A Compositional Exemplar-Based Model for Hair Segmentation

Transcription

1 A Compostonal Exemplar-Based Model for Har Segmentaton Nan Wang 1, Hazhou A 1, and Shhong Lao 2 1 Computer Scence & Technology Department, Tsnghua Unversty, Bejng, Chna ahz@mal.tsnghua.edu.cn 2 Core Technology Center, Omron Corporaton, Kyoto, Japan lao@ar.ncl.omron.co.jp Abstract. Har s a very mportant part of human appearance. Robust and accurate har segmentaton s dffcult because of challengng varaton of har color and shape. In ths paper, we propose a novel Compostonal Exemplar-based Model (CEM) for har style segmentaton. CEM generates an adaptve har style (a probablstc mask) for the nput mage automatcally n the manner of Dvde-and-Conquer, whch can be dvded nto decomposton stage and composton stage naturally. For the decomposton stage, we learn a strong ranker based on a group of weak smlarty functons emphaszng the Semantc Layout smlarty (SLS) effectvely; n the composton stage, we ntroduce the Neghbor Label Consstency (NLC) Constrant to reduce the ambguty between data representaton and semantc meanng and then recompose the har style usng alpha-expanson algorthm. Fnal segmentaton result s obtaned by Dual-Level Condtonal Random Felds. Experment results on face mages from Labeled Faces n the Wld data set show ts effectveness. 1 Introducton In computer graphcs, har acquston [1] [2] and har geometry modelng [3] have acheved sgnfcant progresses. Whle n computer vson, har style analyss or har segmentaton dscussed n ths paper s stll an ongong research ssue. Har s a very mportant part of human appearance especally n consumer mages. In vsual survellance condton or crmnal cases, face detals usually cannot be seen or remembered or descrbed clearly. However, har style s easer to be dentfed and descrbed n most cases, so t usually becomes one of the most mportant descrptors for some specfc target person. For ths applcaton, har segmentaton becomes a necessary ntermedate step to har style dentfcaton. Moreover, wth the rapd development of nternet, onlne makeup has become more and more popular. When people want to see whether or not some har style fts them, a good har style dentfcaton or search tool could help a lot, whch also makes har segmentaton necessary. Nevertheless, there are challenges for segmentng har area n consumer mages because of the varaton of shape and color. Robust har segmentaton s by far an unsolved problem.

2 1474 N. Wang, H. A, and S. Lao Fg. 1: It s easy to tell bald from the long har. But t s extremely hard to tell the long har from longer ones. Yacoob and Davs [4] buld a har color model and then adopt a regon growng algorthm to modfy the har regon. However, ths method wll only work when the har color doesn t change sgnfcantly, especally for the dark har. Consumer mages do not ft n ths constrant. Lee et al [5] gve a more practcal algorthm for consumer mages. They frst cluster har style and the color of har and face nto several typcal patterns manually. And then for each har style, choose the fttest har and face color model and modfy t accordng to the nput mage. A Markov Random Feld s bult and nferred to maxmze the jont probablty dstrbuton of each pxel on each label. The one whose labelng result has the mnmzed dstance to ts correspondng har style s chosen as the fnal har style. Ther work gves a practcal dea to solve the problem; nevertheless there are stll several ssues we need to focus on. Har style classfcaton s a hard ssue. It s dffcult to decde how many patterns are approprate even for just front vew, let alone cases wth sde vew. Wth a predefned cluster label, t s stll hard to decde whch har style an nput mage belongs to. It may be easy to tell bald from long har, but extremely hard to tell long har from longer one, as shown n Fgure 1. Unfortunately, ths classfcaton s vtal because unary term plays domnant role n graph model [6]. In Borensten and Ullman [7], a combned top-down and bottom-up algorthm s proposed to solve the problem of fgure-ground segmentaton. Durng top-down procedure, mage fragments and the correspondng fgure background labels are extracted from tranng data frst and then used to optmally cover an object n a novel mage to nduce the fnal segmentaton result. Wang and Tang [8] approached the problem of face photo-sketch synthess and recognton. The nput mage s normalzed and dvded nto overlapped rectangles. For each rectangle, K canddate patches from the tranng set are selected. A mult-scale Markov Random Feld model s used for the selecton of optmal combnaton of patches. Jolc et al. [9] model the spatal correlatons n mage class structure by ntroducng the Stel to make mage models nvarant to changes n local measurement, whle senstve to changes n mage structure. Inspred by these works, we buld a Compostonal Exemplar-based Model (CEM, secton 2) for har style generaton, whch could generate an approprate

3 A Compostonal Exemplar-Based Model for Har Segmentaton 1475 Fg. 2: Work flow of Compostonal Exemplar-based Model. Color code for labels are: whte - background, yellow - face, black - har and blue - clothes. (Ths fgure s best vewed n color.) har style for the nput mage. In our paper, actually four labels are used: background, face, har and clothes. CEM works n the Dvde-and-Conquer way as llustrated n Fgure 2. In the decomposton stage, we desgn a group of Semantc Layout Smlarty (SLS) features (secton 2.1), whch are combned together to get a strong and effectve smlarty functon for each locaton respectvely. Based on the smlarty functon, canddate segmentaton results are collected for each local patch from a manually labeled lbrary n ths stage. In the composton stage, we ntroduce a Neghbor Label Consstency (NLC) Constrant and organze local patches as a Markov Network (secton 2.2). A well-defned consstency functon promses the regularty [10], whch allows us to optmze the CEM usng α-expanson algorthm [10] [11] [12]. CEM fnally generate a probablstc mask as llustrated n Fgure 2. Wth the favor of the mask, we obtan the fnal segmentaton result usng a dual-level Condtonal Random Felds (secton 3). 2 Compostonal Exemplar-based Model It s hard to model the har styles ntegrally, snce har styles have large varaton as shown n Fgure 1. The basc dea s to decompose a har style nto local patches and model each patch respectvely. The reason s that although har styles can dffer from each other dramatcally n global, they can stll share some common Semantc Layout n local. In our paper, Semantc Layout means the actual label patterns of patches. There s ntutonal evdence n the dagram of the Decomposton Stage n Fgure 2. The purple patch of the nput mage covers forehead and har root regons. The frst three searchng har style are very dfferent from the query one, but just n ths local patch, they seem the same. Ths s why we can model har style locally.

4 1476 N. Wang, H. A, and S. Lao Fg. 3: Ambguty of patches. Although the two green patches seem very smlar to each other n date representaton level, the dark color parts of the patches have totally dfferent semantc meanngs. When neghbor patch (n red) are consdered together, the ambguty can be avoded. In the decomposton stage, canddate segmentaton results are obtaned ndependently. However, the ndependence of searchng wll lead to ambguty sometmes, because we use the smlarty defned n data representaton level to approxmate the actual one n semantc level. We gve an example n Fgure 3, where the local patches from two mages are almost the same n the data representaton level but have totally dfferent meanngs for the dark color part n the semantc level. However, f ts neghbor patch (n the red rectangle) s consdered together, ths ambguty can be avoded most of the tme. From ths pont, we ntroduce the Neghbor Label Consstency (NLC) Constrant to reduce the ambguty. There are two key problems n the model. The frst one s how to defne a smlarty to capture the Semantc Layout nformaton. And the second one s how to select the best canddates for all patches together when NLC Constrant s ntroduced. They wll be descrbed n the next subsectons respectvely. Before that, we defne some notatons. P s the local patch of the mage and ts correspondng label result s denoted as L. The local patches are requred overlappng wth ts adjacent ones. Then the neghbor patch ndces of P s denoted as N (). For each patch P, there s an exemplar lbrary for t, whch s denoted as { P k }. The manually labeled result for the exemplar lbrary s { L k }. The smlarty functon n data representaton level between patch P and Q s defned as H (P, Q). The smlarty functon C (P, Q) for Semantc Layout between patch P and Q s defned as follows: C (P, Q) = 1 δ ( L m p m = L m ) Q where s the sze of regon P and Q. δ ( ) s Kronecker delta functon. (1) 2.1 Learnng Smlarty Functon by SLS features In ths subsecton, we focus on how to defne a smlarty functon to capture the Semantc Layout nformaton. Smlarty can be defned on the statstc nformaton, such as hstograms, or on the data structure, such as Eucld dstance,

5 A Compostonal Exemplar-Based Model for Har Segmentaton 1477 Fg. 4: Green patches of the two mages have very smlar Semantc Layout. However, f the smlarty s defned based on the whole feature of the patch, background dfference wll domnate the smlarty between them and cause a loss of the good exemplar canddate. Our SLS feature s calculated n selected sub-patches, such as the red rectangle. In ths way, better consstency between data representaton and semantc meanngs can be acheved. or on a fuson of them. One thng should be notced n the problem s that the feature compactness of dfferent labels are not the same. For example, face and har have some typcal pattern of color or texture dstrbutons; whle clothes feature dstrbuton s looser and background feature dstrbutons barely share anythng from one mage to another. Ths characterstc wll cause loss of good exemplar labels sometmes, as shown n Fgure 4. To acheve a better consstency between data representaton and semantc meanngs, our smlarty functon s constructed based on the features n local sub-patches. A smlar work to capture the Semantc Layout nformaton s that of Shotton et al. [6] whch presents a dscrmnatve model to fuse shape, appearance and context nformaton to recognze effcently the object classes. Our algorthm s dfferent from that snce we focus on the explct smlarty of Semantc Layout of patches, whle they focus on the classfcaton of pxel usng Semantc Layout as a learnng cue. Formally, denote the SLS feature set Φ = {φ 0, φ 1,, φ M }. Our algorthm use color and texture as basc features, such as RGB, HSL color space, Gabor wavelet, whch are represented as hstograms (Gabor wavelet s transformed as LGBP [13](Local Gabor Bnary Pattern)). Each SLS feature n Φ s determned by a trple F m, R m, B m. F m denotes the feature type, whch can be hstogram of R channel n the RGB color space or LGBP n some specfc frequency and orentaton. R m s the rectangle where F m hstogram s calculated. B m s the bn ndex of the hstogram. Let φ m (P ) = φ {Fm,R m,b m} (P ) be the B m bn value

6 1478 N. Wang, H. A, and S. Lao Table 1: Preference Pars Generaton Algorthm Input: Exemplar lbrary n specfc locaton P k, threshold τ Output: Preference Par Set (Tranng Set) {T j} Intalzaton: {T j} Φ For each P j Sort the other patches based on C `P j, Pk, and get a permutaton of the other patches π (m), whch maps the patch s sortng ndex m to ts orgnal ndex π (m) n P. k For each P π(m), whch satsfes that C Add P j, Pπ(0), P π(m) n {T j} End For End For P j, Pπ(m) < τ of F m hstogram extracted from P n the rectangle R m. Then the weak ranker h m (P, P j ) s calculated as: h m (P, P j ) = (φ m (P ) φ m (P j )) 2 φ m (P ) + φ m (P j ) (2) whch actually s the opposte number of one addend term from the Ch-Square Dstance equaton. So the fnal smlarty functon s a generalzaton of Ch- Square Dstance. To get a good enough smlarty functon, we apply the RankBoost [14] learnng algorthm to select the best SLS features and evaluate ther weghts. For the RankBoost algorthm, preference pars should be defned to serve as the tranng data. In our problem, the preference s defned by the manually labeled result smlarty of the two exemplar patches C (P, P j ). For each exemplar lbrary { P k }, one of them s used as the query patch, and the others are sorted based on C (P, P j ). And we prefer that the smlarty between the query one and the frst one s larger than that between the query one and the end ones. Specfcally, the preference pars (tranng set) generaton algorthm s shown n Table 1. The tranng objectve of our algorthm s to construct a strong ranker functon (smlarty functon n our paper) so that: ( P j, Pπ(0) ) (, P π(m) {T j }, H P j, Pπ(0) ) ( ) > H P j, Pπ(m) The smlarty functon H ( ) s the weghted sum of weak rankers, the same as other boostng algorthm. The detals of RankBoost tranng algorthm can be found n [14]. (3)

7 A Compostonal Exemplar-Based Model for Har Segmentaton Introduce NLC Constrant nto CEM In CEM, NLC Constrant s acheved by enforcng pxel to be assgned the same label no matter whch patch t locates n. So the consstency functon can be defned by C A (P, Q), whch s C (P, Q) restrcted on the overlappng area A of P and Q. The CEM can be represented formally as a Markov Network. The Node s the patch set {P }, and the neghborhood system s just defned before. Suppose C best canddate exemplars are reserved. The optmzaton of CEM can be done by mnmzng the followng energy functon: E (P ) = ϕ (c ) + ϕ,j (c, c j ) (4) j N() where c denotes the ndex of exemplar that P fnally take. The unary functon ϕ (c ) s defned as: ϕ (c ) = log (H (P, P c )) (5) And the parwse functon ϕ,j (c, c j ) s defned as: ϕ,j (c, c j ) = log ( ( C A P c, )) Pcj j However, the straghtforward defnton s not regular [10]. Accordng to the theorem of [10], the regularty of par wse term s a necessary and suffcent condton for graph-representablty. So ths energy functon cannot be mnmzed by graph-cut based algorthm. The problem can be solved by expandng the node label set from L = {0, 1,, C 1} to L = {0, 1,, nc 1}, where n s the vertces number. All possble canddate exemplars of all patches are grouped together. Snce each patch can only take label ranged between C and ( + 1) C 1 actually, the other assgnment should be set as a maxmum value. The mappng functon between label ndex s f (c ) = c L. The unary term s computed as: { ϕ (f (c ϕ (c ) = )) C c < ( + 1) C (7) max others To satsfy the regular condton n [10], the par wse term s modfed as follows: βϕ,j (f (c ), f (c j )) C c < ( + 1) C, jc c j < (j + 1) C ϕ,j (c, c j ) = 0 c = c j max others (8) The proof of the regularty of ϕ,j (c, c j ) s gven n supplementary fles. Wth the constrant of unary term, c and c j wll always satsfy the frst condton n par wse term, when the assgnment s optmal. So the labelng result of graph model wth the expandng label set s equvalent to the former one. Although (6)

8 1480 N. Wang, H. A, and S. Lao Fg. 5: Dagram of Dual-Level Condtonal Random Felds. the expandng label set wll ncrease computaton load, n practce the nference s stll fast enough, because the number of super pxels s very small n general. Denote the optmal soluton of CEM as {L }. The probablstc har style mask s constructed to retan all the nformaton of overlappng patches. The mask M s calculated as: ( ),j P δ L j = l + ɛ M,l = (9),j P 1 + ɛ where M,l denotes the probablty of assgnng pxel wth label l. L j s the manually labeled result of optmal exemplar n ndex j whch s the correspondng ndex of pxel j n patch P. 3 Segmentaton wth Dual-Level Condtonal Random Feld Condtonal Random Fled wth hgher order constraned has been used n segmentaton problem and gets sgnfcant achevement recent years [15] [16] [17]. In ths paper, we use a dual-level CRF to ncorporate hgher order constrant from super pxels obtaned by JSEG [18]. There are two level vertces n the graph model of dual-level CRF. Vertces n level 1 are pxels n mages and vertces n level 2 are super pxels produced by JSEG [18]. The structure of dual-level CRFs s llustrated n Fgure 5. The edges only exst between vertces n level 1 and vertces between the two levels, whle there are no edges between vertces n level 2, because superpxels are used as soft constrant n our model and fnal labelng results are obtaned from level 1. The energy functon s defned as follows: E (x) = φ (x) +,j N() φ,j (x, x j ) + φ (x ) +, R j φ,j (x, x j ) (10) where x s the label assgned to correspondng pxel or super pxel. φ and φ,j s the energy term defned on pxel level. φ s the super pxel unary term.

9 A Compostonal Exemplar-Based Model for Har Segmentaton 1481 φ,j s the par wse term between pxel and ts correspondng super pxel, whch represent the hgher order constrant by super pxel. φ (x ) and φ (x ) have smlar defnton. where φ mask φ (x ) = ω mask φ mask (x ) + ω color φ color (x ) (11) (x ) = log (M,x ). φ color (x ) s defned as the mnus log of probablty that current pxel s color n color dstrbuton for the x label. In our experment, the color dstrbuton s represented as hstograms. In φ (x ), the mask probablty s the average of probabltes of the pxels n ts correspondng superpxel, and the color probablty s defned as the smlarty between color hstogram of superpxel s and correspondng label s. where β s set as ( φ,j (x, x j ) = γ exp β I I j 2) δ (x x j ) (12) ( 2 I I j 2 ) 1. γ s the model parameters. Assumng n level 1, j n level 2 and pxel belongs to super pxel R j, φ,j (x, x j ) s defned as Potts Model: { ( 0 x = x j φ,j (x, x j ) = γ exp β ) R j other (13) where R j s the cardnalty of super pxel R j. β s the nverse of the average over all super pxel szes. γ s model parameters just lke γ. We use α-expanson algorthm to get the labelng result of the dual-level CRF. 4 Expermental Result Frst of all, we label the tranng data, also called exemplar lbrary, manually. Tranng data comes from Labeled Faces n the Wld database [19]. The reason for choosng ths database s that mages n LFW are general consumer mages that are much less constrant than those used n face recognton researches, whch s very good for valdatng the proposed algorthm. We manually labeled 1026 mages. For each mage, each pxel s assgned a label from the label set: background, har, face or clothes. These mages are dvded nto two halves randomly. One of them s used for learnng smlarty functon and the parameters of CEM. The other s used for testng. The tranng and testng procedure s shown n Table 2 and Table 3 respectvely. These dvdng, tranng and testng procedure are repeated 10 tmes to get the experment data. The parameters of CEM are determned emprcally. In consderaton of speed, mages are normalzed as and dvded nto patches wth step of 8 n both x and y drectons. R m n the tranng data are rectangles wth szes of 4 4, 8 8 and The threshold s set as τ = 0.5. The canddate number s set as C = 10. β n formula 8 s 8. For the CRF model parameters,

10 1482 N. Wang, H. A, and S. Lao Table 2: Tranng algorthm Detect Face [20] and Eye locatons [21] for each mage and normalze t n the same sze For each locaton, extracted the exemplar patch set P k Generate tranng data as Table 1. Generate strong ranker usng RankBoost algorthm [14]. End For Table 3: Testng algorthm Detect Face [20] and Eye locatons [21] for each mage and normalze t n the tranng sze For each locaton, extracted the exemplar patch set P k Usng strong ranker H ( ) for current locaton to sort P k Keep C exemplars as canddates End For Optmze CEM by alpha-expanson algorthm and get mask M Inverse transform M to orgnal mage Buld dual-level CRF wth as stated n secton 3. Fnal segmentaton s obtaned by α-expanson [10] [11] [12]. γ = γ = 8, ω mask = 1.6 and ω color = 0.4. Both the max n formula 7 and 8 are set as 1000 to prevent an nvald nference result. In Fgure 6, we show some segmentaton result by our algorthm. Har style changes from bald to long and n dfferent colors, t can be seen that our algorthm works robustly n the condton of large varaton of har shape and color and clutter background. It takes us about 95 hours to tran the SLS-based rankers. The tranng algorthm s appled ndependently for each local patch. So t can be extended on a dstrbuted system easly to shorten the tranng tme. To show the effectveness of our smlarty functon, we used Normalzed Dscounted Cumulatve Gan (NDCG) [22] to estmate the rankng qualty. For a lst of mages sorted n descendng order of the scores output by a learned rankng model, the NDCG score at the m-th mage s computed as: N m = C m m j=1 2 r(j) 1 log (j + 2) (14)

11 A Compostonal Exemplar-Based Model for Har Segmentaton 1483 Fg. 6: Examples of Segmentaton result. (a) Orgnal Image (b) Manually labeled result (c) Our Segmentaton Result. Color code for labels are: whte - background, yellow - face, black -har and blue - clothes. Fg. 7: (a) NDCG at the frst mage. (b) Best Pxel Precson from the frst and the frst ten canddate exemplars where r (j) s the ratng of the j-th mage and C m s the normalzaton constant to make that a perfect orderng gets NDCG scores 1. In our experment, r (j) = C (P 0, P j ). In Fgure 7(a), we llustrate our result of m = 1 n each locaton wth comparson wth a straghtforward rankng algorthm usng hstogram and Eucld dstance n RGB space. Our algorthm outperforms the straghtforward one n almost every locaton. Especally n the dffcult patches, the precson can be mproved by 8% to 10%. And we also test the pxel precson of the best canddate obtaned by our strong rankers. Pxel level segmentaton accuracy defned as: preson = n δ (L = L ) n (15) where n s the sze of the current mage. L and L denotes the label of algorthm result and ground truth of pxel respectvely. In Fgure 7(b), we show

12 1484 N. Wang, H. A, and S. Lao Fg. 8: Comparson between CEM wth and wthout NLC Constrant the pxel precson of the best canddate n each locaton respectvely. For most patches, our ranker can fnd acceptable exemplars for them. In Fgure 8, we gve a qualtatve CEM example wth and wthout neghborhood consstency constrant. As explaned before, ndependent search for exemplar patch can cause ambguty nevtably. Neghborhood consstency constrant enforces the contnuty between overlapped patches to mprove the model robustness for ambguty. CEM wthout neghborhood consstency constrant can acheve a pxel precson of 84.6%. Incorporate the constrant nto CEM can mprove the precson to 86.3%. As numerous work [15] [16] [17] suggested, ncorporatng segments pror benefts the segmentaton accuracy and robustness. In our problem, the precson of fnal segmentaton result by Dual-Level CRF can reach 89.1%, whch outperform Sngle-Level one by 1.5%. Although they brng only a slght ncrease n the segmentaton accuracy quanttatvely, they contrbute sgnfcantly to subjectve qualty mprovement on segmentaton, just as stated n [15], a small ncrease n the pxel-wse accuracy wll actually make a large mprovement on the qualty of segmentaton. We also test mages not ncluded n our manually labeled lbrary. Some of the results are gven n Fgure 9 to demonstrate ts generalzaton ablty. Due to lack of technque detals of [5], we have not tred to compare wth t. Nevertheless we thnk our method s more powerful n dealng wth varous har styles. We tested on 1000 selected face mages n front vew that are somewhat smlar to the exemplars, and about 80% of segmentaton results are subjectvely acceptable. Unsatsfactory cases occur where har s confused wth background or shadows.

13 A Compostonal Exemplar-Based Model for Har Segmentaton 1485 Fg. 9: More Segmentaton Results. However, f a test mage exsts n the exemplar lbrary, t wll get the exact result. Ths characterstcs guarantees our approach s extensblty snce a new har style can be easly extended by addng ts manually labeled result nto the exemplar lbrary. 5 Concluson In ths paper, we propose a novel Compostonal Exemplar-based Model for har style representaton and segmentaton. CEM generates har style for the nput mage n the Dvde-and-Conquer manner, whch can be dvded nto the decomposton stage and composton stage naturally. For the decomposton stage, we desgn a group Semantc Layout Smlarty features and combne them nto a strong ranker by RankBoost algorthm. In the composton stage, we ntroduce the Neghbor Label Consstency Constrant to CEM and defne the consstency functon skllfully to ensure ts regularty. Fnal segmentaton result s obtaned by the nference of Dual-Level Condtonal Random Feld. Experment results on face mages from Labeled Faces n the Wld data set show ts effectveness. In future, we wll try to nclude sde vews nto the lbrary and speed up the searchng procedure. References 1. Pars, S., Brceo, H.M., Sllon, F.X.: Capture of har geometry from multple mages. In: SIGGRAPH. Volume 23., Los Angeles, CA, Unted states (2004)

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