An Active Contour Model Guided by LBP Distributions

Transcription

1 An Actve Contour Model Guded y LBP Dstrutons Mchals A. Savelonas, Dmtrs K. Iakovds, Dmtrs E. Marouls, and Stavros A. Karkans 2 Dept. of Informatcs and Telecommuncatons, Unversty of Athens, 5784, Athens, Greece rtsmage@d.uoa.gr 2 Dept. of Informatcs and Computer Technology, Lama Insttute of Technology, 3 rd Klometer, Old Natonal Road, 3500, Lama, Greece sk@telam.gr Astract. The use of actve contours for texture segmentaton seems rather attractve n the recent research, ndcatng that such methodologes may provde more accurate results. In ths paper, a novel model for texture segmentaton s presented, comnng advantages of the actve contour approach wth texture nformaton acqured y the Local Bnary Pattern (LBP) dstruton. The proposed LBP scheme has een formulated n order to capture regonal nformaton extracted from dstrutons of LBP values, characterzng a neghorhood around each pxel, nstead of usng a sngle LBP value to characterze each pxel. The log-lkelhood statstc s employed as a smlarty measure etween the LBP dstrutons, resultng to more detaled and accurate segmentaton of texture mages. Introducton The automatc segregaton of textures wthn mages s generally vewed as an essental frst step n varous vson applcatons, such as medcal mage analyss, ndustral montorng of product qualty, content-ased mage retreval and remote sensng. Because of ts wde applcalty, texture segmentaton has een the suject of ntensve research n many recent studes [-5]. However, no known approach s ale to consstently and accurately segment textured mages [6]. A commonly used strategy for texture segmentaton s to extract texture features on a pxel-y-pxel ass and then use some technque to segment the mage ased on the extracted features and potentally, on some addtonal spatal constrants. Overall qualty of texture segmentaton s determned y the qualty of oth texture features and the segmentaton technque. Early mage segmentaton approaches have een utlzng oundary-ased local flterng technques such as edge detecton operators, whch requre addtonal edgelnkng operatons n order to estalsh the connectvty of edge segments. Ths prolem has een resolved y employng actve contour models [7], whch drectly result

2 n contnuous curves. These models nvolve the deformaton of ntal contours towards the oundares of the mage regons to e segmented. A recent actve contour model, named Actve Contour Wthout Edges (ACWE) [8] has een ganng ncreasng nterest due to ts advantages: ) t s regon-ased, enalng the delneaton of regons defned y smooth ntensty changes, 2) ts level set formulaton provdes adaptalty to topologcal changes, and 3) t does not mpose any sgnfcant ntalzaton constrant [8]. However, n the scalar ACWE model the contour evoluton depends on the mage ntenstes rather than on the textural content of the mage to e segmented. Consequently, the scalar ACWE model cannot dscrmnate regons of dfferent textures that have equal average ntenstes. Latest advances n actve contour research focus on usng feature vectors to gude contour evoluton, as n the case of the extended ACWE model for vector-valued mages, proposed y Chan et al [9]. Wthn a texture segmentaton framework, such actve contour models use feature vectors that encode the textural content of an mage y means of features dervng from Gaor and wavelet transforms [5], [0-]. The Local Bnary Pattern (LBP) dstruton, ntroduced y Ojala et al. [2], offers an alternatve approach to spatal texture representaton. Unlke the Gaor features, whch are calculated from the weghted mean of pxel values over a small neghorhood, the LBP operator consders each pxel n the neghorhood separately, provdng even more fne-graned nformaton. In addton, the LBP texture features are nvarant to any monotonc change n gray level ntenstes, resultng n a more roust representaton of textures under varyng llumnaton condtons. Comparatve studes have demonstrated that the use of LBP dstrutons may result n hgher classfcaton accuracy than Gaor and wavelet features, wth a smaller computatonal overhead [2]-[4]. In ths paper we ntroduce a novel actve contour model for texture segmentaton guded y LBP dstrutons. Based on the fact that texture s a local neghorhood property, we have consdered usng regonal nformaton extracted from dstrutons of LBP values characterzng a neghorhood around each pxel, nstead of usng a sngle LBP value to characterze each pxel. In accordance wth [5], the smlarty etween the LBP dstrutons s estmated y means of the log-lkelhood statstc. Moreover, tme performance consderatons led us to reduce the length of the LBP dstrutons y lmtng the numer of pxels partcpatng n the estmaton of the LBP values, provded that the resultng LBP operator mantans adequate dscrmnatve capalty. The rest of ths paper s organzed n fve sectons. Secton 2 refly revews the formulaton of the LBP operator. The proposed actve contour model s presented n Secton 3. The results from ts applcaton on two-textured mages are apposed n Secton 4. Fnally, n Secton 5 the conclusons of ths study are summarzed. 2 The Local Bnary Pattern Operator We adopt the formulaton of the LBP operator defned n [5]. Let T e a texture pattern defned n a local neghorhood of a grey-level texture mage as the jont dstruton of the gray levels of P (P > ) mage pxels:

3 T t g g,..., g ) () = ( c, 0 P where g c s the grey-level of the central pxel of the local neghorhood and g p (p = 0,, P-) represents the gray-level of P equally spaced pxels arranged on a crcle of radus R (R > 0) that form a crcularly symmetrc neghor set. Much of the nformaton n the orgnal jont gray level dstruton () aout the textural characterstcs s conveyed y the jont dfference dstruton: T t g g,..., g g ) (2) ( 0 c P c Ths s a hghly dscrmnatve texture operator. It records the occurrences of varous patterns n the neghorhood of each pxel n a P-dmensonal vector. The sgned dfferences g p -g c are not affected y changes n mean lumnance; resultng n a jont dfference dstruton that s nvarant aganst gray-scale shfts. Moreover, nvarance wth respect to the scalng of the gray-levels s acheved y consderng just the sgns of the dfferences nstead of ther exact values: T t s( g g ),..., s( g g )) (3) ( 0 c P c where s ( x) = 0, x 0, x < 0 (4) For each sgn s(g p -g c ) a nomal factor 2 p s assgned. Fnally, a unque LBP P,R value that characterzes the spatal structure of the local mage texture s estmated y: P p (5) LBP P, R s( g p gc) 2 = p= 0 The dstruton of the LBP P,R values estmated over an mage regon comprses a hghly dscrmnatve feature vector for texture segmentaton [4-7]. 3 Actve Contour Model Guded y LBP Dstrutons The proposed actve contour model s nspred y the ACWE model for vector-valued mages [9], whch uses sngle pont nformaton to gude contour evoluton. In what follows, we frstly revew ths orgnal model and secondly we appose the formulaton of the proposed model that uses regonal nformaton to gude contour evoluton. 3. The Orgnal Model The ACWE model for vector-valued mages s ased on Mumford-Shah functonal [8] and the level set formulaton [9]. Ths model was orgnally proposed for the segmentaton of color mages usng vectors formed y the RGB values of the pxel

4 ntenstes. It was later adapted for texture segmentaton usng Gaor transform coeffcents []. The model s formulated as follows: Let u 0 e the orgnal mage, defned on a planar doman Ω wth real values. Let u 0, for =,,, e the components that descre the orgnal mage u 0. Let C e the evolvng contour. The two averages of u 0 nsde and outsde the curve C are denoted as c and c for =,2,,. Followng [9], an energy functonal E s ntroduced whch, when mnmzed wth respect to c = ( c,..., c ), c = ( c,..., c ), and C, performs nary segmentaton: E( C, c, c) = μ length( C) (6) 2 λ u0( c dxdy nsde( C ) = 2 λ u0( c dxdy outsde( C ) = where each value u 0 (, =,,, s defned over a sngle pont (. The postve scalars λ and λ for =,,, are weght parameters for each mage component. Mnmzng the aove energy, one tres to segment possle regons n the mage wth contours gven y C and denoted as nsde C, from a unform ackground denoted as outsde C. In [9] the mplementaton has een done usng the level set method of Osher and Sethan [9], whch gves an effcent method for movng curves and surfaces, on a fxed regular grd, allowng for automatc topology changes, such as mergng, reakng of curves etc. The curve C s represented mplctly, va a level set functon φ, such that C = {( : φ ( = 0}, and φ ( > 0 nsde C, φ ( < 0 outsde C. The energy E s expressed n level set formulaton usng the Heavsde functon H, whch s defned as: H ( x) = 0 and the Drac Delta functon δ(x)=dh(x)/dx., x 0, x < 0 2 λ u0( c dxdy Ω = 2 λ u0( c dxdy Ω = E( c, c, φ ) = μ δ ( φ( ) φ( dxdy (8) Ω Mnmzng E ( C, c, c ) wth respect to the unknown constant vectors c, c the followng relatons are otaned, emedded n a tme-dependent scheme: (7)

5 u0h ( φ ) dxdy (9) Ω c ( t) =, H ( φ) dxdy Ω u0( H ( φ)) dxdy Ω c( t) = H ( φ) dxdy u 0 Ω.e. the averages of component nsde and outsde the curve C respectvely, for =, 2,, where s the numer of components. Mnmzng E ( C, c, c ) wth respect to φ, and parameterzng the descent drecton y an artfcal tme, the followng Euler-Langrange equaton for φ s otaned: φ φ 2 2 = δ ( φ)[ μ dv( ) λ ( u0 c ) λ ( u0 c ) ] = t φ = = (0) 0 where a smooth approxmaton of the Heavsde functon H s used, as n [9]. Startng wth an ntal contour, gven y φ 0, at each tme step the vector averages c, c are updated and the partal dfferental equaton n φ s evolved. 3.2 The Proposed Model The noton of texture s undefned at sngle pxel level and t s always assocated wth some set of pxels [20]. Ths motvated us to replace the sngle pont nformaton quantfed y means of u 0 (, =,,, wth the regonal nformaton captured y the dstruton N( of the LBP P,R values of all pxels that elong to a k k neghorhood, centered at the pxel (. For the sake of effcency, we choose LBP 4, (Fg. ) ecause t nvolves less complex computatons than the standard LBP 8, or other LBP P,R (P > 8, R ) operators and results n a shorter dstruton of 6 ns. The LBP 4, operator mantans adequate dscrmnatve capalty wthn the current segmentaton framework, as demonstrated y our segmentaton results. The use of vector quantzaton alternatves that have een commonly used nstead [6], would ntroduce a sgnfcant computatonal overhead to the estmaton of the feature vectors. g g 2 g c g 0 g 3 g 0 g 3 Fg.. Local neghorhood of pxels for LBP 4,. A rule of thum suggests that the numer of entres for each n of a hstogram should e at least 0. Consderng that the LBP 4, produces a 6-n hstogram, the numer of entres requred for the whole hstogram s at least 6x0=60. Therefore

6 k=3 corresponds to the mnmum neghorhood that satsfes ths requrement (3 2 =69>60). In [5], t s suggested that the smlarty etween the LBP dstrutons can e estmated y means of the log-lkelhood statstc L. Wthn our context, the loglkelhood statstc L can e employed as a smlarty measure etween the LBP proalty dstruton N( and the average LBP proalty dstrutons c and c of the regon nsde and outsde the contour respectvely: L ( N, c ) = N ( log c and L( N, c ) = = = N ( log c where N ( s the proalty correspondng to the -th n of the local LBP dstruton N(, c (c -) s the -th n of the average LBP proalty dstruton c ( c ), and s the numer of ns of the consdered LBP proalty dstrutons (equal to 6 for the operator LBP 4, ). As L s an ncreasng functon of smlarty of the proalty dstrutons N ( and c (c -), we use (-L) as a dstance measure etween the consdered dstrutons, nstead of ther squared dfferences, suggested y equaton (6) of the orgnal model. Thus, (6) s replaced y: E( C, c, c nsde( C) = outsde( C ) = λ ( N ( log( c )) dxdy () ) = μ length( C) (2) λ ( N ( log( c )) dxdy Mnmzng E ( C, c, c ), results n a segmentaton of regons characterzed y a dfferent average LBP proalty dstruton than the rest of the mage. The postve scalars λ and λ for =,,, are weght parameters for the -th n of the LBP dstrutons N(, c and c. Smlarly to (6), the regons to e segmented are defned y contours gven y C and denoted as nsde C, whereas the ackground regon s denoted as outsde C. The Euler-Langrange formulaton of (2), whch corresponds to equaton (0) of the orgnal model ecomes: φ φ = δ ( φ)[ μ dv( ) λ ( N ( log( c )) (3) t φ = = λ ( N ( log( c ))] = 0 where φ s the level set functon, mplctly representng curve C.

7 4 Results The proposed actve contour model s mplemented and appled for the segmentaton of two-texture mages, composed of Brodatz textures [2]. In order to evaluate the contruton of the log-lkelhood statstc to segmentaton accuracy, we perform experments wth: ) the proposed model employng the log-lkelhood statstc, as stated n equaton (2), 2) the proposed model employng the squared dfferences of N ( and c (c -), as suggested y equaton (6) of the orgnal model. Both varatons of the proposed model are mplemented n Mcrosoft Vsual C and executed on a 3.2 GHz Intel Pentum IV workstaton. The model constants are generally chosen as follows: λ λ = , m = 6500 for the frst varaton, and = λ = λ = 750, m = 6500 for the second varaton. The used LBP operator s LBP 4, and each local LBP hstogram s extracted from k k neghorhoods wth k=3, as descred n the prevous secton. Fgures -4 llustrate four example results of the applcaton of oth varatons of the proposed model on two-texture mages. The results of the applcaton of the frst model varaton, employng the log-lkelhood statstc, are depcted on Fg. (a), 2(a), 3(a), 4(a), whereas the results of the second model varaton, employng the squared dfferences of N ( and c (c -), are depcted on Fg. (), 2(), 3(), 4(). The segmentaton results otaned y the frst model varaton, employng the loglkelhood statstc, are very promsng. The frames composed of dfferent texture patterns are very well segmented. Moreover, the segmentaton qualty otaned y the applcaton of the frst model varaton s generally mproved when compared to that otaned y the second model varaton, n the cases of Fg.,3,4 (n the case of Fg. 2, oth varatons acheved a practcally perfect segmentaton result). Ths mprovement ndcates that the log-lkelhood statstc s more descrptve wthn the current segmentaton framework. The computatonal cost of our approach vares etween 40 and 60 seconds.

8 (a) () Fg.. Segmentaton results of the applcaton of the two model varatons on the twotexture mage D4D84, composed of Brodatz textures [2]: (a) segmentaton result of the frst model varaton, () segmentaton result of the second model varaton. (a) () Fg. 2. Segmentaton results of the applcaton of the two model varatons on the twotexture mage D8D84, composed of Brodatz textures [2]: (a) segmentaton result of the frst model varaton, () segmentaton result of the second model varaton.

9 (a) () Fg. 3. Segmentaton results of the applcaton of the two model varatons on the twotexture mage D9D77, composed of Brodatz textures [2]. It should e noted that the groundtruth shape of the regon to e segmented s a rectangular: (a) segmentaton result of the frst model varaton, () segmentaton result of the second model varaton. (a) () Fg. 4. Segmentaton results of the applcaton of the two model varatons on the twotexture mage D7D55, composed of Brodatz textures [2]: (a) segmentaton result of the frst model varaton, () segmentaton result of the second model varaton. 5 Concluson In ths paper, we presented a novel model for texture segmentaton, featurng an actve contour approach. The proposed actve contour model s guded y the texture nformaton, whch s encoded wth the use of a local nary pattern scheme. The texture nformaton s extracted from dstrutons of LBP values, characterzng a neghorhood around each pxel, nstead of usng a sngle LBP value to characterze each pxel. As a smlarty measure etween the LBP dstrutons, we have used the log-lkelhood statstc. We demonstrated that the proposed model acheves hgh qualty segmentaton results y applyng the model on composte texture mages taken from the Brodatz alum. Possle future extensons of ths work nclude : ) an extensve testng on real mages taken from applcatons nstead of the artfcal ones used n ths work, 2) the adopton of a quanttatve measure for a more accurate evaluaton of the segmentaton results, 3) test the model performance when adoptng ru 2 the LBP operator, ntroduced n [5], and 4) extenson of the proposed model for P, R

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