GREY LEVEL CO-OCCURRENCE MATRICES: GENERALISATION AND SOME NEW FEATURES

Iteratioal Joural of Computer Sciece, Egieerig a Iformatio Techology (IJCSEIT), Vol.2, No.2, April 2012 GREY LEVEL CO-OCCURRENCE MATRICES: GENERALISATION AND SOME NEW FEATURES Bio Sebastia V 1, A. Uikrisha 2 a Kaa Balakrisha 1 1 Departmet of Computer Applicatios, Cochi Uiversity of Sciece a Techology, Cochi biosebastiav@gmail.com, mullayilkaa@gmail.com 2 Scietist G, Associate Director, Naval Physical a Oceaographic Laboratory, Cochi uikrisha_a@live.com ABSTRACT Grey Level Co-occurrece Matrices (GLCM) are oe of the earliest techiques use for image texture aalysis. I this paper we efie a ew feature calle trace extracte from the GLCM a its implicatios i texture aalysis are iscusse i the cotext of Cotet Base Image Retrieval (CBIR). The theoretical extesio of GLCM to -imesioal gray scale images are also iscusse. The results iicate that trace features outperform Haralick features whe applie to CBIR. KEYWORDS Grey Level Co-occurrece Matrix, Texture Aalysis, Haralick Features, N-Dimesioal Co-occurrece Matrix, Trace, CBIR 1. INTRODUCTION Texture is a importat characteristics use i ietifyig regios of iterest i a image. Grey Level Co-occurrece Matrices (GLCM) is oe of the earliest methos for texture feature extractio propose by Haralick et.al. [1 ] back i 1973. Sice the it has bee wiely use i may texture aalysis applicatios a remaie to be a importat feature extractio metho i the omai of texture aalysis. Fourtee features were extracte by Haralick from the GLCMs to characterize texture [2 ]. May quatitative measures of texture are fou i the literature [3, 4, 5,6]. Dacheg et.al.[7 ] use 3D co-occurrece matrices i CBIR applicatios. Kovalev a Petrov [8] use special multiimesioal co-occurrece matrices for object recogitio a matchig. Multi imesioal texture aalysis was itrouce i [9], which is use i clusterig techiques. The objective of this work is to geeralize the cocept of co-occurrece matrices to - imesioal Eucliea spaces a to extract more features from the matrix. The ewly efie features are fou to be useful i CBIR applicatios. This paper is orgaize as follows. The theoretical evelopmet is presete i sectio 2, where the geeralize co-occurrece matrices a trace are efie a the umbers of possible co-occurrece matrices are evaluate. Sectio 3 illustrates the use of trace i CBIR by comparig its performace with the Haralick features. Sectio 4 coclues the paper illustratig the future works. DOI : 10.5121/ijcseit.2012.2213 151

Iteratioal Joural of Computer Sciece, Egieerig a Iformatio Techology (IJCSEIT), Vol.2, No.2, April 2012 2. THEORETICAL BACKGROUND I 1973 Haralick itrouce the co-occurrece matrix a texture features for automate classificatio of rocks ito six categories [1 ]. These features are wiely use for ifferet kis of images. Now we will explore the efiitios a backgrou eee to uersta the computatio of GLCM. 2.1. Costructio of the Traitioal Co-occurrece Matrices Let I be a give grey scale image. Let N be the total umber of grey levels i the image. The Grey Level Co-occurrece Matrix efie by Haralick is a square matrix G of orer N, where the (i, j) th etry of G represets the umber of occasios a pixel with itesity i is ajacet to a pixel with itesity j. The ormalize co-occurrece matrix is obtaie by iviig each elemet of G by the total umber of co-occurrece pairs i G. The ajacecy ca be efie to take place i each of the four irectios (horizotal, vertical, left a right iagoal) as show i figure1. The Haralick texture features are calculate for each of these irectios of ajacecy [10]. Figure 1. The four irectios of ajacecy for calculatig the Haralick texture features The texture features are calculate by averagig over the four irectioal co-occurrece matrices. To exte these cocepts to -imesioal Eucliea space, we precisely efie grey scale images i -imesioal space a the above metioe irectios of ajacecy i -imesioal images. 2.2. Geeralize Gray Scale Images I orer to exte the cocept of co-occurrece matrices to -imesioal Eucliea space, a mathematical moel for the above cocepts is require. We treat our uiversal set as Z. Here Z =Z x Z x x Z, the Cartesia prouct of Z take times with itself. Where, Z is the set of all itegers. A poit (or pixel i Z ) X i Z is a -tuple of the form X=(x 1,x 2,,x ) where xi Z i = 1,2,3.... A image I is a fuctio from a subset of Z to Z. That is f : I Z where I Z. If X I, the X is assige a iteger Y such that Y = f ( X ). Y is calle the itesity of the pixel X. The image is calle a grey scale image i the -imesioal space Z. Volumetric ata [11] 3 ca be treate as three imesioal images or images i Z. 2.3. Geeralize Co-occurrece Matrices Cosier a grey scale image I efie i Z. The gray level co-occurrece matrix is efie to be a square matrix G of size N where, N is the N be the total umber of grey levels i the image. the (i, j) th etry of G represets the umber of times a pixel X with itesity value i is separate from a pixel Y with itesity value j at a particular istace k i a particular irectio. where 152

Iteratioal Joural of Computer Sciece, Egieerig a Iformatio Techology (IJCSEIT), Vol.2, No.2, April 2012 the istace k is a oegative iteger a the irectio is specifie by = ( 1, 2, 3,..., ), where {0, k, k} i = 1, 2,3,...,. i 3 As a illustratio cosier the grey scale image i Z with the four itesity values 0, 1, 2 a 3. The image is represete as a three imesioal matrix of size 3 3 3 i which the three slices are as follows. 0 0 1 0 1 2, 0 2 3 1 2 3 0 2 3 0 1 2 a 1 3 0 0 3 1 3 2 1 The three imesioal co-occurrece matrix 4 4 matrix G for this image i the irectio = (1,0,0) is the G 1 3 2 1 0 0 3 1 = 0 1 0 3 1 1 1 0 Note that G 1 0 0 1 3 0 1 1 = = G ' 2 3 0 1 1 1 3 0 It ca be see that X + = Y, so that G = G ', where G ' is the traspose of G. Hece G + G is a symmetric matrix. Sice G = G ', we say that G a G are epeet (or ot iepeet). Therefore the irectios a are calle epeet or ot iepeet. Theorem: If X Z, the umber of iepeet irectios from X i Z is 3 1. 2 Proof: Suppose X Z. If Y Z is such that X+=Y, where = ( 1, 2, 3,..., ). We kow that i {0, k, k}, if the istace betwee X a Y is k. So we ee to cout the umber of possibilities for formig the irectio. There are positios 1,..., 2, 3, each of which ca be fille usig ay of the three umbers 0, k or k. This ca be oe i 3 ways by multiplicatio priciple. Whe all the positios are fille usig 0, we have = (0,0,0,...,0) so that X+=Y implies X=Y. Therefore there are 3 1 irectios from X i which exactly half of the irectios are iepeet. Therefore there are 3 1 iepeet irectios from X i Z. 2 153

Iteratioal Joural of Computer Sciece, Egieerig a Iformatio Techology (IJCSEIT), Vol.2, No.2, April 2012 If two irectios are iepeet, the correspoig co-occurrece matrices are trasposes of each other. The above theorem iicates that the umber of possible co-occurrece matrices for a -imesioal image is 3 1. 2 2.4. Normalize Co-Occurrece Matrix Cosier Let 1, which is the total umber of co-occurrece pairs i i j N= G (i,j) GN ( i, j) = G ( i, j). N G. GN is calle the ormalize co-occurrece matrix, where the (i, j)th etry of GN ( i, j ) is the joit probability of co-occurreces of pixels with itesity i a pixels with itesity j separate by a istace k, i a particular irectio. 2.4. Trace I aitio to the well kow Haralick features such as Agular Seco Momet, Cotrast, Correlatio etc. liste i [1], we efie a ew feature from the ormalize co-occurrece matrix, which ca be use to ietify costat regios i a image. For coveiece we cosier =2, so that the image is a two imesioal grey scale image a the ormalize co-occurrece matrix becomes the traitioal Grey Level Co-occurrece Matrix. Figure 2. Sample images take from Broatz texture album Cosier the images take from the Broatz texture album give i figure 2. The majority of the ozero etries of the co-occurrece matrices lie alog the mai iagoal [12] so that we treat the trace (sum of the mai iagoal etries) of the ormalize co-occurrece matrix as a ew feature. Trace of GN ( i, j ) is efie as Trace = i GN (, ) i i From the efiitio of the co-occurrece matrix, it ca be see that a etry i the mai iagoal is the (i, i) th etry. This implies two pixels with the same itesity value i occur together. Thus higher values of trace implies more costat regio i the image. The compute values of the trace of the ormalize co-occurrece matrices i Figure 2 with k=1 are 0.0682, 0.2253 a 0.2335 for the left, mile a right images respectively. Obviously the left image cotais less 154

Iteratioal Joural of Computer Sciece, Egieerig a Iformatio Techology (IJCSEIT), Vol.2, No.2, April 2012 amout of costat regio a the other two images cotai almost the same amout of costat regios. The value of the trace iicates the same. 3. METHODOLOGY Here we preset the use of trace i cotet base image retrieval. The goal of image retrieval is to compare a give query image with all potetial target images i orer to obtai umerical measures of their similarity with the query image. Our atabase cotais 333 images take from the Broatz texture album which cotais 36 classes, each class cosistig of 9 images. Retrieval results are evaluate by calculatig average precisio. Precisio is the proportio of retrieve images that are relevat to the query. 3.1. Image Retrieval Usig Trace The umerical value of trace provies oly a measure of the amout of costat regio i a image. Thus we ivie the mai iagoal etries of the co-occurrece matrix ito four equal parts a the sum of the elemets i each quarter is take to be a measure of the image texture feature for image retrieval, givig a four imesioal vector. The atabase is querie usig the first a the fourth images from all the 36 ifferet classes. Eight images are retrieve i each ru. The average precisio is fou to be 0.8194. Figure3. Scree shots of the output for the same query image usig the trace features (left) a the Haralick features (right) 3.2. Compariso of Results with Haralick features Couctig the same experimet usig the well kow Haralick features Cotrast, Correlatio, Eergy a Homogeeity we obtai a average precisio of 0.7222. Here also we use a four imesioal feature vector for queryig the atabase. This is a clear iicatio of the improvemet of performace usig the propose features. 155

Iteratioal Joural of Computer Sciece, Egieerig a Iformatio Techology (IJCSEIT), Vol.2, No.2, April 2012 4. CONCLUSION This paper illustrates the possible theoretical extesios of Grey Level Co-occurrece Matrices. The use of trace i texture aalysis is fou to be promisig. Trace itself ca be use as a feature which outperforms the Haralick features. Trace combie with Haralick features provies better results. Oly oe thir of the images from Broatz texture atabase are use for testig. Our future work is to ivestigate the performace of trace with the complete set of images i the atabase. Trace extracte from three imesioal images is also to be ivestigate. The use of the theoretical evelopmets to -imesioal Eucliea space ee to explore. REFERENCES [1] R. Haralick, K. Shamugam, a I. Distei, (1973) Textural Features for Image Classificatio, IEEE Tras. o Systems, Ma a Cyberetics, SMC 3(6):610 621 [2] R. M. HARALICK, (1979) Statistical a structural approaches to texture, Proc. IEEE, pp. 786-804, May 1979 [3] T. Ojala, M. Pietikaie, T. Maepaa, (2004) Multiresolutio Gray-Scale a Rotatio Ivariat Texture Classificatio with Local Biary Patters, IEEE. Tras. O Patter aalysis a Machie itelligece, Vol.24 [4] M. H. Bharati, J. Liu, J. F. MacGregor, (2004) Image Texture Aalysis: methos a comparisos, Chemometrics a Itelliget Laboratory System,s Volume 72, Issue 1, Pages 57-71 [5] J. Zhag, T. Ta,(2002) Brief review of ivariat texture aalysis methos, Patter Recogitio 35, 735-747 [6] Tou, J. Y., Tay, Y. H., & Lau, P. Y. (2009). Recet Tres i Texture Classificatio: A Review. Proceeigs Symposium o Progress, i Iformatio a Commuicatio Techology 2009 (SPICT 2009), Kuala Lumpur, pp. 63-68. [7] T. Dacheg, L. Xuelog, Y. Yua, Y. Neghai, L. Zhegkai, a T. Xiao-ou.(2002) A Set of Novel Textural Features Base o 3D Co-occurrece Matrix for Cotet-base Image Retrieval, Proceeigs of the Fifth Iteratioal Coferece o Iformatio Fusio, volume 2, pages 1403 1407 [8] V. Kovalev a M. Petrou, (1996) Multiimesioal Co-occurrece Matrices for Object Recogitio a Matchig, Graph. Moels Image Processig, vol. 58, o. 3, pp. 187 197 [9] K. Hammouche, (2008) Multiimesioal texture aalysis for usupervise patter classificatio, Patter Recogitio Techiques, Techology a Applicatios, pp 626 [10] F. I. Alam, R. U. Faruqui, (2011) Optimize Calculatios of Haralick Texture Features, Europea Joural of Scietific Research, Vol. 50 No. 4, pp. 543-553 [11] A. S. Kurai, D. H. Xu, J. Frust, (2004) Co-occurrece matrices for volumetric Data, The 7th IASTED Iteratioal Coferece o Computer Graphics a Imagig - CGIM 2004, Kauai, Hawaii, USA [12] A. Eleya, H. Demirel, (2009) Co-Occurrece base Statistical Approach for Face Recogitio, Computer a Iformatio Scieces 156

Authors Iteratioal Joural of Computer Sciece, Egieerig a Iformatio Techology (IJCSEIT), Vol.2, No.2, April 2012 Bio Sebastia V, bor i 1975 receive his M. Sc egree i Mathematics a M. Tech egree i Computer a Iformatio Sciece from Cochi Uiversity of Sciece a Techology, Cochi, Iia i 1997 a 2003 respectively. He is curretly workig with Mar Athasius College, Kothamagalam, Kerala, Iia, as a Assistat Professor i the Departmet of Mathematics. He is pursuig for his Ph. D egree i the Departmet of Computer Applicatios, Cochi Uiversity of Sciece a Techology Dr. A Uikrisha, Grauate from REC (Calicut), Iia i Electrical Egieerig(1975), complete his M. Tech from IIT, Kapur i Electrical Egieerig(1978) a PhD from IISc, Bagalore i Image Data Structures (1988). Presetly, he is The Associate Director Naval Physical a Oceaographical Laboratory, Kochi which is a premiere Laboratory of Defece Research a Developmet Orgaisatio. His fiel of iterests iclue Soar Sigal Processig, Image Processig a Soft Computig. He has authore about fifty Natioal a Iteratioal Joural a Coferece Papers. He is a Fellow of IETE & IEI, Iia. Dr. Kaa Balakrisha, bor i 1960, receive his M. Sc a M. Phil egrees i Mathematics from Uiversity of Kerala, Iia, M. Tech egree i Computer a Iformatio Sciece from Cochi Uiversity of Sciece & Techology, Cochi, Iia a Ph. D i Futures Stuies from Uiversity of Kerala, Iia i 1982, 1983, 1988 a 2006 respectively. He is curretly workig with Cochi Uiversity of Sciece & Techology, Cochi, Iia, as a Associate Professor i the Departmet of Computer Applicatios. Also he is the co ivestigator of Io-Sloveia joit research project by Departmet of Sciece a Techology, Govermet of Iia. He has publishe several papers i iteratioal jourals a atioal a iteratioal coferece proceeigs. His preset areas of iterest are Graph Algorithms, Itelliget systems, Image processig, CBIR a Machie Traslatio. He is a reviewer of America Mathematical Reviews a several other jourals. 157