On combining Learning Vector Quantization and the Bayesian classifiers for natural textured images

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1 On combining Learning Vector Quantization and the Bayeian claifier for natural textured image María Guiarro Dept. Ingeniería del Software e Inteligencia Artificial Facultad Informática Univeridad Complutene 8040 Madrid mariaguiarro@gmail.com Raquel Abreu Dpto. Informática y Automática ETS Ingeniería Informática Univ. Nacional Educación a Ditancia 8040 Madrid raquel.abreuhernando@telefonica.e Gonzalo Paare Dept. Ingeniería del Software e Inteligencia Artificial Facultad Informática Univeridad Complutene 8040 Madrid paare@dacya.ucm.e Abtract One obective for claifying texture in natural image i to achieve the bet performance poible. Unupervied technique are uitable when no prior knowledge about the image content i available. The main drawback of unupervied approache i it wort performance a compared againt upervied one. We propoe a new unupervied hybrid approach baed on two wellteted claifier: Vector Quantization (VQ) and Bayeian (BY). The VQ unupervied method etablihe an initial partition which i validated and improved through the upervied BY. A comparative analyi i carried out againt claical claifier, verifying it performance.. Introduction Nowaday the increaing technology of aerial image i demanding olution for different image-baed application. The natural texture claification i one of uch application due to the high patial reolution achieved in the image. The area where texture are uitable include agricultural crop ordination, foret or urban identification and damage evaluation in catatrophe or dynamic path planning during recue miion or intervention ervice alo in catatrophe (fire, flood). Different claical technique have been tudied for image texture claification, namely: Bayeian, K-Nearet, Neural Network, Vector Quantization [, 5, 6, 7, 0]. Thee claifier are upervied method, which perform appropriately if a correct partition i ued for training them. Thi implie that the ample have been correctly aigned a belonging to each cluter. Unfortunately, the variety of texture in aerial image could become high or even if unpredictable. Hence, unupervied automatic claification approache hould be uitable in order to etablih the bet cluter partition. The Vector Quantization approach (VQ) i one of the poible unupervied approache, the main drawback of VQ i it trong dependency from the threhold ued for the partition and the order in which the ample are proceed. We propoe the ue of the unupervied VQ claifier upervied by the Bayeian (BY) claifier. Hence, the cluter partition upplied by the VQ i verified by the BY. Thi i a hybrid approach which making the main finding of thi work. There are pixel-baed and region-baed approache. A pixel-baed approach trie to claify each pixel a belonging to one of the clae. The region-baed identifie pattern of texture within the image and decribe each pattern by applying filtering (law mak, Gabor filter, Wavelet, etc.), it i aumed that each texture diplay different level of energy allowing it identification at different cale [], []. The behaviour of feature ha been alo tudied in texture claification, where the et of feature decribe each pattern [3, ]. Thi i out of the cope of thi paper. The aerial image ued in our experiment do not diplay texture pattern. Thi implie that textured region cannot be identified by applying region-baed. In thi work we ue a pixel-baed approach under red-green-blue (RGB) colour repreentation becaue it perform favourably againt other colour mapping a reported in []. Hence, the three RGB pectral value are the feature ued in our method.

2 96 II Congreo Epañol de Informática The paper i organized a follow. Section decribe the deign of the automatic hybrid claifier, where the VQ and BY method are briefly decribed. Section 3 how experimental and comparative reult. Finally, in the ection 4 the concluion are preented.. Automatic Unupervied Claifier Our ytem work in two tage: training and claification. The training phae trie to obtain the bet partition for the available training pattern. The claification phae ue the reult obtained during the training and claifie the new incoming pattern. Figure diplay the training ytem architecture with two main module (VQ and BY). x i training pattern T VQ P v BY modify T m C Figure. Combination of Claifier valid fuzzy partition? no KB P v m C The working proce i decribed below, ) The VQ module receive the training pattern x i and a threhold T and provide a partition (cluter) P. Thi mean that the BY module receive the number of cluter (c), their centre (v ) and the training ample x belonging to each cluter w. ) The BY module etimate the cluter centre (m ) and covariance matrice C. Thi allow u to verify the partition validation. 3) If P i a valid partition it i tored in the knowledge bae (KB) o that the cluter centre are available during the claification phae after the training one. 4) If P i not validated, the threhold T i modified and a new partition, with the initial et of training ample available, i intended until the i ye validation i achieved. A before the new partition i generated by the VQ module. 5) During the claification phae the ytem recover, from the KB, the cluter centre v, m and C obtained during the training phae. Each new pattern i claified a belonging to the available cluter by applying the Baye approach. Hence, thi pattern will belong to each cluter with a different probability value. The final deciion i made baed on the maximum probability value... Vector Quantization The VQ approach [,4] tart with the obervation of a et X of n training pattern, i.e 3 X x, x,..., x. The ample are threedimenional becaue the feature are the three n pectral RGB value. The VQ proce i a follow: ) Define the threhold T value and elect a metric ditance (euclidean). ) For each training pattern x i compute it ditance to each cluter centre v, d i (x i, v ). If x i i the firt pattern it i the firt centre, i.e. v = x i. 3) Compute d ik (x i, v k ) < d i (x i, v ) k. If d ik (x i,v k ) < T then aign x i to the cluter aociated to the centre v k which give the minimum ditance and update thi centre v k by averaging the ample belonging to thi cluter. 4) If d ik (x i, v k ) T then a new cluter i created and it new cluter centre i exactly the ample, i.e. v k = x i. After thi proce a partition P i obtained with c cluter, each one with it cluter centre v where =,,,c and a ubet X X of n pattern ample belonging to each cluter w... Bayeian approach The BY module receive the partition, i.e. the ample ditributed into the cluter. Given a pattern vector x, under the Bayeian framework, the main problem to be olved are the etimation of a et of cla-conditional probability denity function p x w ) and the a ( priori probabilitie P ( w ) for each cla w [4]. The probability denity function p( x) can be

3 IV Taller de Minería de Dato y Aprendizae 97 modelled a a mixture denity ditribution coniting of c denity component aociated to the c cluter, c p( x ) p x w P( w ) () The method i ummarized a follow, ) For each cla w compute it aociated mean vector m ) With the n ample x belonging to the cla w compute de covariance matrix a follow, C t m x m n x i i () n where t denote tranpoe. 3) Once the parameter m and C are etimated, the cla conditional probability denity function i given by, p x w r C exp.3. Partition validation i t x m C x m (3) The next tep conit in the partition validation. Thi i carried out by computing the divergence between two cluter w i and w through the equation (4) according to Jenen [8]. C C C C Diverg Tr i i i (4) t Trm m C C m m i i i where Tr i the trace for the matrix; m i, C i and m C are the mean and covariance matrice for cluter w i and w repectively; t denote tranpoe. The divergence i a meaure of eparability between two cluter, o that the higher the divergence, the higher the cluter eparation. In order to determine the validity of the partition, we compute the divergence between each two cluter and then average the value of the divergence. The maximum value of the averaged divergence for different value of c determine the bet partition, i.e. the bet number of cluter for the et of training ample available. Value of the divergence greater than 80 are acceptable. Following the cheme in the figure and baed on the averaged divergence value, if the partition i reected then the threhold T mut be modified in order to try a new better partition P; otherwie if the current partition i accepted, it i tored in the KB. Different partition are intended by upplying the ample in different order of proceing. The order i randomly etablihed. In our experiment, we have verified that the divergence value range between 0 and 30. Hence we map linearly thee divergence value o that they range in [0,] a D D 30 i i. Moreover, we are uing RGB value a feature ranging in [0,55]. Thi implie that the cluter (ample) are mapped into the 3- dimeninal pace, where each axi varie between 0 and 55. Therefore, the maximum Euclidean ditance d E in thi pace i given by the two oppoite point (0,0,0) and (55,55,55) reulting the following value d E 44. Hence, thi will be the maximum threhold value T. It minimum value i bounded by cero. We define the following quantum magnitude Q d E 40. The modification proce for T i expreed by (6). We have pecified the iteration a k T ( k) T ( k ) Q D (5) where D i the averaged divergence value ranging in [0,+]. Initially we et T(0) = 0 and D = 0, i.e. T() = Q..4. Deciion proce During thi on-line proce new image and conequently new pattern ample are to be proceed by the ytem. A deciion mut be made about them. With uch purpoe, we recover the cla conditional probability denity function tored in KB and etimated through the equation (3) during the off-line proce. Now, given a new ample x, the problem i to decide what cla it belong to. Thi i carried out by applying the Baye rule, in order to obtain the poterior probabilitie P x w. A poterior probability determine the memberhip degree of

4 98 II Congreo Epañol de Informática x to the cla w once the ample ha been oberved and become available. We compute the a priori probability following the Bayeian framework [4], a follow, x w Pw px p P w x (6) So, the deciion i made a follow, h w x Pw x x w if P h (7) The equation (7) can be re-written avoiding p(x ), a it appear in both member of the inequality, x w p x w P( w ) px w h if h P( w ) h (8) We till require computing the prior probabilitie P ( w ) and P ( w ) involved in (8) becaue h p x w ) and p x w ) can be obtained ( ( h through the equation (3). The computation of the a priori probabilitie i carried out by exploiting the information provided previouly by the VQ approach. Indeed, given x we compute the Euclidean ditance d k (x,v ) from x to each cluter centre v w, where the centre have been provided by the VQ module. The correponding a priori probability i computed by applying the logitic function [4] a follow, P( w ) Ad (, ) k x v e (9) The contant A i included to avoid evere bia, it i et to 0 - in thi paper after trial and error experimentation. Now, the final deciion can be made through the equation (8). A one can ee the deciion i made by combining two claifier: VQ and BY. Thi i a uitable practice for olving claification problem [9]. 3. Comparative and performance evaluation We have ued a et of 6 digital aerial image acquired during May in 006 from the Abadia region located at Lugo (Spain). They are multipectral image with 5x5 pixel in ize. The image are taken at different day from an area with everal natural texture. The initial training pattern are extracted from 0 image of the full et. The remainder 6 image are ued for teting and four et, S0, S S and S3 of four image each one, are proceed during the tet according to the trategy decribed below. The image aigned to each et are randomly elected from the 6 image available. 3.. Deign of a tet trategy In order to ae the validity and performance of the propoed hybrid VQ and BY method we obtain two initial partition, namely: P VB and P MI. P VB i the automatic validated partition obtained by the unupervied procedure decribed in thi paper, Figure. P MI i a manual partition obtained a decribed below. Each partition i ued a the initial training et of ample by the following three upervied claical clutering procedure [4]: a) VQ; b) BY and c) the Self-Organizing feature map (SO). Thi i intended in order to verify the performance of the propoed fuion approach, hereinafter VB, againt the ingle method VQ, BY and SO. The tet i carried out according to the following tep: ) STEP 0 (initial partition): for each image (from the 0 available) we perform a down ampling by a factor of 6, obtaining 0x3x3 training ample, i.e. n = 040. ) We apply our VB approach tarting with the threhold T = Q until the partition i validated. At thi time we have available the final P VB partition i.e. the number of cluter c and their correponding cluter centre are known. Now, we manually elect n training pattern from the ame et of the 0 image and build c cluter driven by the previou cluter center. Each manually elected training ample i compared with each cluter center and it i aigned to the cluter which give the minimum feature (pectral)

5 IV Taller de Minería de Dato y Aprendizae 99 ditance between the ample and the correponding cluter center. So, we obtain the manual initial partition P MI. The P VB and P MI partition are ued for claifying the new pattern ample during the next tep. 3) STEP : given the image in the et S0 and S, claify each pixel a belonging to a cluter according to the VB, BY, VQ and SO method. 4) Compute the percentage of uccee according to the ground truth defined for each cla and for each image. The claified pattern ample from S are added to the previou training ample and a new training proce i carried out according to each method. The et S0 i ued a a ample et in order to verify the performance of the training proce a the learning increae. 5) Perform the ame proce for STEP and 3 but uing the et S and S3 repectively intead of S. Note that S0 i alo proceed a before. The number of training ample added at each STEP i 4x5x5 becaue thi i the number of pixel claified during the STEP to 3 belonging to the et S, S and S3. Figure 3 diplay: (a) a repreentative original image to be claified belonging to the et S0; (b) the inter-cluter correpondence between the original colour and the label aigned to each cluter; (c) the labelled image after the claification with our VB approach and (d) the ground truth for the cluter number two. Each ground truth i built by applying the BY and then modifying the reult manually according to the human expert criterion. The colour for each cluter, Figure 3(b), matche with the natural colour aigned to the correponding cluter centre. The label are artificial colour derived from a colour map identifying each cluter. The correpondence between label and the different texture i a follow: ) yellow with foret vegetation; ) blue with bare oil; 3) green with agricultural crop vegetation and 4) red with building and man made tructure. 3.. Analyi of reult Figure diplay different threhold value againt the averaged divergence, attached i diplayed the number of cluter obtained. The bet mean Divergence core value i obtained for the threhold T et to 70.83, obtaining four cluter. Larger threhold value reult in two cluter and with value greater than 60 a unique cluter i obtained (they are not diplayed). (a) (b) Figure. Threhold value againt averaged divergence core (attached i the number of cluter centre) (c) (d) Figure 3. (a) original image; (b) colour and label; (c) labelled texture; (d) ground truth for the cluter number two Table how the percentage of uccee in term of correct claification obtained for the different method and for each initial partition. For each STEP we how the both et of teting image proceed SP0 and SP/SP/SP3. Thee percentage are computed taking into account the correct claification for the four cluter according to the correponding ground truth.

6 00 II Congreo Epañol de Informática Figure Percentage of uccee obtained for the method analyed for each partiton at the three STEP. % STEP STEP STEP 3 Partition Method SP0 SP SP0 SP SP0 SP3 VB P VB BY VQ SO VB P MI BY VQ SO From reult in table, one can ee that the performance obtained with the initial partition P VB i comparable to that obtained when P MI i ued for all method and the three STEP. Thi mean that the propoed unupervied approach perform in a imilar fahion than the upervied one. The wort reult are obtained with VQ when it i ued iolated, but it combination with BY give acceptable reult. Thi behaviour wa expected becaue upervied approache perform better than unupervied one. We can infer that the performance of the different method improve a the number of training ample increae, i.e. high learning rate obtain better performance than low one a expected in any learning proce. 4. Concluion We propoe a new unupervied hybrid and automatic making deciion proce for claifying natural texture. The propoed method combine the unupervied VQ and the upervied BY trategie achieving reult which are comparable to thoe obtained by the upervied one. The performance of our propoed approach i analyed with different claical method, including the method which are combined, verifying that it perform favourably in the et of aerial image teted. The method i applicable to other textured image even if uing different attribute. The unique adaptation for new attribute come from the computation of the attribute value. In the future, additional experiment hould be required in order to deal with illumination variability. Thi i becaue the image are normally acquired during different day and obviouly under different illumination condition. Reference [] Chan, J.W.C., Laporte, N. and Defrie, R.S., Texture Claification of logged foret in tropical Africa uing machine-learning algorithm. Journal Remote Sening. 4(6), , 003. [] Cherkaky, V., Mulier, F., Learning from data: concept, theory and method, Wiley, New York, 998. [3] Drimbarean, P.F. and Whelan, P.F., Experiment in colour texture analyi. Pattern Recognition Letter,, 6-67, 00 [4] Duda, R.O., Hart, P.E. and Stork, D.G., Pattern Claification, Jhon Willey and Son, New York, 00. [5] Frate, F. del, Pacifici, F., Schiavon, G. and Solimini, C., Ue of Neural Network for Automatic Claification from High- Reolution Image. IEEE Tran. Geocience and Remote Sening. 45(4), , 007. [6] Giacinto, G., Roli, F. and Bruzzone, L., Combination of neural and tatitical algorithm for upervied claification of remote-ening. Pattern Recognition Letter. (5), , 000 [7] Hanmandlu, M., Madau, V.K. and Vaikarla, S., A Fuzzy Approach to Texture Segmentation. Proc. IEEE Int. Conf.

7 IV Taller de Minería de Dato y Aprendizae 0 Information Technology: Coding and Computing (ITCC04), The Orlean, La Vega, Nevada, , 004. [8] Jenen J.R., Introductory Digital Image Proceing, Prentice-Hall, Englewood Cliff, NJ, 98. [9] Kittler, J., Hatef, M., Duin R.P.W. and Mata, J., On Combining Claifier IEEE Tran. on Pattern Analyi and Machine Intelligence, 0(3), 6-39, 998. [0] Lam, E. P., Wavelet-baed texture image claification uing vector quantization. In: Atola, J.T., Egiazarian, K.O and Dougherty, E.R. (ed.): Proc. SPIE, Image Proceing: Algorithm and Sytem V, vol. 6497, , 007. [] Maillard, P., Comparing Texture Method through Claification. Photogrammetric Engineering and Remote Sening, 69(4) (003) , 003. [] Puig, D. and García, M.A.: Automatic Texture Feature Selection for Image Pixel Claification. Pattern Recognition, 39() , 006.

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