g. on images 863e and 3fb9). TheEuclidean metric performs worst, which is not surprising since it ismore susceptible to noise that a learned metric will often suppress.ITML yields about the same performance as the Euclidean distancefor train images 3e12 and 3fb9, which is likely because that these im-ages only contain two and three material classes, respectively. Thequantity of training samples is small for these two images, and ITMLinadequately determines which spectral bands are the most promi-nent. However, ITML still exhibits improved generalization perfor-mance on test data over the baseline Euclidean distance, indicatingthat some noise characteristics are potentially captured. This is alsoreflected in the summary statistics per-image for each segmentationmetric given in Table 1.

Figure 4 shows a set of resulting segmentation maps for whichthe Euclidean metric, and LDA/ITML-learned metrics produced acomparable number of segments. Visually, the LDA-based segmen-tation produces segments that better match the underlying morphol-ogy of the image data. The Euclidean-based segmentation, and to alesser degree, the ITML-based segmentation, both suffer from col-umn striping artifacts as noisy bands are not properly weighted bythese metrics.

Table 2 gives the percentages of pure segments for each materialspecies for the three segmentation metrics. Both learned metrics out-perform the baseline, with LDA improving over the Euclidean metricfor material classes FeMg Smectite, Montmorillonite and Nontron-ite. ITML gives comparable performance to LDA for most materi-als, but the gains are not as significant for the Montmorillionite andNontronite classes.

5. DISCUSSION AND FUTURE WORK

The superior performance of LDA over ITML is somewhat surpris-ing, considering the simplicity of the LDA projection in comparisonto the expectedly more robust optimization performed by ITML. Anissue with ITML (as observed by Parameswaran et al. in [11]) isthat the (global) metric is not optimized locally, which can causeproblems with overfitting to multi-modal data distributions. Con-versely, (regularized) LDA does not suffer (to the same degree) fromsuch overfitting issues. Additional training samples or alternativeregularization schemes would likely improve ITMLs generalizationcapabilities.

One avenue which we are currently exploring is the potentialfor learning class structure across multiple, related images. We havedeveloped an technique, Multi-Domain/Multi-Class LDA (MDMC-LDA) and a corresponding regularization scheme which allows LDAto exploit class structure local to an individual image while simulta-neously capturing class relationships common to other images withrelated classes [12].

Acknowledgements: We thank Brown University and the CRISMteam for the use of their CAT software package. Erzsebet Merenyiand Lukas Mandrake provided valuable advice and support. A por-tion of the work described in this manuscript was carried out at theJet Propulsion Laboratory with support from the NASA AMMOSMultimission Ground Systems and Services office. Copyright 2011California Institute of Technology. All Rights Reserved. U.S. gov-ernment support acknowledged.

6. REFERENCES

[1] D. R. Thompson, L. Mandrake, M.S. Gilmore, and R. Castano,“Superpixel Endmember Detection,” Geoscience and RemoteSensing, IEEE Transactions on, vol. 48, no. 11, pp. 4023–4033,2010.

[2] Y. Tarabalka, J. Chanussot, and J.A. Benediktsson, “Segmen-tation and classification of hyperspectral data using watershedtransformation,” Pattern Recognition, vol. 43, no. 7, pp. 2367–2379, 2010.

[3] A. Mohammadpour, O. Feron, and A. Mohammad-Djafari,“Bayesian segmentation of hyperspectral images,” BayesianInference and Maximum Entropy Methods in Science and En-gineering, vol. 735, pp. 541–548, 2004.

[4] Pedro F. Felzenszwalb and Daniel P. Huttenlocher, “Efficientgraph-based image segmentation,” Intl. J. Computer Vision,vol. 59:2, September 2004.

[5] S. Murchie et al., “CRISM (Compact Reconnaissance Imag-ing Spectrometer for Mars) on MRO (Mars ReconnaissanceOrbiter),” J. Geophys. Res, vol. 112, no. E05, 2007.

[6] R.A Fisher, “The statistical utilization of multiple measure-ments.,” Annals of Eugenics, vol. 8, pp. 376–386, 1938.

[7] J Davis, B Kulis, P Jain, S Sra, and I Dhillon, “Information-theoretic metric learning,” Proceedings of the 24th interna-tional conference on Machine learning, Jan 2007.

[8] Jason V. Davis, Brian Kulis, Prateek Jain, Suvrit Sra, and In-derjit S. Dhillon, Information Theoretic Metric Learning, UT,Austin, http://www.cs.utexas.edu/users/pjain/itml/.

[9] Research Systems Inc, ENVI 4.6 Users Guide, 2008, 1196 pp.

[10] F. Morgan, F. Seelos, and S. Murchie, “Cat tutorial,” in CRISMData Users Workshop, Lunar Planetary Sci. Conf., 2009.

[11] S Parameswaran and Kilian Q Weinberger, “Large marginmulti-task metric learning,” Proceedings of NIPS 2010, 2010.

[12] D. Hayden, S. Chien, D. Thompson, and R. Casta no, “Usingclustering and metric learning to improve science return in re-motely sensed imagery,” in In Proceedings, ACM Transactionson Intelligent Systems and Technology. 2011, ACM, (submit-ted).

RGB Composite

Fig. 4. Expert-labeled SAM class map for image 863e (left), RGB composite image (2nd from left), and the segmentation maps producedusing Euclidean distance (center), LDA (2nd from right), and ITML (right). We overlay each segmentation map on a single color-stretchedband (wavelength 1.25µm). The LDA-based segmentation is less susceptible to column striping artifacts, and better characterizes imagemorphology.

LDA projection in comparison to the more theoretically elegant op-timization performed by ITML. An issue with ITML (as observedby Parameswaran et al. in [14]) is that the (global) metric is not op-timized locally, which can cause problems with overfitting to multi-modal data distributions. Regularized LDA does not suffer (at least,to the same degree) from such overfitting issues. Also, it may be nec-essary to use more samples per class to learn the metric using ITML.We expect additional training samples or alternative regularizationschemes will likely yield improved results using ITML.

One avenue we are exploring is learning class structure acrossmultiple, related images. We have developed an technique, Multi-Domain/Multi-Class LDA (MDMC-LDA) and a correspondingregularization scheme which allows LDA to exploit class structurelocal to individual images while simultaneously capturing class re-lationships common to other images with similar classes [15].

Acknowledgements: We thank Brown University and the CRISMteam for the use of their CAT software package. Erzsebet Merenyiand Lukas Mandrake provided valuable advice and support. A por-tion of the work described in this manuscript was carried out at theJet Propulsion Laboratory with support from the NASA AMMOSMultimission Ground Systems and Services office. Copyright 2011California Institute of Technology. All Rights Reserved. U.S. gov-ernment support acknowledged.

6. REFERENCES

[1] Y. Tarabalka, J. Chanussot, and J.A. Benediktsson, “Segmen-tation and classification of hyperspectral data using watershedtransformation,” Pattern Recognition, vol. 43, no. 7, pp. 2367–2379, 2010.

[2] A. Mohammadpour, O. Feron, and A. Mohammad-Djafari,“Bayesian segmentation of hyperspectral images,” BayesianInference and Maximum Entropy Methods in Science and En-gineering, vol. 735, pp. 541–548, 2004.

[3] Pedro F. Felzenszwalb and Daniel P. Huttenlocher, “Efficientgraph-based image segmentation,” Intl. J. Computer Vision,vol. 59:2, September 2004.

[4] J Davis, B Kulis, P Jain, S Sra, and I Dhillon, “Information-theoretic metric learning,” Proceedings of the 24th interna-tional conference on Machine learning, Jan 2007.

[5] J Goldberger, S Roweis, G Hinton, and R Salakhutdinov,“Neighbourhood components analysis,” Advances in NeuralInformation Processing Systems, Jan 2005.

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[7] S. Murchie et al., “CRISM (Compact Reconnaissance Imag-ing Spectrometer for Mars) on MRO (Mars ReconnaissanceOrbiter),” J. Geophys. Res, vol. 112, no. E05, 2007.

[8] D. R. Thompson, L. Mandrake, M.S. Gilmore, and R. Castano,“Superpixel Endmember Detection,” Geoscience and RemoteSensing, IEEE Transactions on, vol. 48, no. 11, pp. 4023–4033,2010.

[9] R.A Fisher, “The statistical utilization of multiple measure-ments.,” Annals of Eugenics, vol. 8, pp. 376–386, 1938.

[10] Jason V. Davis, Brian Kulis, Prateek Jain, Suvrit Sra, and In-derjit S. Dhillon, Information Theoretic Metric Learning, UT,Austin, http://www.cs.utexas.edu/users/pjain/itml/.

[11] Research Systems Inc, ENVI 4.6 Users Guide, 2008, 1196 pp.

[12] F. Morgan, F. Seelos, and S. Murchie, “Cat tutorial,” in CRISMData Users Workshop, Lunar Planetary Sci. Conf., 2009.

[13] GW Pouch and DJ Campagna, “Hyperspherical direction co-sine transformation for separation of spectral and illuminationinformation in digital scanner data,” Photogrammetric Engi-neering and Remote Sensing, vol. 56, no. 4, pp. 475–479, 1990.

[14] S Parameswaran and KQ Weinberger, “Large margin multi-task metric learning,” Proceedings of NIPS 2010, 2010.

[15] David S. Hayden, Steve Chien, David R. Thompson, and Re-becca Castano, “Using onboard clustering to summarize re-motely sensed imagery,” IEEE Intelligent Systems, vol. 25, pp.86–91, 2010.