MULTISPECTRAL IMAGES CLASSIFICATION BASED ON KLT AND ATR AUTOMATIC TARGET RECOGNITION Paulo Quntlano 1 & Antono Santa-Rosa 1 Federal Polce Department, Brasla, Brazl. E-mals: quntlano.pqs@dpf.gov.br and paulo.quntlano@terra.com.br Unversty of Brasla, Insttute of Geoscences & Department of Computer Scence, Brasla, Brazl. E-mal: nuno@cc.unb.br SUMMARY In ths paper we propose an Automatc Target Recognton - ATR approach, wth the goal of automatcally classfy multspectral mages, based on KLT - Karhunen-Loève Transform. We used bands 4, 5 and 3 of Landsat satellte mages. Our approach performs dmensonalty reducton, usng only the egenvectors wth the hghest egenvalues, generatng an egenspace of low dmenson. The target recognton s done fndng out the shortest Eucldean dstance among the prmtves of the new mages and the prmtves of the worked classes. We used 3 classes, and we bult a classfed map. INTRODUCTION Pattern Recognton s a complex and mportant problem of Computer Vson. There are constant efforts of computer scentsts amng to fnd out best solutons for them [1,, 4 and 6]. The problem even becomes more complex when we work wth very large mages and, mostly, wth multspectral or hyperspectral mages. In ths case, t s very mportant to use some dmensonalty reducton technques, n order to become possble the processng of the mages and the pattern recognton. In ths paper, we propose KLT to reduce the mages dmensonalty, wthout loss of mportant and necessary data to the pattern recognton procedures [3 and 5]. Thus, the multspectral mages are reduced to two dmensons, and they are submtted to KLT n order to reduce ther dmensonaltes. The egenvectors based transforms have been largely used on pattern recognton, usng gray levels mages [4 and 6]. However, we ddnt fnd any pattern recognton results usng multspectral or hyperspectral mages, based on KLT. PROBLEM STATEMENT Ths paper has the goal of automatcally classfy multspectral mages. For that we propose an Automatc Target Recognton approach based on KLT. The experments made and presented on ths paper show a practcal mplementaton of Landsat satellte mage classfcaton, of 1600x1600 pxels, usng bands 4, 5 and 3. We used the 3 next classes: (1) water, () forest/feld and (3) reforestaton areas. Fgure 1 shows the mage used to test the model, already segmented n 16 blocks of smaller mages of 400x400 pxels. We used an mage coverng the area around Brasla cty, the Captal of Brazl. APPROACH AND TECHNIQUES All the 16 mages blocks are submtted to the model. The algorthms process those mages
blocks, cuttng out 400 wndows of 0x0 pxels n each block, summarzng 6400 mages, to be treated n ths format. So, we construct the mages space. We start from the set of M=400 mage wndows, cut from each one of the 16 blocks, dentfed as Γ ( = 1,..., M ) and referenced as the test set. These mages are used to the performance model verfcaton. They are threedmensonal matrces of NxNxB pxels, therefore havng each mage BN pxels, n whch B s the number of spectral bands and N s the number of lnes and columns of these squared mages. For the results presented n ths artcle, we are usng B=3 and N=0. Fgure 1. Image used to the tests of the proposed model.
Prelmnarly, all these M mages are converted nto column vectors, so they have BN x1 dmenson, wth BN pxels. In ths same procedure, these 3D mages are reduced to column vectors by processng the whole mage, lne by lne, and takng every lnes and concatenatng them, one after to another. All pxels are treated as they were vectors wth B elements, and they are processed on a smlar way to be transported to the vector Γ. Thus, we buld that bg vector, n the followng way:,1 On the processng of each one of the 16 mages blocks, we calculate the average Ψ of the each 400 mages. So, we assemble a new Φ mages set, obtaned from the dfference between each mage from the test set and the average mage. Fgure -A shows the average mage of all wndows from the tests set of the block 1. Fgure -B to -E show some mages of the tests set, all wth 0x0x3 pxels. The numbers between parentheses ndcate the mage relatve poston nsde the block 1. Γ,1 = Γ j, k, p ( = 1,..., BN j, k = 1,..., N; p = 1,..., B) ; (1) Fgure. Average mage and some mages of the tests set. From the new set of the M mages Φ, we assemble the matrx A, of dmenson BN xm, takng each one of the M vectors Φ and placng them n each column of the matrx A, n the followng way: A = Φ (), j j;,1 From the new matrx A, we assemble the covarance matrx C, by means of external product, wth dmenson BN xbn. So, the egenvalues λ of the covarance matrx C and the egenvectors x are calculated. We assembled the matrx C n the followng way: T C = AA (3) We appled a supervsed tranng on the model, n whch we chose 6 samples for each class, generatng an average mage from the samples of each class. The mages of the averages classes are used n the tranng stage. And for the verfcaton and tests we used all M mages of the tests set. The classes mages averages are projected nto the egenspace generated, based n the egenvectors extracted from the covarance matrx. Based on our experments, we verfed that just some few egenvectors wth the larger egenvalures are enough for the target recognton, because of
that we just used (M <M) egenvectors, n the obtanment of the data presented on ths paper, wth M`=30. Ths projecton s made n the followng way: T Ω = U ( Γ Ψ), 1,..., Nc. (4) = Where the matrx Ω, of dmenson ( M xnc), contans Nc egenvectors, of dmenson ( M x1), from the matrx L, and t s used for comparson wth the new mages ntroduced for comparson and recognton. Nc s the number of exstng classes n the tests set. As the projecton of the new mages on egenspace descrbes the dstrbuton varaton of the mages, t s possble to use these new prmtves for classfcaton of these mages. In ths artcle, ATR s performed by means of extractng the prmtves of the new mages submtted for recognton and comparng them wth the prmtves of the classes prevously stored on the data base of classes standards, calculated n the same way. The methodology used to do ths comparson s the Eucldean dstance. So, the mages submtted to ATR are projected n the egenspace, obtanng the vector Ω, on the followng way: T Ω = U ( Γ Ψ) (5) The vector Ω, of dmenson (M x1), s compared wth each one of the vectors Ω ( = 1,..., Nc), representatves of the classes. If the Eucldean dstance found between Ω and any Ω ( = 1,..., Nc) s nsde the threshold of the class and t was the smaller dstance, then there was the recognton of Ω belongng to class of Ω. The Eucldean dstance s calculated by means of the of the mnmum square method, on the followng way: ε = Ω Ω, ( = 1,..., Nc) (6) Our proposal fnds one threshold for each class, wth the am of obtanng a better performance on the recognton step. The thresholds θ ( = 1,..., Nc) defne the maxmum dstance allowed among new mage submtted to recognton and each one of the classes. If the dstance found between new mage and one of the classes s the mnmum and s nsde the threshold of the class, then there was the automatc target recognton. The thresholds are adjusted by a varable k, whch defnes the degree of fault tolerance. The calculaton of the Nc thresholds, on whch Nc s the quantty of worked classes, s done on the followng way: θ k 1 = max{ Ω Ω j } k (, j = 1,..., Nc; k = 1,...,10) RESULTS (7) Based on worked data, and usng the egenvectors wth the 30 larger egenvalues, we assembled a map wth the found classfcaton, as shown n Fgure 3. Some pxels are marked n blank, because the found results were not nsde the threshold of the respectve class, ndcatng that n these cases the model ddnt fnd out any answer, for not beng enough sure and not havng suffcent nformaton.
Fgure 3. Map from the results. As the wndows of pxels used n the classfcaton are very large, of 0x0 pxels of the orgnal mage, correspondng to an area of 600m x 600m, furthermore orgnal mage s very complex, havng several dfferent classes, the model could not classfy n detals the referred scenery. For example, the model dd not manage to classfy some ponts of the lake, because half wndow s lake and other half s vegetaton. EXAMPLES The mage 310, shown on Fgure, has around ½ of ts area nsde the lake and has other half n the vegetaton. Because of that, the mnor dstance found out among prmtve
of ths mage and the classes occurred wth class 3, as t can be observed n the Table 1. However, the found dstance stayed outsde threshold. The values n ths table were dvded by 1.0e+010. About the mage 31, the Eucldean dstance s small and postoned nsde threshold of the class. The mage 311 has an Eucldean dstance more than three tmes superor than mage 31, because t has other knd of target n your top left corner. About the mage 316, as one can see at the same Fgure, around 1/3 of ts area s covered for other knd of target. Because of that, the Eucldean dstance between ths mage and the class was very large, as shown on Table 1, however ts a lttle smaller than threshold, thats why ts classfcaton stayed n the class 1. Table 1. Results of comparson of some mages. Images Class Eucldean Thresholds Dstance 310 3.749.016 311 1 0.1565.5546 31 1 0.0505.5546 316 1.06.5546 CONCLUSION We managed to do the automatc target recognton n multspectral mages, usng 3 spectral bands. We also managed to assemble a classfed map, n accordance wth the accomplshed tranng, usng KLT for the dmensonalty reducton of the data and the measurements of the Eucldean dstance among mages of the test set and the worked classes. REFERENCES [1] Black, M. J. e Jepson, A. D., 1996. EgenTrackng: Robust Matchng and Trackng of Artculated Objects Usng a Vew-Based Representaton. In: ECCV, Cambrdge, pp. 39-34. [] Brennan, V. e Príncpe, J., Multresoluton usng Prncpal Component Analyss, 1999, Unversty of Florda, Ganesvlle, FL, USA. [3] Fernandez, Gabrel e Wttembrnk, C. M., Regon Based LKT for Multspectral Image Compresson, 1999, Unversty of Calfórna, Santa Cruz, Santa Cruz, CA, USA. [4] Krby, M. e Srovch, L., "Applcaton of the Karhunen-Loève Procedure for the Charactersaton of Human Faces", IEEE Transactons on Pattern Analyss and Machne Intellgence, 1990. [5] Nasr, M.; Kusuma, J. e Ramchandran, K., Random Varables, Random Processes and Karhunen-Loève Transform, 00, Unversty of Calforna, Berkeley, CA, USA. [6] Turk, Matthew e Pentland, Alex, Egenfaces for Recognton, Vson and Modelng Group, The Meda Laboratory, MIT, In: Journal of Cogntve Neuroscence, Volume 3, Number 1, pp. 71-86, 1991.