Automated Identification of Endmembers from Hyperspectral Data Using Mathematical Morphology

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1 Automated Identfcaton of Endmembers from Hyperspectral Data Usng Mathematcal Morphology Antono Plaza a, Pablo Martínez a, J. Anthony Gualter b, Rosa M. Pérez a a GRNPS, Departamento de Informátca, Unversdad de Extremadura, Span. b Global Scence and echnology. NASA/Goddard Space Flght Center, Greenbelt, MD, U.S. ABSRAC One of the most wdely used approaches to analyze hyperspectral data s pxel unmxng, whch reles on the dentfcaton of the purest spectra from the data cube. Once these elements, known as endmembers, are extracted, several methods can be used to map ther spatal dstrbutons, assocatons and abundances. A large varety of methodologes have been recently proposed wth the purpose of extractng endmembers from hyperspectral data. Nevertheless, most of them only rely on the spectral response; spatal nformaton has not been fully exploted yet, specally n unsupervsed classfcaton. he ntegraton of both spatal and spectral nformaton s becomng more relevant as the sensors tend to ncrease ther spatal/spectral resoluton. Mathematcal morphology s a non-lnear mage analyss and pattern recognton technque that has proved to be especally well suted to segment mages wth rregular and complex shapes, but has rarely been appled to the classfcaton/segmentaton of multvarate remote sensng data. In ths paper we propose a completely automated method, based on mathematcal morphology, whch allows us to ntegrate spectral and spatal nformaton n the analyss of hyperspectral mages. he accuracy of the proposed algorthm s tested by ts applcaton to real hyperspectral data, and the results provded are compared to those found usng other exstng endmember extracton algorthms. Keywords: Remote Sensng, Hyperspectral Data, Spatal/Spectral Analyss, Endmember Extracton, Image Processng.. INRODUCION Durng the last several years, a great deal of new arborne, satellte and spaceborne sensors have been developed or mproved for hyperspectral remote sensng applcatons. In the near future, these sensors wll be producng a near contnual stream of hgh dmensonal data, resultng n a massve data volume that wll requre faster means for storage, transmsson and analyss. A very useful approach for hyperspectral data analyss and classfcaton has been spectral unmxng 3,4,5. he basc assumpton s that each pxel can be modeled as a lnear combnaton of component consttuents, known n the lterature as endmembers 6. If a set of ndvdual endmembers have been prevously dentfed, a lnear mxture of ground components can be quantfed and dscrmnated by several methodologes 3. herefore, a partcular scene can be decomposed n such a way as to recover the fractonal contrbutons of the fundamental consttuents, provdng an effcent mechansm for subpxel analyss. In order to perform such analyss, some researchers have taken the approach of constructng spectral lbrares of pure elements that can be matched wth every pxel n order to classfy a scene 7. Nevertheless, when no such references are avalable, the analyst must derve the endmembers drectly from the data cube, whch s not an obvous task. In the followng secton, an overvew of the exstng endmember extracton technques s provded.. ENDMEMBER EXRACION ECHNIQUES A large varety of methodologes have been recently proposed wth the purpose of extractng endmembers from hyperspectral data cubes. Next, some of the most well-known methodologes are summarzed. a E-mal: aplaza@unex.es, pablomar@unex.es, rosapere@unex.es. b E-mal: gualt@peep.gsfc.nasa.gov. 78 Image and Sgnal Processng for Remote Sensng VII, Sebastano Bruno Serpco, Edtor, Proceedngs of SPIE Vol. 454 () SPIE X//$5.

2 Pxel Purty Index (PPI) he Pxel Purty Index (PPI) algorthm 3 s based on the geometry of convex sets. A dmensonalty reducton s frst performed usng the MNF transform. Next, a pxel purty ndex s calculated for each pont n the mage cube by randomly generatng lnes n the N-dmensonal space comprsng a scatterplot of the MNF transformed data. All of the ponts n the space are now projected onto the lnes and those ones that fall at the extremes of the lnes are counted. After many repeated projectons to dfferent lnes, those pxels that count above a certan threshold are declared pure. hese potental endmember spectra are loaded nto an N-dmensonal vsualzaton tool and rotated n real tme untl extremtes n the data cloud, that wll lkely correspond wth scene endmembers, are vsually dentfed. Orass. hs algorthm uses a process called Exemplar Selecton to thn the data set 8. here s no prevous dmensonalty reducton over the data. he procedure rejects redundant spectra by calculatng the angle between spectral vectors. Any vector whch s not separated by a certan threshold angle s thnned from the data. he procedure then fnds a bass set of much lower dmenson than the orgnal data by a modfed Gram-Schmdt process. he exemplar spectra are then projected onto ths bass subspace and a smplex s found through a mnmum volume transform. N-FINDR. he nput to ths algorthm s the full spectral mage cube, wthout any dmensonalty reducton. he procedure must examne the full data set to fnd those pure pxels that can be used to descrbe the varous mxed pxels n the scene. hs algorthm fnds the set of pxels wth the largest possble volume by nflatng a smplex nsde the data. he procedure begns wth a random set of vectors. In order to refne the ntal estmate of endmembers, every pxel n the mage must be evaluated as to ts lkelhood of beng a pure or nearly pure pxel. o do ths, the volume s calculated for every pxel n place of each endmember. A tral volume s calculated for every pxel n each endmember poston by replacng that endmember and fndng the volume. If the replacement results n an ncrease n volume, the pxel replaces the endmember. hs procedure s repeated untl there are no more replacements of endmembers 9. Iteratve Error Analyss (IEA). hs algorthm s also executed drectly on the data wth no prevous dmensonalty reducton. An ntal vector (usually the mean spectrum of the data) s chosen to start the process. A constraned unmx s then performed and the error mage s formed. he average of the vectors wth the largest error (dstance from the ntal vector) s assumed to be the frst endmember. Another constraned unmx s then performed and the error mage formed. he average of the vectors wth the largest error (dstance from the frst endmember) s assumed to be the second endmember. hs process s contnued untl the predetermned number of endmembers s found. 3. INEGRAION OF SPECRAL AND SPAIAL RESOLUION he methods addressed n secton can be used to extract endmembers from hyperspectral data n automated or semautomated (PPI) fashon. Nevertheless, the major drawback of all these approaches s that they only take nto account the spectral nformaton contaned n the data cube, dsregardng spatal nformaton. Remote sensng data has the unque ablty of beng represented as an mage, but conventonal analyss technques have tradtonally focused on analyzng the data wthout ncorporatng any nformaton on the spatally adjacent data;.e. the data s not consdered as an mage but as an unordered lstng of spectral measurements that can be shuffled arbtrarly wthout affectng analyss. If we consder hyperspectral data as an mage, then a partcular pxel s characterzed by spectral and spatal propertes. he spectral nformaton concerns the value of the pxel ndependently of the values of ts neghbors, whle the spatal nformaton concerns the relatonshp between the pxel value and those of ts neghbors. It s qute clear at ths pont that all the methods addressed n secton focus exclusvely on the spectral propertes of the data. Proc. SPIE Vol

3 Our man goal n the present work s the development of a new methodology that ntegrates both spatal and spectral nformaton n the analyss of multvarate remote sensng data. We strongly beleve that there s a need to ncorporate the mage representaton n the analyss of hyperspectral data. Some authors have prevously consdered the need to ntegrate spatal nformaton to the spectral content n order to perform unsupervsed classfcaton of multvarate data. We propose a novel approach to ths task whch reles on the use of extended morphologcal operatons. Mathematcal morphology theory 3,4 s a wdely used mage analyss technque that provdes powerful tools for extractng geometry and representng shapes n bnary and grayscale mages. Morphologcal operators focus on the spatal nformaton of the objects present n an mage, and allow a detaled descrpton of an mage through the spatal characterstcs of the objects under study (sze, orentaton, overlappng, ). We need not doubt that ths analyss has nterested many scentsts from many dfferent areas 5, but few authors have exploted ts possbltes n the analyss/classfcaton of hyperspectral remote sensng data 6. hs paper ntroduces a new, completely automated approach to the unsupervsed analyss of hyperspectral mage scenes usng mathematcal morphology concepts 7. he extenson of classc morphologcal operatons to the N-dmensonal doman allows us to ntegrate spectral and spatal nformaton n the analyss process and thus ncorporate the dea of mage n the feld of hyperspectral data analyss. In the followng secton, a schema to extend the classc morphologcal operatons to multvarate data and the proposed analyss methodology are descrbed. he accuracy of ths method s tested by applyng t to real hyperspectral data (secton 5). he paper ends wth some concludng remarks n secton MEHODS 4. Extendng mathematcal morphology to hyperspectral mages Mathematcal morphology was orgnally defned for bnary mages. he two basc operatons of bnary morphology are eroson and dlaton, whch consst of the transformaton of a set X (mage objects) by another set K, known as the structurng element 3. he prncples of mathematcal morphology have also been extended to the grayscale mage case 8. In greyscale morhology, mages and structurng element sets are contnuous valued sets. Let f be a grey level functon representng the mage and k a structurng element. hen eroson and dlaton can be respectvely wrtten as follows. ( f k)(x, y) = Mn { f (x + s, y + t) k(s, t) } (s, t) k ( f k)(x, y) = Max{ f (x s, y t) + k(s, t) } (s, t) k () () he man computatonal task whle tacklng greyscale morphologcal operatons s the query for local maxma or mnma n a certan search area whch s determned by the sze and spatal propertes of the used structurng element. hs fact mples an orderng relaton, but n the case of hyperspectral mages there s no natural means for total orderng of multvarate pxels. hen, the major challenge n the task of extendng morphology to the hyperspectral mage case s the defnton of a vector orderng relaton to determne the supremum and the nfmum of any famly of N-dmensonal vectors 9. We propose to mpose a lattce structure onto the spectral space and defne morphologcal operators by extenson as follows. Let x, x,, x n be a set of multvarate pxels that have been selected by a structurng element at a certan pxel spatal neghborhood. A measure of the spectral dssmlarty between two of those pxels,.e. x a and x b, s calculated by the angular dstance functon, expressed n radans. x a x b dst (x = a, x b ) cos (3) x a x b From ths measure, the followng scalar quantty can be calculated to determne the cumulatve dstance between a partcular pxel x and a set of spatal neghbors, j =...m, j. x j 8 Proc. SPIE Vol. 454

4 d dst(x, x = m j ) j= (4) From the prevous defnton, the calculaton of the maxmum and the mnmum of a set of x, =...n multvarate pxels s straghtforward. hese elements are respectvely defned by the followng expressons. D = arg max d and E arg mn d = (5) Where D s the most spectrally sngular pxel n a spatal neghborhood and E s nothng else than the medan of the pxels n the neghborhood, accordng to the classcal vector medan defnton 9. It s now easy to perform basc morphologcal operatons such as eroson and dlaton by maxmum and mnmum operatons. he result of applyng an eroson/dlaton operaton to a hyperspectral dataset s a new data cube, wth exactly the same dmensons as the orgnal. Let X be a hyperspectral mage and K a square-shaped 3x3 structurng element. he structurng element s moved, pxel by pxel, through the mage, defnng a local spatal search area around each target pxel. he maxmum (dlaton) or mnmum (eroson) pxel n the search area s calculated accordng to the prevously descrbed schema, as depcted n fgure. K = N A N B N C N D N E N F N G N H = = arg max d E {, N, N,..., N } A B H D = arg mn d X = {, N (Orgnal mage) X {, N,..., N } A B H E D X KK (Eroded mage) X KK (Eroded mage) Fgure. Hyperspectral eroson and dlaton. 4. Proposed methodology We propose a fully automated methodology to extract endmembers from hyperspectral mages based on morphologcal eroson and dlaton operatons. he algorthm s called AMEE (Automated Morphologcal Endmember Extracton). he nput to ths method s the full data cube, wth no prevous dmensonalty reducton. It s desrable to work wth normalzed pxel spectra (scaled to make the norm constant among all pxels) to remove the nformaton related to the total radance, whle retanng the spectral pattern. he method conssts of the followng steps. Proc. SPIE Vol

5 Applcaton of morphologcal endmember detectors Morphologcal detectors are used to fnd endmembers as extreme pxels n spectral and spatal space. he detectors are based on a combnaton of morphologcal operatons. Frstly, a hyperspectral eroson s appled over the orgnal mage and, secondly, the spectral dssmlarty between the resultng eroded mage and the orgnal s calculated followng a pxel-by-pxel bass (see equaton 3). Fgure llustrates the local effect of the proposed detector on synthetc hyperspectral mages formed by two ground components: a spectrally pure one (good canddate for beng selected as an endmember) and other formed by a mxture of elements. In ths example, we consder a square-shaped 3x3 structurng element. Not pure Pure Not pure Pure N A N B N C N D N E N F N G N H arget pxel N A N B N C N D N E N F N G N H a) Low output b) Low output Not pure Pure Not pure Pure N A N B N C N D N E N F N G N H arget pxel N A N B N C N D N E N F N G N H c) Hgh output d) Low output Fgure. Workng procedure of a morphologcal endmember detector. he addressed detector produces a hgh output n fgure.c. In ths case, the eroson operaton selects the mnmum pxel n the neghborhood,.e., one of the pxels n the zone labeled as not pure, and the spectral dfference between the selected pxel and the target pxel s hgh. Note that belongs to the zone labeled as pure. On the other hand, a low value s obtaned n fgure.b snce the selected pxel and the target pxel belong to the same zone. Fnally, n fgures.a and.d, the detector produces a low output (all the pxels n the neghborhood have smlar purty ). From ths example t can be deduced that f a larger neghborhood had been consdered (for example, a 5x5 structurng element), the output at the target pxel fgure.d would have been hgh, as t could be expected. he prevous consderaton ndcates that a mult-scale spatal analyss of the hyperspectral mage s requred. he procedure descrbed n fgure must then be repeated for each pxel of the orgnal mage usng structurng elements of progressvely ncreased sze. hs results n spatal/spectral nformaton at each pxel of the scene. From ths nformaton, a probablty mage s generated followng the basc dea of algorthms lke the PPI: those pxels that are repeatedly selected durng the process ncrease ther probablty of beng declared pure. he resultng probablty mage can be represented n the form of a greyscale mage where hgher values ndcate more purty and lower values ndcate lower purty, takng nto account that the term purty refers n ths case to the spatal and spectral nature of the data. 8 Proc. SPIE Vol. 454

6 Automated endmember selecton and regon growng Endmember spectra are automatcally extracted from the probablty mage obtaned after spatal/spectral processng of the data, as descrbed n the prevous secton. hs s done by a smple thresholdng technque. here are plenty of automated procedures for thresholdng greyscale mages avalable n the lterature. From all of them, one that produces partcularly good results n our applcaton s Otsu method, whch s based on the mnmzaton of the weghted sum of group varances. Let w, b and t be the wthn-class, between-class and total varance, respectvely. An optmal threshold t can be determned by maxmzng one of the followng crteron functons wth respect to t. b b t λ = η = = w t w κ (6) hresholdng the probablty mage results n a set of unconnected regons that are used as seeds from whch a regon growng process s performed. It s based on the approach proposed by Bateson et al. to create endmember bundles: ntally, a bundle s created from each seed regon, contanng the spectra assocated to all the pxels n the regon. hen, a medan spectrum s constructed to act as a seed endmember for the bundle. Spatal neghbors are ncorporated to the bundle f they are smlar enough (spectral angle <.) to the seed endmember. When no sutable neghbors are found to be ncorporated n the bundle, the growng process fnshes and the medan spectrum of the bundle s selected as a fnal endmember. 5. RESULS We have appled our endmember extracton algorthm to real hyperspectral data obtaned from the AVIRIS magng spectrometer for a partcular scene: Salnas 98 taken n the Salnas Valley, Calforna on October 9, hs data was avalable only as at-sensor radance data and ncludes vegetables, bare sols and vneyard felds. We have selected a subscene of the Salnas 98 dataset called Salnas A, whch comprses 83x86 pxels and ncludes sx classes. Ground truth s avalable for ths mage, as descrbed n fgure 4 (at the end of the paper). he spatal/spectral characterstcs of the Salnas A dataset make t partcularly sutable for testng the accuracy of our method. Ground truth nformaton reveals zones where broccol wth weeds, senesced corn and romane lettuce are present. he romane lettuce s at dfferent weeks snce plantng (from 4 to 7) and wth growth ncreasngly coverng the sol. A reference dataset of endmembers was obtaned for ths partcular mage usng the PPI procedure. he endmembers extracted by ths wdely accepted supervsed methodology wll be compared to those found by our algorthm. Some consderatons about the applcaton of AMEE algorthm are provded next. Square-shaped structurng elements were used n the endmember dentfcaton stage. he sze of the structurng elements ranged from 3x3 pxels to 3x3 pxels n order to provde a detaled spatal-spectral descrpton of the scene. he resultng probablty mage was automatcally thresholded usng Otsu s algorthm, resultng n a set of unconnected regons. hese regons were grown usng the regon growng algorthm descrbed n subsecton 4.. Medan spectra were calculated for the grown regons and used as endmembers for lnear spectral unmxng 3. hrough effcent mplementaton of the algorthm, the full process of autonomous endmember dentfcaton was accomplshed n approxmately mnute usng a Pentum III 5 MHz personal computer wth 8 megabytes of RAM. Fgure 3 shows the full set of endmembers extracted by both PPI and AMEE methodologes, as well as a comparson between the ndvdual spectra. he avalablty of ground truth allows us to dentfy the zones that those endmembers represent. In partcular, four endmembers were extracted by both approaches, correspondng to the zones labeled n fgure 3 as broccol, romane_lettuce_4wk, romane_lettuce_7wk and corn_senesced_green_weeds. It s mportant to emphasze that the mxture stuaton n the romane lettuce zones s correctly modeled: the zone at 4 weeks snce plantng s mostly sol whle the one at 7 weeks s mostly lettuce. he remanng lettuce areas can be expressed as a Proc. SPIE Vol

7 lnear combnaton of these two endmembers. he comparson addressed n fgure 4 reveals that the spectral dfference between the endmembers obtaned by our method and those found by the PPI s very low. Also, the number of endmembers found by both approaches s the same. PPI Endmembers AMEE Endmembers Radance 5 Radance Wavelength ( mcrometers) Wavelength ( mcrometers) PPI vs AMEE endmember (broccol): Spectral Angle=.5 5 PPI vs AMEE endmember (lettuce_romane_4wk): Spectral Angle= Radance 5 Radance 5 5 Wavelength ( mcrometers) Wavelength ( mcrometers) 75 PPI vs AMEE endmember (lettuce_romane_7wk): Spectral Angle=.94 5 PPI vs AMEE endmember (corn_green_weeds): Spectral Angle=.74 Radance 5 5 Radance 5 Wavelength ( mcrometers) Wavelength ( mcrometers) Fgure 3. A comparson between the endmembers found by the PPI methodology and AMEE algorthm. Fgure 5 (at the end of the paper) shows greyscale abundance maps representng the fractonal composton of endmember materals n the scene. hese maps have been obtaned by the Lnear Spectral Unmxng procedure usng the endmembers obtaned by the PPI procedure (upper row) and our algorthm (lower row), and have been rescaled to le n..55. In these greyscale abundance maps, values close to whte ndcate a large abundance of the endmember consttuent. A color composte mage obtaned through the Spectral Angle Mapper algorthm 3 s also addressed for each methodology. he colors of the resultng classes are equvalent to those shown n fgure 3, whle black s assocated to unclassfed pxels. A vsual comparson of the results provded n fgure 5 reveals that the results obtaned by PPI and AMEE are n essence the same. he prevous consderatons lead us to conclude that, from a quanttatve pont of vew, our method appears to produce results very smlar to those found by wdely accepted methodologes lke the PPI procedure. Snce no human supervson s needed durng the process, the use of our algorthm results n an mportant reducton n the overall 84 Proc. SPIE Vol. 454

8 computatonal tme. On other hand, although n ths case the results are smlar, we beleve that the ncorporaton of spatal propertes n the analyss of hyperspectral data may lead to much mproved results n more complcated datasets. 6. CONCLUSIONS he ntegraton of spectral and spatal nformaton n the analyss of hyperspectral data s becomng more relevant as the spatal/spectral capabltes of magng spectrometers are constantly mproved. Most of the avalable methodologes rely exclusvely on the spectral nformaton of the data cube, wthout takng nto account the exstng spatal correlaton of the data. In ths work, the fundamentals of a new autonomous method to fnd endmembers n hyperspectral remote sensng data are descrbed. he method reles on mathematcal morphology, a wdely used tool to study the spatal nformaton contaned n bnary and greyscale mages. For the sake of usng morphologcal operatons to fnd endmembers n spatal/spectral space, a schema to extend the basc morphologcal operatons to hyperspectral mages s proposed and dscussed. Although no prevous dmensonalty reducton or data thnnng s requred, the proposed morphology-based approach s capable of rapd and accurate determnaton of endmember spectra from hgh dmensonal hyperspectral mages. Some prelmnary results obtaned after applyng ths algorthm to real AVIRIS sensor data show that t s successful n the task of ntegratng spatal and spectral nformaton n the analyss process. Although the results found are encouragng, some work s stll needed n order to extrapolate our conclusons to other hyperspectral datasets and evaluate the nfluence of spatal correlaton n the fnal classfcaton. ACKNOWLEDGEMENS he authors would lke to thank L.F. Johnson of NASA/AMES for sharng the Salnas 98 data and ground truth. Fundng from Spansh Government (CICY-FEDER program) under the IC--739-C4-3 grant s also gratefully acknowledged. REFERENCES. Greeen, R.O., Edtor, AVIRIS Earth Scence Workshop Proceedngs, Avalable at adjudn, S. and Landgrebe, D., Classfcaton of Hgh Dmensonal Data wth Lmted ranng Samples, PhD thess, School of Electrcal Engneerng and Computer Scence, Purdue Unversty, May, 998. Avalable as R- ECE-98-9 from 3. Boardman, J.W., Kruse, F.A. & Green, R.O., Mappng arget Sgnatures va Partal Unmxng of AVIRIS Data, Summares of the V JPL Arborne Earth Scence Workshop, Masell, F., Multclass Spectral Decomposton of Remotely Sensed Scenes by Selectve Pxel Unmxng, IEEE rans. Geoscence and Remote Sensng, vol. 36, ssue: 5, part, pp: 89 8, Sept Martínez P., Pérez R.M., Agular P.L., Bachller, P. and Daz, P., A Neuronal ool for AVIRIS Hyperspectral Unmxng, Summares of the IX JPL Arborne Earth Scence Workshop, pp 8-86, JPL/NASA, Kruse, F.A., Spectral Identfcaton of Image Endmembers Determned from AVIRIS Data, Summares of the VIII JPL Arborne Earth Scence Workshop, Roberts, D.A., Dennson, P., Ustn, S., Reth, E., Moras, M., Development of a Regonally Specfc Lbrary for the Santa Monca Mountans Usng Hgh Resoluton AVIRIS Data, Summares of the VIII JPL Arborne Earth Scence Workshop, Palmadesso, P., Antonades, J., Baumback, M., Bowles, J. & Rckard, L.J., Use of Flter Vectors and Fast Convex Set Methods n Hyperspectral Análss, Proceedngs of SPIE, 999. Avalable at 9. Wnter, M.E., Fast Autonomous Spectral Endmember Determnaton n Hyperspectral Data, Proc. 3 th Internatonal Conference on Appled Geologc Remote Sensng, vol II, pp , Vancouver, Canada, Nevlle, R.A., Staenz, K., Szered, R., Lebfebre, J., Hauff, P., Automatc Endmember Extracton from Hyperspectral Data for Mneral Exploraton, Proc. 4 th Internatonal Arborne Remote Sensng Conference, vol. II, pp , Ottawa, Canada, 999. Proc. SPIE Vol

9 . Madhok, V. and Landgrebe, D., Spectral-Spatal Analyss of Remote Sensng Data: An Image Model and A Procedural Desgn. PhD thess, School of Electrcal Engneerng and Computer Scence, Purdue Unversty, May, 998. Avalable as R-ECE-99- from pdf.. Jménez, L.O., Rvera-Medna, J., On the Integraton of Spatal and Spectral Informaton n Unsupervsed Classfcaton for Multspectral and Hyperspectral Data, EUROPO Conference on Image and Sgnal Processng, Proceedngs of SPIE Vol. 387, Serra, J., Image Analyss and Mathematcal Morphology. Academc Press, London, Serra, J., Image Analyss and Mathematcal Morphology, Volume. Academc Press, London, Plaza, A., Cernadas, E., Durán, M.L., Sánchez, Antequera,., Drectonal Morphologcal Operators to Detect Fat Streaks n Iberan Ham, VIII Natonal Symposum on Pattern Recognton and Image Analyss, pp , Blbao (Span), Solle, P., Morphologcal Parttonng of Multspectral Images, Journal of Electronc Imagng, Vol. 5(3), pp. 5-65, July Plaza, A., Martínez, P., Gualter, J.A., Pérez, R.M., Spatal/Spectral Endmember Extracton from AVIRIS Hyperspectral Data Usng Mathematcal Morphology, Summares of the X JPL Arborne Earth Scence Workshop,. 8. Sternberg, S.R., Greyscale Morphology, Computer Vson Graphcs and Image Processng, 35, 83-35, Lambert, P., Chanussot, J., Extendng Mathematcal Morphology to Color Image Processng, CGIP, Sant- Etenne, France,.. Sahoo, P.K., Soltan, S. & Wong, A.K.C., A Survey of hresholdng echnques, Computer Vson, Graphcs and Image Processng, 4, pp. 33-6, Otsu, N., A hreshold Selecton Method from Gray-Level Hstograms, IEEE rans. Systems, Man, and Cybernetcs, Vol.SMC-9 No., Jan Bateson, C.A., Asner, G.P., Wessman, C.A., Endmember Bundles: A New Approach to Incorporatng Endmember Varablty nto Spectral Mxture Analyss, IEEE rans. Geoscence and Remote Sensng, vol. 38, no., pp: 83 94, March. 3. Gualter, J.A., Bechdol, M., Chettr, S., Robnson, J.W., Garegnan, J., Vermeulen, A., Antonlle, S., From Spectra to Classfcaton, echncal Report, NASA/GSFC,. 86 Proc. SPIE Vol. 454

10 Fgure 4. A subscene of the Salnas 98 dataset, showng known ground truth as polygons contanng sold colors bounded by black lnes and surrounded by thumbnal fgures of the ground truth taken at the tme of the data acquston. he outlned box n red shows the subscene boundares of the scene called Salnas A. Fgure 5. Greyscale abundance maps for the endmembers extracted by PPI (upper row) and AMEE (lower row). Along wth these maps, a fnal classfcaton mage obtaned usng the SAM algorthm s addressed for each method. Proc. SPIE Vol