Comparison Study of Textural Descriptors for Training Neural Network Classifiers

Transcription

1 Comparson Study of Textural Descrptors for Tranng Neural Network Classfers G.D. MAGOULAS (1) S.A. KARKANIS (1) D.A. KARRAS () and M.N. VRAHATIS (3) (1) Department of Informatcs Unversty of Athens GR Athens Greece d.uoa.gr (3) Department of Mathematcs Unversty of 0 Patras Patras Greece vrahats@math.upatras.gr () Department of Busness Admnstraton Unversty of Praeus Greece Dakarras@ Abstract: - In ths paper the use o feedforward f neural networks n the characterzaton of mages by texture content s nvestgated. An n depth expermental study s conducted comparng several well known textural feature extracton technques along wth a novel dscrete wavelet transform based methodology. It s demonstrated that the new technque leads to the desgn and selecton o feedforward f neural networks archtectures wth the best texture classfcaton accuracy. Key-words: - Feature extracton texture classfcaton wavelet-based texture descrptors cooccurrence matrces gray level run length moments fractal dmenson statstcal texture analyss feedforward neural networks tranng. IMACS/IEEE CSCC'99 Proceedngs Pages: Introducton The problem of texture-based segmentaton and classfcaton of mages s of consderable nterest n many mage-processng applcatons lke remote sensng medcal magng and qualty control. Analyss of textures requres the dentfcaton of proper descrptors or features that dfferentate the textures n the mage for further segmentaton classfcaton and recognton. f Technques capable of producng approprate textural descrptors nclude smple statstcal measures of gray level dstrbuton measures of local densty or other gradent features the use of run lengths and the computaton of second order statstc lke s the cooccurrence matrce s [][3][8][1]. The emergence of the -D wavelet transform [7][10][13][14] as a popular tool n mage processng offers the ablty of robust feature extracton n mages. Due to ther strong localzaton propertes wavelets have been prov n to e be approprate for the descrpton of the textural nformato n the n mage provdng a rcher problem specfc-nformaton. Furthermore second order statstcal measures can be evaluated on the output of the D wavelet transformaton n order to create a more relable framework for the generaton of the textural descrptors [13]. In ths paper we propose a novel methodology for texture classfcaton of mages by examnng the dscrmnaton abltes of ther textural propertes. Besdes neural network classfers and the -D wavelet transform a c the tools utlzed n ths paper are the cooccurrence matrces the fractal dmenson and the gray level run length methods for textural feature extracton. The contrbuton of the paper les on the use of a novel texture descrptor for a classfcaton scheme based on Feedforward Neural Networks (FNNs ) and on the nvestgaton of the effects of dfferent textural descrptors on FN N learnng and generalzaton capabltes. The expermental study conducted n ths paper ams precsely at llustratng ths latter nvestgaton.

2 Textural Descrptors used In ths secton three wdely known feature extracton methods are brefly descrbed..1 The cooccurrence matrces Cooccurrence matrces [] represent the spatal dstrbuton and the dependence of the gray levels wthn a local area. Each ()th entry of the matrces represents the probablty of gong from one pxel wth gray level () to another wth a gray level () under a predefned dstance and angle. From these matrces sets of statstcal measures are computed (called feature vectors) for buldng dfferent texture models. In our experments we have consdered four angles namely as well as a predefned dstance of one pxel n the formaton of the cooccurrence matrces. Therefore we have formed four cooccurrence matrces. Accordng to our experments the followng four statstcal measures out of the 14 orgnally proposed by Haralck [][3] provde hgh dscrmnaton accuracy that can be only margnally ncreased by addng more measures n the feature vector: Energy - Angular Second Moment f 1 = p( ) Correlaton f = N N g g ( * ) p( ) xx y µ µ = 1 = 1 σxσy Inverse Dfference Moment 1 f 3 = 1+ p Entropy f 4 = - p( ) log p( ). Thus usng the above mentoned four cooccurrence matrces we have obtaned 16 features descrbng spatal dstrbuton n each wndow.. The run-length encodng descrptor The run length matrx P wth elements p() where the ()th dmenson corresponds to the gray level and has a length equal to the maxmum gray level n whle the ()th dmenson corresponds to the run length and has length equal to the maxmum run length l represents the frequency that () ponts wth a gray level () contnue n the drecton q [1]. As wth the cooccurrence matrx q = 0 ï 45 ï 90 ï and 135 ï offer the greatest nterest. Fve features can be calculated from the run length matrx as shown n the equatons below: Long Run Emphass p r 1 = ( ) p Short Run Emphass p r = ( ) p Gray Level Nonunformty r 3 = p( ) p ( ) Run Length Nonunformty r 4 = p( ) p ( ) Run Percentage p r 5 = N where N s the number of ponts n the mage. The run lengths are expected large for coarse textures especally structural textures but can be qute small for fne textures. The nonunformty features are

3 small when the gray levels or the run lengths are smlar throughout the matrx whle the long run length s large when there s hgh ntensty clusterng n the texture..3 The fractal dmenson The fractal dmenson s a feature that characterzes the roughness of an mage [8]. A well-known method for evaluatng the fractal dmenson s a varaton of the well-known box-countng procedure whch s effcent and accurate for texture classfcaton tasks [11]. Followng ths approach the grey-level mage s consdered as a 3-dmensonal space ( x y z) wth ( x y) denotng a -dmensonal locaton and ( z) denotng the grey level. Ths 3-dmensonal space s parttoned nto cubes of sze r r r. The poston of x y pxel the columns of the cubes vertcal to the plane s assgned as ( ) where ( ) = ( x r y r) and the boxes are enumerated from bottom to top. In every column ( ) the cubes k and l whch contan the mnmum and maxmum grey levels of the column respectvely are found. The fractal dmenson D s estmated through the least mean square lnear ft of log( N r ) aganst log( 1 r ) for dfferent values of r : ( N r ) D = log log / r ( 1 r ) The number N r s computed as N = n r where nr ( ) = l k + 1. It s possble that two mages of dfferent texture and dfferent optcal appearance have the same fractal dmenson. Thus the dscrmnaton capablty of the fractal dmenson n some cases s problematc. In order to allevate ths problem the fractal dmenson has been computed n the orgnal submage as well as n the frst two lower resoluton versons of the orgnal submage and the frst two sets of detal submages contanng hgher horzontal and vertcal frequency spectral nformaton. Decomposng the. orgnal mage through the dyadc wavelet transform [6] has produced the submages. The above feature extracton procedure s orgnally proposed n [4]. Followng ths technque seven-dmensonal tranng patterns can be created from each mage regon. 3 A Novel DWT Textural Descrptor The problem of texture dscrmnaton amng at labelng mage areas s consdered n the wavelet doman snce t has been demonstrated that dscrete wavelet transform (DWT) can lead to better texture modelng [13]. We use the popular -D DWT schemes [6][14] performng a one-level wavelet decomposton of the mage regons thus resultng n four wavelet channels. Concernng the wavelet decomposton of the mage regons among the one approxmate and the three detal wavelet channels 3 4 (frequency ndex) we have selected for further processng only the three detal channels whose varances are the largest snce they mght carry more nformaton than the approxmate one. A more sophstcated approach s proposed by applyng cooccurrence analyss to the three detal wavelet channels and extractng 3 16 = 48 relevant measures [13][14]. 3.1 The wavelet transform Wavelets offer a general mathematcal approach for herarchcal functon decomposton. Accordng to ths transformaton a functon whch can be a functon representng an mage a curve sgnal etc. can be descrbed n terms of a coarse level n addton wth detals that range from broad to narrow scales. Wavelets offer an novel technque for computng the levels of detal present under a framework that s based on a chan of approxmaton vector spaces {V L ( R ) Ζ } and a scalng functonφ such that the set of functons / { ( ) } φ t k : k Ζ form an orthonormal bass for V. These two components ntroduce a mathematcal framework presented by Mallat [6] and called multresoluton analyss.

4 A MultResoluton Analyss (MRA) scheme of L ( R ) can be defned as a sequence of closed subspaces {V L ( R ) Ζ } satsfyng the followng propertes : Contanment: V V L ; for all Ζ. 1 Decrease: lm V = 0.e. I V = for all N. Increase: lm V = Dlaton: > N L.e. UV = L for all N. < N u t V u t V 1 Generator: There s a functon φ V 0 whose translaton φ( t k: k Ζ) forms a bass for V 0. { } By defnng complementary subspaces W = V 1 V so that V 1 = V + W then we can wrte accordng to the ncrease property that L R = (1) W Ζ The subspaces W are called wavelet subspaces and contan the dfference n sgnal nformaton between the two spaces V and V 1. These sets contrbute to a wavelet decomposton of L. accordng to Eq.(1). 3. Selectng feature descrptors n the wavelet doman The problem of texture classfcaton amng at dscrmnatng among varous texture classes s consdered n both the tme and the wavelet doman snce t has been demonstrated that dscrete wavelet transform (DWT) can lead to better texture modellng [7]. In ths way we can better explot the well known local nformaton extracton propertes of the wavelet sgnal decomposton as well as the features of the wavelet denosng procedures [10]. It s expected that ths knd of nformaton consdered n the wavelet doman should be smooth due to the tme-frequency localzaton propertes of the wavelet transform. It s nterestng that only the -D Haar wavelet transform whch s consdered as a smple one compared wth the other wavelet bases has exhbted the expected and desred propertes. We have performed a one-level wavelet decomposton of the mages thus resultng n four wavelet channels. As already mentoned among the three channels 3 4 (frequency ndex) the one whose hstogram presents the maxmum varance whch s the channel that represents the most clear appearance of the changes between the dfferent textures has been selected for further processng. The subsequent step n the proposed methodology s to obtan mage wndows from the selected wavelet channel and the orgnal mage of dmensons M M and M M respectvely. Feature extracton s conducted by usng the nformaton that comes from the cooccurrence matrces []. Among the 14 statstcal measures orgnally proposed by Haralck [3] that are derved from each cooccurrence matrx we have consdered only four of them: angular second moment correlaton nverse dfference moment and entropy. These measures as experments ndcated provde hgh dscrmnaton accuracy that can be only margnally ncreased by addng more measures n the feature vector. Usng the above mentoned cooccurrence matrces 16 features descrbng spatal dstrbuton n each wndow n the wavelet doman have been obtaned. For each wndow n the mage of the selected wavelet channel a feature vector contanng 16 features that unquely characterzes t n the wavelet doman has been formed. For each such wndow a set of four features has been obtaned by calculatng the above four mentoned statstcal measures. Fnally these 48 dmensonal feature vectors form the nput vector of the neural classfer. 4 Comparatve Expermental Study A total of 1 Brodatz texture mages [1] of sze has been used. They are shown n Fgure 1. From each texture mage 10 submages of sze wth 56 gray levels depth were randomly selected and the feature extracton methods descrbed n Sectons and 3 have been appled. For each feature extracton method 30 smulaton runs have been performed usng FNNs wth 5 to 60 neurons n the hdden layer n order to fnd the archtecture wth the best average generalzaton capablty. The best avalable archtecture for each case s exhbted n Table 1.

5 functon evaluatons needed to reach the termnaton condton. It s worth notng that n practce the computatonal cost of a gradent evaluaton s consdered at least three tmes more than the cost of an error functon evaluaton. 100% of success has been acheved for the three algorthms n the tranng phase. Fgure 1. Twelve texture patterns obtaned by dgtzng mages found n the "Brodatz Album". Textures: For example an FNN wth 48 nput neurons 30 hdden and 1 output neurons wth sgmod actvaton functon and bas exhbted the best performance for the DWT dstrbuton estmaton method. Textural Descrptor FNN DWT dstrbuton estmaton Fractal dmenson BP MBP BPVS DWT Fractal dmenson Cooccurrence Run length Table. Average of gradent (frst lne n every row) and error functon evaluatons (second lne n every row). The generalzaton capablty of the 30 FNNs has been tested usng patterns from 0 submages of sze randomly selected from each mage. As shown n Fgure the three tranng algorthms exhbted the best generalzaton performance when traned wth DWT extracted patterns. In ths case an average performance of 99% has been reached. Note that the average performance of BPVS traned FNNs n all cases was the best. DWT Cooccurrence analyss Run length moments Table 1. The best avalable FNN archtectures. Fractal dmenson Run length moments Cooccurrence BPVS MBP BP The smulatons have been performed usng three batch tranng algorthms: the standard backpropagaton (BP) [9] the momentum back-propagaton (MBP) [9] and the back-propagaton wth varable stepsze (BPVS) [5]. Tranng termnated when the classfcaton error was less than 3%. Detals on the performance of the algorthms are presented n Table. The frst lne n every row contans the average number of gradent evaluatons and the second one the average number of error Average generalzaton performance (%) Fgure. Average generalzaton performance of the traned FNNs. Detaled generalzaton results for the BPVS traned FNNs are exhbted n Fgure 3. As shown by the number of msclassfed test patterns out of a set of 40 patterns from each feature extracton method the FNNs that have been traned wth DWT dstrbuton

6 estmaton patterns had better generalzaton capablty than all the others Number of msclassfed texture patterns out of 40 DWT Fractal dmenson Run length moments Cooccurrence Fgure 3. Number of BPVS traned FNNs wth respect to ther correspondng number of msclassfed test patterns for the four texture extracton methods. For example 7 FNNs traned wth DWT dstrbuton estmaton patterns msclassfed only 6 test patterns out of 40. On the other hand 18 FNNs traned wth Run length patterns msclassfed 8 test patterns out of 40. Note that one FNN traned wth DWT dstrbuton estmaton patterns acheved 100% classfcaton success.e. t exhbted 0 msclassfcatons. 5. Conclusons A novel DWT dstrbuton estmaton technque has been suggested for texture descrpton. Ths method along wth three other well known feature extracton technques have been comparatvely nvestgated n terms of ther effects on the tranng and generalzaton performance of the neural network component of a texture classfcaton scheme. The prelmnary results ndcate that the proposed approach s consderably relable for demandng applcatons. References: [1] Brodatz P. Textures-a photographc album for artsts and desgner Dover [] Haralck R.M. Shanmugam K. and Dnsten I. Textural Features for Image Classfcaton IEEE Trans. Systems Man and Cybernetcs [3] Haralck R.M. Statstcal and structural approaches to texture IEEE Proc [4] Karayanns Y.A. and Stourats T. Texture classfcaton usng the fractal dmenson as computed n a wavelet decomposed mage n Proc. IEEE Work. Nonln. Sgn. & Image Proc. Greece [5] Magoulas G.D. Vrahats M.N. and Androulaks G.S. Backpropagaton tranng wth varable stepsze Neural Networks [6] Mallat S. and Zhong S. Characterzaton of sgnals from multscale edges IEEE Trans. Pattern Analyss and Machne Intellgence [7] Meyer Y. Wavelets: Algorthms and Applcatons Phladelpha: SIAM [8] Pentland A.P. Fractal-based descrpton of natural scenes IEEE Trans. Pattern Analyss and Machne Intellgence [9] Rumelhart D.E. Hnton G.E. and Wllams R.J. Learnng Internal Representatons by Error Propagaton n D. E. Rumelhart and J. L. McClelland (eds.) Parallel Dstrbuted Processng: Exploratons n the Mcrostructure of Cognton MIT Press Cambrdge MA [10] Ryan T.W. Sanders D. Fsher H.D. and Iverson A.E. Image Compresson by Texture Modelng n the Wavelet Doman IEEE Trans. Image Processng [11] Sarkar N. Chaudhur B.B. An Effcent Approach to Estmate Fractal Dmenson of Textural Images Pattern Recognton [1] Sew L.H. Hodgson R.M. and Wood E.J. Texture measures for carpet wear assessment IEEE Trans. Pattern Analyss and Machne Intellgence [13] Unser M. Texture Classfcaton and Segmentaton Usng Wavelet Frames IEEE Trans. Image Processng [14] Wckerhauser M.V. Adapted Wavelet Analyss from Theory to Software IEEE Press 1994.