Mixture Models and the Segmentation of Multimodal Textures. Roberto Manduchi. California Institute of Technology.

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1 Mxture Models and the Segmentaton of Multmodal Textures oberto Manduh Jet ropulson Laboratory Calforna Insttute of Tehnology asadena, CA Introduton Abstrat Aproblem wth usng mxture-of-gaussan models for unsupervsed texture segmentaton s that a \multmodal" texture (suh as an often be enountered n natural mages) annot be wellrepresented by a sngle Gaussan luster. We propose a dvde-and-onquer method that groups together Gaussan lusters (estmated va Expetaton Maxmzaton) nto homogeneous texture lasses. Ths method allows to suesfully segment even rather omplex textures, as demonstrated by expermental tests on natural mages. Algorthms for mage segmentaton an be roughly dvded nto two ategores: those that use statstal models for desrbng the behavor of vsual features, and those that only requre some measure of \smlarty" between features [9][11]. eent graph uttng tehnques [10] are an nstane of the latter. These algorthms partton a graph desrbng the nterrelaton between mage pxels by mnmzng a sutable funtonal of the related \anty matrx". The entry of the anty matrx at poston ( m; n)saom- bnaton of the derene n appearane between the m-th and the n-th pxels and of ther dstane n the mage plane. Thus, these approahes seamlessly ntegrate spatal and appearane oherene n a elegant and general framework. Unfortunately, handlng relatonal graphs bult from all the pxels n an mage s very hallengng n terms of memory and omputatonal power even for moderate sze mages (e.g., pxels), therefore heavy mage subsamplng s n order. Statstal tehnques stand on the other sde of the 1 spetrum. They assume that mage features obey a probablst model, and approah segmentaton as a 1Statstal and graph-theoret tehnques are not neessarly dsont. For example, one may use knowledge about lass statsts to desgn more eetve dstane metrs for use n the anty matrx. general lusterng problem, drawng on lassal results of pattern reognton. Bayesan approahes maxmze the probablty that a pont harater- x zed by the mage feature ( x) belongs to the luster,.e., ( ( x)). Interdependene among nearby pxels s taken nto aount, for example, by means of Markov andom Feld models. An advantage of statstal tehnques s that the nal segmentaton s \soft", beng expressed n terms of posteror probabltes. Ths faltates ntegraton wth other vsual features and/or wth a pror, \supervsed" nformaton [6]. Ths paper proposes a smple statstal parametr tehnque for texture segmentaton. The statstal desrpton of textures has reeved muh attenton n reent years. Texture features ( x) are typally extrated from the output of a set of saled/orented lters, whh are supposed to apture loal salent nformaton n the neghborhood of eah magepont. Several non-parametr tehnques an be found n the lterature for estmatng the margnal denstes p( ( x)) n the ase of homogeneous textures [8][][5]. arametr mxture models are the framework of hoe for segmentaton. These models assume that a feature s generated by one of possble proesses (\omponents"). The probablty densty funton of an thus be expressed by amxture dstrbuton p() ( p ) (1) 1 where p( ) s the ondtonal lkelhood of the feature generated by the omponent and ( ) s the pror probablty of the omponent (alled mxng parameter). The posteror probabltes ( ( x)) are derved straghtforwardly from the mxture model usng Bayes' rule, and are used for the nal segmentaton. ote that eah omponent of the model orresponds to exatly one mage segment. In the ontext of ths paper, mage segments are not nees-

2 Mxture models owe ther popularty n part to the exstene of an eent tehnque (the Expetaton- Maxmzaton algorthm) for the maxmum lkelhood parameters estmaton [7]. In ts smplest formulaton, the EM algorthm reles on two hypotheses: 1) a sutable model for the ondtonal lkelhoods s known, and ) the observed samples are statstally ndependent. ether of these hypotheses s vered n typal textures. The problem of sample ndependene 3 s farly well understood; extensons of the EM algorthm that use MF modelng of the lass label dstrbuton have been proposed [15][14]. In ths paper we takle the rst problem, the determnaton of a statstal model for feature generaton wthn eah texture lass, orgnatng our argument from the observaton that smple Gaussan models are nadequate to desrbe \multmodal" textures, suh as an be often enountered n prate. Mxture of Gaussans are the most ommon nstane of mxture models, one reason beng that Gaussan ondtonal lkelhoods allow for the E- and M- steps of the EM algorthm to be solved n losed form [7]. Eah Gaussan luster represents a \mode" of the mxture dstrbuton. Malk et al. [3] all the luster enters \textons" and use them for ompat texture representaton (va vetor quantzaton). Our man pont here s that t s often neessary to use more than one Gaussan luster to represent an homogeneous texture feature dstrbuton. For example, onsder the 4 mage of Fgure 1(a), omposed by the uxtaposton of a Brodatz texture and of the same texture rotated by 45. In ths smple experment, we used a bank of Gabor lters at four orentatons to extrat texture features. It s easy to onvne oneself that the feature dstrbuton n eah texture path s bmodal, due to the two presene of two prnpal orentatons. Therefore, a -omponents mxture-of-gaussans model fals to represent the whole sene gvng, for example, the norret segmentaton of Fgure 1 (note that, due to the symmetry of the dstrbutons n orentaton spae, there are other possble statonary ponts the algorthm may onverge to, nludng the \orret" one). To deal wth multmodal textures lke the one n Fgure 1(a), we propose an unsupervsed dvde-andonquer strategy. Frst, extrat a sutable number of sarly (and usually are not) onneted. 3There are atually two knds of dependeny, one onernng the underlyng lass label dstrbuton, and the other onernng the feature dstrbuton wthn eah lass[15]. 4Of ourse, one may argue that four homogeneous textures an be seen n the sene, dependng on the sale of the observaton wndow used. (a) mxture omponents usng the EM algorthm; then, group together those lusters whh are lkely to belong to the same texture. For example, n Fgure 1 we show the EM segmentaton usng sx Gaussan omponents. By sutably groupng these omponents nto two sets, we obtan the orret segmentaton of Fgure 1. In ths ase, eah texture s desrbed by a mxture of three Gaussans. How an we estmate the orret assgnments luster{texture? Our algorthm determnes a ost funton of luster groupng that keeps spatal oherene nto aount. A smple, non-teratve tehnque allows us to determne the luster groupngs that mnmze suh funton, and the nal Bayesan assgnment s performed based on the new ombned posteror dstrbuton. esults on natural textured sene show the eetveness of the proposed method. Multmodal texture segmentaton.1 roblem statement Our strategy for segmentng multmodal textures s based on \groupng together" some of the omponents of a gven mxture model. More presely, onsder a partton fi 1;:::;I^g of the dsrete set I f1 ;:::;g. Let p^( k) 1 Ik Ik Ik ^( k) Fgure 1: (a): Orgnal mage. Inorret segmentaton usng a mxture of two Gaussans. Segmentaton wth sx Gaussan lusters. Segmentaton nto two texture lasses, eah one of whh s represented by a mxture of three Gaussan lusters. p( ; ) ()

3 We an rewrte (1) as ^ k1 The ndex k n (3) labels the derent texture lasses n the sene; the ndex n () enumerates the lusters wthn eah texture lass. A feature s assgned k k p to the texture that maxmzes ^( )^( k) I p( ). It s mportant to note that, n general, the set of pxels that are assgned to a lass k k by means of (3) s not the unon of the sets of pxels assgned to the lasses f Ikg: groupng together lusters determnes new Bayesan assgnments that are not trvally derved from the orgnal ones. As antpated n the Introduton, we wll determne the groupngs n (3) by explotng the spatal oherene of the lass assgnment funton. More presely, we observe that the posteror probabltes k( 1( x)) and k( ( x)) for two lusters 1 and belongng to the same texture k are typally spatally orrelated. They an assume hgh values ( 1) only n mage areas orrespondng to the same texture; for homogeneous textures, t s reasonable to assume that, wthn a \wndow of observablty" of sutable sale, we wll normally nd both pxels assgned to luster 1 and pxels assgned to luster. Ths noton s exploted n the ontext of the reently proposed maxmum desrptveness rteron [6] for groupng \redundant" lusters n a mxture model. We rst dsuss the maxmum desrptveness rteron, referrng the reader to [6] for more detals. We then show ts applaton n the ontext of ths work.. Model desrptveness Consder a mxture model wth densty p()ex- pressed by (1). The desrptveness D of the model [6] s dened by 1 p() ^( k)^( p k) (3) Z D D ; D p( ) ( ) d (4) where the posteror probabltes ( ) are derved from (1) usng Bayes' rule: ( ) ( p p ) (). Let us examne eah term of the sum n (4). The - th luster \desrbes" eah feature by means of the ondtonal lkelhood p( ). The posteror probablty ( ) spees n a \soft" fashon whh features are atually assgned by the model to the -th luster. Thus, the ntegrals n the sum determne how well eah luster desrbes the features that are assgned to t. It s easly seen that models wth \hard" assgnment rules have the hghest desrptveness (whh an only be less than or equal to ). Models wth hghly overlappng denstes p( )have smaller desrptveness for the same number of lasses. The lowest value of the desrptveness ( D1) s aheved when all of the ondtonal lkelhoods are dental. Avery useful property of the desrptveness s that t an be easly estmated: a smple applaton of Bayes' rule proves the followng dentty: D 3 E ( ) where E[ 1] s the expetaton omputed wth respet to the densty p(). Thenumerator of eah term (5) an thus be estmated by smply averagng ( ( x)) over the mage. The denumerator s estmated by averagng ( ( x)) over the mage. For our purposes, the desrptveness of a model s not used by tself; t s ts varaton when two ormore lusters are grouped together whh sofnterest to us. Suppose that a new model s generated by groupng two lusters (say, lusters and ) nto a new \superluster" [ aordng to the followng rules: ( [ ) ()+ () ( [ ) ( )+ ( ) ( ) ( ) p ( [ ) p ( ) + p ( ) ( )+ ( ) ( )+ ( ) (6) ote that the ondtonal lkelhood dened n the last row of (6) s suh that the densty p( ) dened by the model does not hange: our groupng operaton (whh s equvalent to (3)) s purely formal. However, the model desrptveness D wll hange (n general) as an eet of luster groupng. Indeed, t an be shown that the model desrptveness D may only derease or reman unhanged when two or more lusters are grouped together. The desrptveness dereases the most when lusters wth well-separated ondtonal dstrbutons are grouped together, whle hghly overlappng dstrbutons an be grouped wth lttle desrptveness loss. To dede whh lusters should be grouped together nto a super-luster as by (6)(or(3))nor- der to redue the number of texture lasses, we may look at the orrespondng model desrptveness derement 1 D. The ntuton s that lusters whh are hghly overlappng n feature spae (small 1 D) are the \safest" hoe for groupng. Thus, we should hoose the luster groupng sheme that yelds the smallest value of 1 D. We wll all ths strategy the maxmum desrptveness rteron. A fast sub-optmal tehnque for mnmzng the desrptveness loss over luster groupngs has been proposed n [6]. Ths al- (5)

4 gorthm greedly groups two lusters at a tme, eah ntutve ustaton of suh a rteron s provded tme mnmzng 1 D. by the followng observaton. Let us rewrte equaton There s an nterestng nterpretaton of the desrptveness whh wll be useful for our work. Suppose we D^ H( ) 0 EH [ ( ( ))] (11) (10) as are groupng together two lusters of ndes and. Then, from (5) and (6) we have that where now the expetaton s omputed over the densty p( ), and H( 1) s the entropy operator. Maxmzng ^ orresponds to mnmzng [ ( ( ))] (whh E D EH 1 D D D () [ ( ) ( )] + + represents the mean \softness" of posteror assgnment), whle at the same tme maxmzng the entropy (7) The last term n the sum above s the ross-orrelaton of the dstrbuton of the prors. Thus, our rteron favors models haraterzed by \hard" assgnments and between the two dstrbutons, normalzed wth respet to the average of the orrespondng prors. Thus, homogeneous pror dstrbuton. for gven luster desrptveness D, D and pror probabltes, ( ), the two lusters wll determne a ng ths mutual nformaton rteron are often less Expermental tests have shown that the results us- large 1D when grouped together f the two orrespondng dstrbutons are unorrelated. Sne these those obtaned wth the desrptveness rteron de- onvnng from a \pereptual" pont of vew than dstrbutons are atually a funton of the spatal poston x of the features ( x), wemay use the sgnal perature" of the orgnal lusterng algorthm, the ensrbed n Seton.. Indeed, dependng on the \tem- proessng denton of ross-orrelaton as a funton tropy of the pror dstrbuton may domnate the sum of the dsplaement : n (11), n whh ase ths rteron smply tres to make the dstrbuton of the prors as unform as pos- C E x x and rewrte the last term of (7) as 0. C(0) + ( )..1 Comparson wth a rteron based on mutual nformaton D ( ) [ ( ( )) ( ( + ))] (8) Equaton (4) may be rewrtten as follows: Z 1 p ( ;) p d E p ( ; ) () () p() where now the expetaton s omputed over the ont densty p ( ;). Equaton (9) suggests another rteron for luster groupng, based on the maxmzaton of the followng funtonal: D^ E p ( ;) log p() Here D^ s the Kullbak-Lebler (K-L) dvergene between the ont densty p ( ;) and the produt of the margnal densty p( ) and of the mass dstrbuton,whh an be onsdered a generalzed form of mutual nformaton. Thus, D^ represents the expeted dependene between the observed data and the underlyng generatve model. Beng a K-L dvergene, D^ s always non-negatve; t s shown n the Appendx that D^ never nreases when two lusters are grouped together. Hene, we mayhoose to group together those lusters whh yeld the smallest derement ofd^. An (9) (10) sble..3 Cluster-texture assgnment Our goal s to nd a rteron that tells us when two lusters belong to the same texture, so that we an group them together as n (3). The maxmum desrptveness rteron desrbed n the prevous seton s not helpful f appled dretly to the posteror probabltes ( ): two derent lusters belongng to the same texture lass may bewell separated n feature spae, as n the ase of Fgure 1. Instead, we propose to apply the same rteron to the spatally ltered versons of the posteror probabltes. The ntuton behnd ths strategy s the followng. As observed earler, we expet that the posteror dstrbutons for derent lusters belongng to the same texture should be spatally orrelated. By spatally smoothng these dstrbutons, we expet that a pont that was assgned wth hgh probablty to ust one luster wll now be softly assgned to a number of lusters belongng to the same texture. Cluster groupng s then determned by applyng the maxmum desrptveness algorthm to the smoothed posteror dstrbutons. ote that ths proedure s used only to nd the orrespondene luster-texture: the nal segmentaton s operated usng the model (3),.e., based on non-ltered dstrbutons (see Fgure ). We nowgve a more thorough ustaton of our method. Let gx ( ) be an sotrop Gaussan kernel of sutable sale, normalzed to unt area. Let ( x) ( ()) t g( x0 t) dt be the ltered verson of the posteror dstrbuton ( ( x)) (we dropped

5 Orgnal mage Flter bank Texture features Expetaton Maxmzaton (a) Smoothng Cluster-texture assgnment osteror dstrbutons Cluster groupng { Ik ( )} osteror dstrbutons { k ( ) } Fgure 3: (a): \Zebras" mage. : Segmentaton usng three lusters. Segmentaton usng eght lusters. : Segmentaton nto thee texture lasses by luster groupng. Fgure : Sheme of our strategy for luster groupng. The mages n the sheme refer to Fgure 1. the dependeny on beause now ( x) s a funton of a whole ensemble of features n a neghborhood of x). Sne gx ( ) has unt area, t s easly proved that ( x) for 1 s stll a mass dstrbuton 3 for eah x.furthermore, ( ) E ( x). ow, onsder the ross-orrelaton funton Z 3 C E x x C C xg0xdx where C( x) was dened n (8) and gx ( ) gtgt () ( 0 xdx ) (note that gx ( ) s a unt-area Gaussan kernel wth standard devaton ). Therefore, C (0) s a weghted average of the values of the ross{ orrelaton between the -th and the -th posteror dstrbutons wthn a neghborhood of radus proportonal to (whhwe wll all the observaton wndow). ow onsder the derement of desrptveness 1D onsequent to groupng two lusters and after spatal smoothng: 1D D ( ) ( ) ( ( + ) (1) It s easy to prove that ( ) ( )( ) (13) D + + C (0) (14) From (14) we mantan that, for gven ( ( x)), ( ( x)) and prors,,thevalue 1D depends on the degree of loal spatal orrelaton between the two posteror dstrbutons. Thus, the maxmum desrptveness algorthm appled to the smoothed dstrbutons wll orretly determne whh luster posteror dstrbutons best orrelate, and wll group them together nto ommon texture lasses. An nstane of applaton of the proposed algorthm s shown n Fgure 1; more examples are desrbed n the next seton..4 Experments We present here the segmentaton results usng our method on three real-world textured mages: the \Zebras" mage (Fgure 3(a)), the \Cheeta" mage (Fgure 4(a)) and the \ebbles" mage (Fgure 5(a)). The vetors formed by the magntude of the output of omplex Gabor lters at three sales and four orentatons have been used as texture features. The Gaussan lter used to smooth the posteror dstrbutons for luster-texture assgnment had standard devaton 40, seven tmes larger than the standard devaton of the Gaussan envelope of the largest Gabor lter used. In both ases, we started wth a mxture model omposed by eght Gaussan lusters. Ths number has been hosen arbtrarly; valdaton mehansms for seletng a \sutable" number of lusters an be found n the lterature [1]. The EM algorthm was bootstraped wth ntal parameter values determned by a prevous K-means lusterng, and was stopped after twenty teratons.

6 (a) (a) Fgure 4: (a): \Cheeta" mage. : Segmentaton usng three lusters. Segmentaton usng eght lusters. : Segmentaton nto thee texture lasses by luster groupng. In passng, we note that nreasng the number of lusters redues the rsk of mssng global mnma n the EM teratons. A smple post-proessng tehnque [15] was used to enfore spatal oherene on the resultng multmodal posteror dstrbutons. Ths algorthm s n essene a \soft" verson of Besag's Iterated Condtonal Modes [1]; ts relaton to the mean eld theory s dsussed n [16]. The segmentatons relatve to the orgnal lusterngs nto eght lusters are shown n Fgures 3, 4 and 5. After luster groupng, we obtan the segmentatons of Fgures 3 and 4 (three texture lasses), and 5 (two texture lasses). For omparson, the dret EM segmentaton nto the same number of lasses s shown n Fgures 3, 4 and 5. In the ase of the \Zebras" mage, our algorthm suesfully segmented the strped regons orrespondng to the zebras (5 lusters), and alloated one texture lass ( lusters) to the grass and the large bush. Dret EM lusterng fals to segment the zebras nto one lass due to the large varane n orentaton and sale orrespondng to the dstntve strpes. In the ase of the \Cheeta" mages, we note that the shapes of the foreground branh and of the heeta have been dented (although not perfetly). Several small areas around the larger tree branh are mslassed due to ther smlarty wth the polka-dot texture on the heeta's skn. More remarkably, the luttered bakground has been segmented almost ompletely nto ust one lass, the unon of sx dstnt lusters. In the ase of the\ebbles" mage, one texture lass (1 3 Conlusons and dsusson Fgure 5: (a): \ebbles" mage. (: Segmentaton usng two lusters. Segmentaton usng eght lusters. : Segmentaton nto two texture lasses by luster groupng. luster) has been alloated to the haraterst surfae of some at roks n the sene. ote that the \bakground" texture lass ontans lusters orrespondng to dark and brght areas as well as to edge areas. In terms of mplementaton omplexty, we observe that the bulk of the omputaton s due to the EM teratons (for whh, however, aeleraton method exst [7]). The determnaton of the luster-texture assgnments takes a proportonally neglgble tme, usng the greedy maxmum desrptveness strategy of [6]. We presented a dvde-and-onquer strategy for texture segmentaton. The behavor of the texture features n the sene s rst modeled by a number of Gaussan lusters, estmated va Expetaton Maxmzaton. Then, seleted luster sets are grouped together to form texture lasses. Spatal orrelaton of the posteror luster dstrbutons s at the bass of our luster groupng rteron. Despte ts smplty, ths algorthm an model even omplex and multmodal dstrbutons, typal of natural outdoor mages. It s nstrutve to ompare our method wth other statst-based tehnques whh perform lusterng on parameter vetors obtaned by loal statstal analyss. Indeed, some of the earlest lter{based segmentaton algorthms [13][4] estmate the loal varane of the analyss lter outputs (by performng squarng followed by spatal smoothng) and use these values for

7 1 segmentaton. More reent varatons ompute loal hstograms of the lter outputs. Suh approahes are haunted by the problem of seletng an approprate sale of the analyss wndow, be t the standard devaton of the smoother or the sze of the regon used for omputng loal hstograms. The larger the analyss wndow, the more aurate the loal statsts, but the oarser the resoluton of the nal segmentaton. Our methods works dretly on the texture features, not on ther loal statsts. Of ourse, we needtoselet a sale for the \observaton wndow", but ths value does not aet the resoluton of the nal lass assgnment, whh s performed usng unsmoothed posteror dstrbutons. A drawbak of our tehnque s that lusters are grouped by the \hard" sheme of (). Ths an ause problems f the same luster appears n two ormore texture lasses. A more general groupng soluton, whh s the obet of urrent researh, would dene the mxture model (3) wth p k 1 k( ) p( ) 1 k ( ) ^ where k 0and k k 1. The parameters 1 fkg should be hosen so as to maxmze the resultng Appendx Aknowledgments ^( k) ^( ) model desrptveness. We wll prove that term D^ n (10) an never nrease f two lusters ( ; ) are grouped together as n (6). We have that k (15) 1D^ ( ) ( ) p() ( )log d + p() ( )log d0 ( ) ( )+ ( ) p()( ( )+ ( )) log d + ( ) ( )( ( )+ ( )) p() ( )log d+ ( ( )+ ( )) ( )( ( )+ ( )) p() ( )log d ( )( ( )+ ( )) p( ) p( ) p( )log d + p( )log d p( [ ) p( [ ) (16) Thus, 1D^ s a lnear ombnaton wth nonnegatve oeents of two Kullbak-Lebler dvergenes, and therefore t s always non-negatve. The work desrbed was funded by the TMOD Tehnology rogram and performed at the Jet ropulson Laboratory, Calforna Insttute of Tehnology under ontrat wth the atonal Aeronauts and Spae Admnstraton. eferene heren to any spe ommeral produt, proess, or serve by trade name, trademark, manufaturer, or otherwse, does not onsttute or mply ts endorsement by the Unted States Government or the Jet ropulson Laboratory, Calforna Insttute of Tehnology. eferenes [1] J. Besag. On the statstal analyss of drty ptures. J.. Statst. So. B, 48(3):59{30, [] J.S. De Bonet and. Vola. Texture reognton usng a non-parametr mult-sale statstal model. ro. IEEE CV, 641{647, Santa Barbara, June [3] J. Malk, S. Belonge, J. Sh, T. Leung. Textons, ontours and regons: ue ntegraton n mage segmentaton. ro. ICCV, 918{95, Kerkyra, [4] J. Malk and. erona. reattentve texture dsrmnaton wth early vson mehansms. Journ. Optal Soety of Amera, 7(5):93{93, May [5]. Manduh, J. ortlla. Independent omponent analyss of textures. ro. ICCV, 1054{1060, Kerkyra, [6]. Manduh. Bayesan fuson of texture and olor segmentatons. ro. ICCV, 956{96, Kerkyra, [7] G.J. MLahlan, T. Krshnan. The EM algorthm and extensons. John Wley and Sons, [8] K. opat and. ard. Cluster-based probablty model and ts applaton to mage and texture proessng. IEEE Trans. Image ro., 6():68{84, February [9] Y. ubner and C. Tomas. A metr for dstrbutons wth applatons to mage databases. ro. 6th ICCV, 59{66, Bombay, [10] J. Shy and J. Malk. ormalzed uts and mage segmentaton. ro. IEEE CV, 731{737, Santa Barbara, [11] J. Shy and J. Malk. Self{ndung relatonal dstane and ts applaton to mage segmentaton. ro. ECCV, 538{543, [1]. Smyth. Clusterng usng Monte Carlo ross{ valdaton. ro. Int. Conf. on Knowl. Ds. and Data Mn., 16{133, [13] M. Unser and M. Eden. Multresoluton feature extraton and seleton for texture segmentaton. IEEE Trans. att. Anal. Mah. Intell., (7), 717{78, [14] Y. Wess and E.H. Adelson. A uned mxture framework for moton segmentaton: norporatng spatal oherene and estmatng the number of models. ro. IEEE CV, 31{36, [15] J. Zhang, J.W. Modestno, and D.A. Langan. Maxmum-lkelhood parameter estmaton for unsupervsed stohast model-based mage segmentaton. IEEE Trans. Image ro., 3(4), 404{40, July [16] J. Zhang and J.W. Modestno. The mean{eld theory n EM proedures for Markov random elds. ro. IEEE ISIT, Budapest, 1991.