A PATTERN RECOGNITION APPROACH TO IMAGE SEGMENTATION
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1 1 THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Seres A, OF THE ROMANIAN ACADEMY Volume 4, Number 2/2003, pp A PATTERN RECOGNITION APPROACH TO IMAGE SEGMENTATION Tudor BARBU Insttute of Computer Scence, Iaş, Romana E-mal: tudcont@t.t.tuas.ro The obectve of the present paper s to descrbe a pattern recognton approach for mage segmentaton. Frst, n the ntroducton, we descrbe the general aspects of unformty and texture recognton. Then we provde a mean-based feature extracton approach for unformty analyss and a moment-based one for texture analyss. In the classfcaton stage we propose both supervsed and also unsupervsed clusterng algorthms. The graphcal results of our mplementatons are also presented. Key words: pattern recognton, classfcaton, mage segmentaton, unformty analyss, texture analyss Recommended by Hora-Ncola TEODORESCU, Member of Romanan Academy 1. INTRODUCTION Image pattern recognton represents an mportant computer vson doman, consstng of classfcaton of the patterns of a gven mage, based on varous smlarty crterons. In ths paper we consder the mage regons as patterns. The mage segmentaton task conssts of dvdng the nput mage n a number of dfferent obects called mage segments or clusters, such that all the pxels from a segment have a common property called smlarty crteron. There are varous segmentaton methods, such as the boundary-based approaches ([1],[2],[7],[8]), whch use edge-detecton for segments' extracton, or ampltude thresholdng approaches ([1],[2]). We have used a regon-based approach ([1],[2],[3]) wth an unformty or texture based smlarty crteron. A color mage, or a grayscale one, contans a fnte set of unform and texture regons. If there are no textures n the mage, t s called nontextured. An unform regon s composed from pxels wth closed values. For example, a connected set of pxels wth the same RGB value represents a unform blue, yelow (or other color) regon. A textured regon represents a specal case of unformty, based on the repetton of basc texture unts called texels. Frst our aproach decdes on the nput mage's type: textured or nontextured. Ths can be done nteractvely, the user decdng the type of the mage dsplayed on computer screen. Dependng on the mage's character and state several enhancement flterng actons ([1],[2],[3],[4]) are appled n the preprocessng state: mage smoothng, edge enhancement or contrast adustment. For the resulted enhanced mage, as the one n Fgure 1 (b), we have to solve a texture (or unformty) recognton problem: for each texture or unform pattern of the mage to fnd all ts occurences, whch means the clusterng of all mage regons n a proper number of categores, dependng on ther unformty or texture. In the fltered mage we can dstngush two textured regons and nne unform regons whch should be grouped n a number of classes. Ths work has contrbutons both n the feature extracton stage and also n the classfcaton stage. Our proposed moment-based approach states that a gven nput texture can be unquely descrbed by ts up to order three moments. In the classfcaton step we have developed a varant of VQ k - means supervsed algorthm and a varant of regon-growng unsupervsed method. We have performed a MATLAB mplementaton for the algorthms of the proposed approaches and have obtaned some graphcal results. In
2 Tudor BARBU 2 the next sectons we present the two man steps of the pattern recognton method ([1],[3],[10],[12]): feature detecton and pattern classfcaton. Fg.1 2. SOME FEATURES EXTRACTION APPROACHES For the unform regons case we have consdered a sngle characterstc value n the features vector. A regon R of a gven mage I ( R I ) s unform f the dfference between the greatest pxel value and the smallest pxel value s below a small enough chosen threshold, whch s equvalent wth: ( ) p R, p mean R < T, (1) where p s a pxel and T the chosen threshold. Therefore we use a mean-based unformty analyss approach. For each pattern (pxel) we have computed the mean of ts n n neghborhood and consder the obtaned value as a feature vector. The block dmenson n must have an odd value such that the current pxel can be ts center. We choose a greater or a smaller value for n dependng on the mage nose's amount and the unform regons' szes. If a certan amount of nose s stll present n the mage, one should choose an n value greater than 1 ( n 3). Otherwse, n the smooth mage case, n could be 1 (the feature set for a gven pxel s the pxel's value). The value of n could be set nteractvely by the user, but t should be chosen such that all the regons of nterest be preserved (a large n could delete the small unform regons). The patterns wth ther feature values are then passed to the classfcaton stage. Feature detecton s more dffcult for textured regons. Texture analyss has a long hstory, many approaches beng developed for texture dentfcaton, classfcaton and segmentaton. There are many texture retreval methods based on Gabor flterng([5],[9]) or multresoluton flterng technques such as the wavelet transform ([11]). There are also hstogram-based and boundary-based approaches ([1],[2],[3]) for texture analyss. We have used a moment-based approach ([1]) for texture features extracton. In the dscrete case f represents an N p + q th order moment wll be: M mage regon and ts ( ) M N x = 1 y = 1 ( x, y), p q m = x y f p, q = 0, 1,... p,q (2) We have an mportant result gven by the Moment Representaton Theorem: Image functon f s determned unquely by ts set of moments m, therefore a texture regon of nput mage s determned by p, q ts moments up to a gven order. For each pxel an n n neghborhood s consdered, as n the unform regons case, n 1 beng an odd number and the current pxel beng the center of the neghborhood. For ths n n regon a set of moments s computed and consdered as a feature vector. We have computed for each pxel ts neghborhood's moments up to order 3 :
3 3 A pattern recognton approach to mage segmentaton V = [ m, m, m, m, m, m, m, m, ] m We have used V as the features vector for texture clusterng but we have also tested the mean value of V whch gves smlar results and s more advantageous because of an easer mplementaton n the classfcaton stage and a shorter processng tme. (3) 3. CLASSIFICATION METHODS AND SEGMENTATION RESULTS Havng now a feature vector for each pxel of the mage (textured or not), pattern classfcaton can be done n a supervsed manner or n a nonsupervsed one. A supervsed learnng can be appled to a classfcaton problem f the number of classes s known and also the set of classes' prototypes or a tranng set are avalable. If no nformaton about classes s avalable or only a lttle s known about them (for example we know ther number only and do not have any tranng set), the problem requres an unsupervsed learnng. Frst we present our dstrbuton-free supervsed classfcaton approach based on a VQ ( Vector Quantzaton) method. We have proposed a VQ classfer and have developed a varant of the k - means algorthm for t. Let C,C,...,C be the classes, K beng the only nformaton we know about them, and 1 2 K x 1,..., x N be the obects we want to cluster. Ther feature vectors, V ( x ) 1, N order. Let v = mn V ( x ), v = max V ( x ), = 1, N, and ( v, v ) 1 K 1 2 d( v,v ) ths dstance to K 1 we obtan K equally spaced vectors, = are sorted n ascendng d the dstance between them. Dvdng 1 K v,v,...,v, beng the dstance 1 2 K k 1 V, for whch ths between 2 succesve vectors. For each, mn d( v,v ( x ) s computed and ( x ) mnmum Eucldean dstance s obtaned, s ncluded n the tranng set. The feature vector ( ) V s then elmnated from the avalable feature space and the reasonng s repeated untl tranng set wll contan K vectors. Ths method for obtanng the tranng feature vectors works not only n the mage segmentaton case but also n a general pattern classfcaton problem. For the mage clusterng problem the x x, = 1, N obects are the mage pxels, N beng the mage area, and V ( x ) are ther feature vectors. The number of classes K s set nteractvely by dsplayng the mage on the screen. We can obtan the tranng vectors va the descrbed approach but also we have tested an user nteractvely approach. The user can select K pxels rght--clckng K tmes on approprate dfferent unform or texture regons of the mage I (Matlab faclty), ther feature vectors workng as a tranng set. Wth ths set our k - means algorthm computes successfully the classes' prototypes, as can be seen below: For = 1 to K do 1. C : = {} t ; = 1, K beng the tranng vectors Repeat For = 1to K do mn d V x, mean C s obtaned 2. Fnd for whch ( ( ) ( ) If V ( x ) C then {poston change} 3. C := C { V ( x )}; 4. Fnd C l,l, such that ( x ) Cl 5. C : = C \ { V ( x )} ; l l V ;
4 Tudor BARBU 4 Untl no poston change {optmzaton crteron} The prototype feature vectors are the centrods of the C sets, = 1, N. The proposed optmzaton crteron s the condton that all the feature vectors are n the rght place and no more poston changes are needed. The algorthm realzes a supervsed classfcaton, the sets C beng the obtaned classes. For our mage segmentaton problem, C,C,...,C are classes of pxels. Dsplayng the result of ths classfcaton, 1 2 K the classes C appear as dsconnected regons, each of them represented by a dfferent color, as one can see below. We have nteractvely chosen K = 7 and a neghborhood dmenson n = 3. Fg. 2 As shown by Fgure 2, each class contans one or more mage obects havng the same unformty or texture and beng dsplayed wth the same color. The unformty recognton and texture recognton problems are therefore solved. For solvng the segmentaton problem too, the component obects of each class have to be extracted. Ths can be done consderng the pxels of each class, at a tme, as beng the mage foreground (settng them to 1 - whte) and the others as beng the background (settng them on 0 - black). The connected regons of each bnary mage bult ths way are then determned and each of them consdered as a segment (cluster) n the ntal mage. We present the segmentaton results n Fgure 3: 11 mage clusters have been obtaned, each of them marked by a dfferent color. Unsupervsed learnng (classfcaton) conssts of a natural groupng n the feature space. In unsupervsed clusterng the classes prototypes are not known and no tranng sets are used. Fg.3
5 5 A pattern recognton approach to mage segmentaton There are many unsupervsed learnng approaches for pattern recognton such as SOM (Self-- Organzng feature Maps) methods developed by Kohonen ([10]). We propose a regon - growng algorthm for classfcaton and provde two forms of t. In the frst case the number of classes s ntroduced nteractvely by the user, as n the supervsed case. Let consder K the classes' number and V the feature space. The next pseudocode presents the algorthm: For = 1 to K 1. C = { V ( x )} ; 2. C = {}; ndex = 1;{ C - helpng set}, Repeat 2. m : = number of C ' s (ntally N) ; For = 1 to m 1 For = 1 to m ( ) mn( mean( C ), mean( C ) If mean( C ), mean( C ) d = {smallest overall dst.} then 3. C( ndex ):= C C 1 1, 1 ; {regon mergng} 4. nc(ndex); For = 1 to ndex 1 5. C : = C() ; Untl m = K {optmzaton crteron} For our segmentaton problem the regons are the pxels at the begnnng. At each loop the most closed regons (whch have closest mean values) are merged n a new regon. The process contnues untl the optmzaton crteron s satsfed: regons' number equals the classes' number. We could obtan a more natural groupng f we elmnate the knowng of classes' number and therefore the user nteractvty. If the number of clusters s unknown our regon growng algorthm has to be modfed to work properly. At step 3 we ntroduce one more condton for the unfcaton of two classes: C and C are merged f d( ( C ), mean( C ) T mean <, where T s a threshold dependng on values from C and C. The optmzaton crteron s modfed too: Repeat... untl there are no more regons' unfcatons. We have tested as threshold a fracton of the mnmum between the compared means, therefore 1 T = mn( mean( C ), mean( C ). If the regons to be dscrmnated are very closed, α has a large value. α The results obtaned wth the unsupervsed technque are smlar wth those presented n Fgure 2, but the computng tme s larger because regon- growng algorthm has a hgher complexty than the k - means algorthm. The classes C, = 1, 7 represent not only classes of pxels but also classes of obects wth the same unformty or texture. For mage segmentaton the reasonng contnues as n supervsed case and we get smlar results wth those n Fgure CONCLUSIONS We have descrbed our pattern recognton method for the segmentaton of both textured and also nontextured mages and presented ts results. Our man contrbutons are the choosng of a proper moments' set whch gves a good texture descrpton and the development and mplementaton of the two descrbed clusterng algorthms.
6 Tudor BARBU 6 The results of ths paper could be succesfully appled n another mage recognton feld: the mage obects recognton. We wll present n our next work an obects recognton approach based on composng the detected unform and texture regons. REFERENCES 1. ANIL K. JAIN, Fundamentals of Dgtal Image Processng, Prentce--Hall Internatonal, Inc., Englewood Clffs New Jersey, WILLIAM K. PRATT, Dgtal Image Processng, John Wley and Sons, Inc, THEO PAVLIDIS, Algorthms for Graphcs and Image Processng, Computer Scence Press, Inc, JAN T. YOUNG, JAN. J. GERBRONDS, LUCAS J. VAN VLIET, Fundamentals of Image Processng, Tu-Delpht Interactve Course, B.S. MOUNJUNATH, W.Y. MA, Texture Features for Browsng and Retreval of Image Data, IEEE Transactons on Pattern Analyss and machne Intellgence, vol. 18, No. 8, August DENHSHENG ZHANG, GUOJUN LU, Enhanced generc Fourer descrptors for obect-based mage retreval, Internatonal Conference on Acoustcs, Speech and Sgnal Processng, TOLL, WILLIAM E., Pont Based Approaches n Graphcs, Ph. D. dssertaton, Computer Scence Department, Unversty of Kentucky, Lexngton, KY, B.S. MOUNJUNATH, W.Y. MA, Edge flow: a framework of boundary detecton and mage segmentaton, Proc. IEEE Internatonal Conference on Computer Vson and Pattern Recognton, San Juan, Puerto Rco, June 1997, pp JAN T. YOUNG, L. J. VAN VLIET, M. VAN GINKEL, Recursve Gabor flterng, IEEE Transactons on Sgnal Processng, Vol. 50, No. 11, , T. KOHONEN, Self-Organzng Maps, Sprnger Seres n Informaton Scences, Vol. 30, Sprnger, Berln, Hedelberg, New York, 1995, 1997, Thrd Extended Edton, 501 pages. ISBN , ISSN X 11. ANDREW LIAN, JIAN FAN, An Adaptve Approach for Texture Segmentaton by Multchannel Wavelet Frames, Center for Computer Vson and Vsualzaton, August RICHARD O. DUDA, Pattern Recognton for HCI, Department of Electrcal Engneerng San Jose State Unversty, Receved March 11,2003
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