TOPOLOGY PRESERVING GRAPH MATCHING FOR PARTIAL FACE RECOGNITION

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1 TOPOLOGY PRESERVING GRAPH MATCHING FOR PARTIAL FACE RECOGNITION Yueq Duan 1,2,3, Jwen Lu 1,2,3,, Janjang Feng 1,2,3, Je Zhou 1,2,3 1 Department of Automaton, Tsnghua Unversty, Bejng, Chna 2 State Key Lab of Intellgent Technologes and Systems, Bejng, Chna 3 Tsnghua Natonal Laboratory for Informaton Scence and Technology (TNLst), Bejng, Chna duanyq14@mals.tsnghua.edu.cn; {lujwen,jfeng,jzhou}@tsnghua.edu.cn ABSTRACT In ths paper, we propose a topology preservng graph matchng (TPGM) method for partal face recognton. Most exstng face recognton methods extract features from holstc face mages, yet faces n real-world unconstraned envronments are usually occluded by objects or other faces, whch cannot provde the whole face mages for recognton. Latest keypont-based partal face recognton methods only match on the detected keyponts to remove the occluded regons. However, they smply measure the node-wse smlarty wthout hgher order geometrcal graph nformaton, thereby dependng heavly on descrptors whch are susceptble to noses. To address ths, our TPGM method estmates a non-rgd transformaton encodng the second order geometrc structure of the graph, so that more accurate and robust correspondence can be computed wth the topologcal nformaton. Expermental results on three wdely used face datasets show that the proposed TPGM outperforms most exstng state-of-the-art partal face recognton methods. Index Terms Partal Face Recognton, Graph Matchng, Keypont, Topology-Preservng 1. INTRODUCTION Face recognton s a longstandng computer vson problem and a number of face recognton approaches have been proposed over the past three decades [1 6]. Whle most methods have acheved mpressve performance under controlled condtons where frontal holstc face mages are prealgned and normalzed, there are stll challenges for unconstraned face recognton n many real-world applcatons. Typcal face recognton applcatons nclude smart survellance systems * Correspondng author. Ths work was supported n part by the Natonal Key Research and Development Program of Chna under Grant 2016YFB , the Natonal Natural Scence Foundaton of Chna under Grants , , , and , the Natonal 1000 Young Talents Plan Program, the Natonal Basc Research Program of Chna under Grant 2014CB349304, the Mnstry of Educaton of Chna under Grant , and the Tsnghua Unversty Intatve Scentfc Research Program. and handheld devces, where faces may be occluded by objects or other faces under crowded scenes. In such scenaros, only partal faces can be obtaned and face algnment may fal to work wth facal landmarks occluded. Most face recognton methods ncludng the state-of-theart CNN approaches [3 6] utlze the whole face mages for recognton, whch are not applcable to partal face recognton. On the one hand, they assume that each mage have the same content of the algned whole face and descrbe the holstc facal mages for representaton, yet the contents of mages may be dfferent even for the same person n partal face recognton, e.g. one mage wthout the left eye and another wthout the mouth. On the other hand, the occluded objects are ncluded n the representaton, whch harms the dscrmnatve power. Therefore, t s requred to desgn a partal face recognton method whch drectly recognzes partal faces and s robust to occlusons. In order to better recognze partal faces, the occluded facal parts should be removed when computng the smlartes between probe partal faces and gallery faces. Inspred by the motvatons above, a few keypont-based methods have been proposed by computng the smlartes over the detected feature keyponts on the face mages [7, 8], such as mult-keypont descrptor wth Gabor ternary pattern (MKD- GTP) [7] and robust pont set matchng (RPSM) [8], whch acheve the state-of-the-art performance on partal face recognton. However, they only explot node-wse smlarty, whch depend heavly on descrptors and are susceptble to llumnaton, deformaton and other noses. Graph matchng s an effectve manner to address such unstableness by explotng geometrc structure of the graph, whch enhances the robustness of feature matchng n varous of vsual analyss tasks such as object categorzaton [9], feature trackng [10] and acton recognton [11]. Inspred by the fact that graph matchng delvers hgher matchng accuracy and stronger stableness, we propose a topology preservng graph matchng (TPGM) method for partal face recognton by estmatng a non-rgd transformaton encodng the topologcal structure and measurng the correspondence between nodes and edges. Fg. 1 llustrates the ppelne of our proposed TPGM method /17/$31.00 c 2017 IEEE 1494

2 Fg. 1. The flowchart of our proposed TPGM approach for partal face recognton. For each par of mages, we frst detect SIFT keypont descrptors on both faces marked as green dots. Then, the keyponts are coarsely matched and selected based on Lowe s method, where green lnes represent the correct matches whle the red ones lnk the wrong matchng keypont pars. We construct the graphs for both mages by deployng Delaunay trangulaton wth blue lnes. In TPGM procedure, a non-rgd transformaton s estmated encodng the structural graph teratvely, wth outlers removed durng the teraton. Fnally, the probe partal face s algned and recognzed wth the transformaton and the matchng result. Expermental results on LFW [12], AR [13] and PubFg [14] show the effectveness of the proposed approach. 2. RELATED WORK There have been extensve work on robust face recognton wth occlusons n recent years [15, 16]. These methods requre face algnment, whch has been proved to be crtcal by Ekenel and Stefelhagen [17]. However, these face algnment based methods fal to work well wth unknown mssng facal portons. A number of part-based representatons have also been proposed, whch can be manly classfed nto subregonbased methods [1, 2] and component-based methods [18, 19]. However, as occluded face regons n real-world applcatons are exceedngly unstructured, both subregon-based methods and component-based methods may fal wth ncorrect occluson detecton or occluded facal components. More recently, a few keypont-based approaches have been proposed [7, 8] whch remove the occluded facal regons by computng on the detected feature keyponts. Lao et al. [7] have proposed a MKD-GTP method whch presented a general formulaton of the keypont-based partal face recognton. Weng et al. [8] have appled pont set matchng method by consderng the frst-order compatblty between pont sets, whch acheved the state-of-the-art performance. However, these methods only explot node-wse unary smlarty wthout hgher order geometrcal graph nformaton, whch depend largely on descrptors and are susceptble to noses. 3. PROPOSED APPROACH In ths secton, we frst model the partal face recognton as a geometrc graph matchng problem. Then, we present our TPGM approach and the optmzaton detals. Fnally, we ntroduce how to use TPGM for partal face recognton Feature Extracton and Keypont Flter In order to present TPGM to match a par of partal faces, we frst extract features on both mages, and then flter the canddate matchng keyponts. We follow [8] to extract the SftSurfSILBP descrptor. More specfcally, we frst utlze Scale-Invarant Feature Transform (SIFT) to detect and descrbe the local keyponts [20], whch s the most successful keypont descrptor n the lterature. We then concatenate the SIFT descrptor wth the Speeded Up Robust Features (SURF) to enhance ts robustness aganst llumnaton varatons [21], and apply the Scale Invarant LBP (SILBP) features [22] to obtan more detaled facal textures wth four dfferent sets of {P,R} values ncludng {8,1}, {8,2}, {16,2} and {16,3} to obtan four SILBP hstograms. SftSurfSILBP combnes the dscrmnatve power of SIFT, SURF and SILBP, presentng robustness to rotaton, scale and llumnaton, whch s crtcal for partal face recognton. The number of keyponts detected by SIFT n a typcal face mage can be hundreds, whch suffer from heavy computatonal cost f we drectly apply graph matchng on the keyponts. Therefore, we apply Lowe s matchng method to flter out obvous outlers at frst, and then perform our TPGM method only on the canddate keypont pars Topology Preservng Graph Matchng In order to ncorporate the parwse nformaton, we utlze Delaunay trangulaton to construct a graph for each mage, and present each graph as a 4-tuple g = {P, Q, T, G}. We 1495

3 denote P =[p 1,...,p n ] R 2 n as the set of nodes and Q = [q 1,...,q m ] R 2 m as the set of edges, where edges are the coordnate dfferences between nodes, and n and m are the number of keyponts and edges, respectvely. Also, we denote the textural features of each node as T = [t 1,...,t n ] R dt n, and the node-edge ncdence matrx as G {0, 1} n m to encode the topology of the graph, where g c =1f the cth edge connects the th node. In partcular, g P = {P P, Q P, T P, G P } represents the 4-tuple from the probe set, and g G = {P G, Q G, T G, G G } s from the gallery. Let f p ( ) be the non-rgd transformaton functon of nodes, and f q ( ) be the transformaton functon of edges, where f q (q c )=f p (p ) f p (p j ) for q c = p p j. Let h p ( ) be the matchng map to connect each probe node to the correspondng gallery node, and X {0, 1} np ng be the bnary correspondence matrx between nodes, where X j =1 for the matched th probe keypont and jth gallery keypont. We can represent the mappng as h p (p P )=PG X T. Smlarly, we denote h q ( ) as the matchng functon of edges, and defne Y {0, 1} mp mg as the bnary correspondence matrx between edges. For q P = p P k pp l and q G j = pg k pg l, Y j =1f X kk =1and X ll =1: [ ] Y = 1 (G P ) T XG G > 1, (1) where 1(true) =1and 1(false) =0. The physcal meanng of (G P ) T XG G {0, 1, 2} mp mg s the number of matchng nodes connected wth the correspondng edges, and edges are matchng only f both the two pars of connected nodes are matchng. Wth the denotatons above, we formulate the objectve functon for the partal face matchng as follows: mn J = K t (t P,h t (t P )) + λ p K p (f p (p P ),h p (p P )) + λ q K q (f q (q P ),h q (q P )), (2) where the frst term s to mnmze the dfferences of textural features between the matched nodes, the second term ams to mnmze the dstances between the transformed matched nodes and the physcal meanng of the thrd term s dstances between the transformed matched edges. Textural Matchng Cost: The frst term n (2) measures the dfference n texture feature. We sum up the textural dfference of the correspondng feature descrptors to obtan the overall textural matchng cost: n p K t = T j X j = tr(t T X), (3) n g j where T j = ((t P t G j )T (t P t G j )). Node Geometrc Matchng Cost: The second term n (2) measures the postonal dfferences of transformed probe keyponts and correspondng gallery keyponts. In order to ncorporate the non-rgd transformaton, we apply the thn plate splne (TPS) model, whch s wdely used for representng flexble coordnate transformatons. The bendng energy of TPS s defned as follows: n g K p = f p (p P ) h p (p P ) 2 2 ) 2 + λ [( 2 f p ) 2 ( 2 f p λ p x 2 + x y ( 2 f p ) 2 ] + y 2 dxdy, (4) where f p (p P ) s computed as f p (p P )=A 2 2 p P + b WΦ() n 1, Φ() np 1 = p P p P log ( p P p P 1 2 2). p P p P n p 2 2 log ( p P p P n p 2 2). (5) In (5), we denote A and b as the affne transformaton matrx and the bas vector, W as the weght matrx and Φ as the TPS kernel. We substtute L1 norm for the L2 norm for lnearzaton and rewrte the node geometrc matchng cost as follows: K p = AP P 2 n p + b1 T n p + WΦ np n p P G 2 n g X T n g n p 1 + λ λ p WΦ 1. (6) Edge Geometrc Matchng Cost: The thrd term n (2) measures the geometrc dfferences of transformed probe edges and correspondng gallery edges. We calculate the dstance between edges by the squared L2 norm of vector dfference. Let q P = p P 1 pp 2 and qg = p G 1 pg 2, and we can obtan: m p K q = (f p (p P 1) f p (p P 2)) (h p (p P 1) h p (p P 2)) 2 2. (7) Reformulatng and lnearzng the above equaton nto a matrx form result n: K q = AQ P 2 m p + W 2 np (ΦP ΦP j ) np m p Q G 2 m g Y T m g m p 1. (8) 3.3. Optmzaton Detals As the objectve functon s NP-hard wth dscrete constrants whch cannot be effcently solved, we perform a lnearzaton and rewrte the objectve functon nto a lnear programmng (LP) form: mn J = tr(t T X)+λ p 1 T 2 U1 np + λ1 T 2 V1 np + λ q 1 T 2 M1 mp λ x 1 T n p X1 mp, (9) 1496

4 subject to U AP P + b1 T n p + WΦ P G X T U, V WΦ V, M AQ P + W(ΦP ΦP j ) Q G Y T M, U 0, V 0, M 0, X j 1, X j 1, X j 0, j A 1,1 = A 2,2, A 1,2 = A 2,1. (10) In (9), the bnary constrant of X j {0, 1} np ng s relaxed to a contnuous doman 0 X j 1, and U R 2 np, V R 2 np and M R 2 mp are auxlary matrces representng upper bounds of K p1, K p2 and K q respectvely. As there are the degenerate cases when the optmal soluton of {A, W, X, b} are all zeros, we add a penalty term of X n the formulaton. Regon Shrnkage: We apply the successve trust regon shrnkage [23, 24] to solve the LP model. For each keypont p P n the probe mage, we set a trust regon D n the gallery mage, whch s a crcle wth center pont f p (p P ) and a radus of r. Only keyponts nsde the correspondng trust regon are consdered as the matchng canddates, whle others are excluded n the optmzaton process by settng X j =0. The trust regon cover the entre gallery mage at frst, and then gradually shrnks to refne the matchng canddates durng the teraton, whch s formulated as: r (n+1) = α 1 r (n), where 0 <α 1 < 1. Parameter Shrnkage: As face mages are globally rgd and locally non-rgd, we confne the transformaton to be rgd n the global exploraton perod, and then gradually convert to non-affne transformaton n the local explotaton perod. As λ controls the energy of non-affne transformaton, we ntalze λ to a relatvely large value, whch s gradually reduced t durng teratons. Specfcally, we apply λ (n+1) = α 2 λ (n+1), where 0 <α 2 < 1. Outler Removal: We remove the outler matchng pars durng the teraton by calculatng the summaton of each row of X. For an outler probe p P j, all elements n the jth row of X are close to 0. Gven a threshold 0 < τ < 1, f np k=1 X jk <τ, we consder the p P j as an outler and remove t from the canddate keyponts. Algorthm 1 summarzes the detaled procedure of the proposed TPGM method. As the physcal meanng of the frst three lambdas are smlar wth [8], we drectly followed the same parameters by settng λ p =0.01, λ x = mn(c) and λ =5for smplcty and a far comparson. λ q s fnally fxed to 0.05 for all the experments Partal Face Recognton Usng TPGM We obtan the average matchng cost d = J mn /(,j X j) smply dvdng the matchng cost by the number of matchng Algorthm 1: TPGM Input: Probe mage P, Gallery mage G, teraton number T and parameters λ p, λ x, λ, λ q, τ, α 1 and α 2 Output: A, b, W, X, Y 1: Detect keyponts and extract SftSurfSILBP features. 2: Usng Lowe s method to flter the keyponts and construct the graph g P and g G. 3: Intalze r = r nt and set the constrant set Φ =. 4: for t =1, 2,,T do 5: Construct Φ. 6: Obtan A, b, W, X, Y usng (9). 7: Clear the constrant set Φ to. 8: Fnd the outsders of the trust regon and construct the constrant set Φ. 9: Shrnkage: r (n+1) = α 1 r (n) and λ (n+1) 2 = α 2 λ (n+1) 2. 10: Remove p P, X :,f j Xj <τ. 11: Remove p G j, X :j,f 12: end for 13: Bnarze X. 14: return A, b, W, X, Y Xj <τ. keyponts. We further defne the dstance between the probe and the gallery as follows: d J d = mn,j X = j (,j X j) 2 = K t + λ p K p + λ q K q (,j X j) 2. (11) In (11), We separate the dstance nto two parts, the texture matchng dstance and the graph matchng dstance. It s proportonal to the average matchng cost whch ndcates the affnty of the matchng dfference, and t s nversely proportonal to the number of matchng pars whch ndcates the area of smlar parts n two mages. 4. EXPERIMENTS We evaluated the performance of our proposed TPGM on LFW [12], AR [13] and PubFg [14], where LFW and Pub- Fg are holstc face datasets and AR s a partal face dataset. We compared the proposed TPGM to several state-of-the-art methods on partal face recognton tasks, whch llustrated the effectveness and robustness of the proposed approach. 1 For LFW and PubFg, we added random transformaton (e.g. random occluson, rotaton) based on the orgnal face mages to evaluate the proposed method on partal face recognton tasks. 2 For AR, we tested on the orgnal AR datasets wth varant mage szes and dsalgnment. In the experments, we compared aganst 5 baselne algorthms, where three of them are algnment-free matchng methods and others are state-of-the-art partal face recognton approaches, ncludng Locally Affne Invarant Robust Pont 1 As the key contrbuton of the proposed method s for partal face recognton, we only conduct experments on partal face settngs. 2 We wll provde the modfed data along wth the codes for reproducton and evaluaton. 1497

5 Table 1. Mean verfcaton rate (VR) and correspondng standard devatons (%) comparson on LFW. Method VR ± S E HDLBP ± 1.09 CNN ± 1.38 CPD-SftSurfSILBP ± 1.19 MKD-SRC-GTP ± 1.77 MLERPM-SftSurf ± 1.53 MLERPM-SftSurfLBP ± 1.83 LAIRPM-SftSurf ± 1.02 LAIRPM-SftSurfSILBP ± 1.68 RPSM-SftSurf ± 1.46 RPSM-SftSurfSILBP ± 1.57 TPGM-SftSurfSILBP ± 1.12 set Matchng (LAIRPM) [8], Robust Pont Set Matchng (RPSM) [8], Metrc Learned Extended Robust Pont Matchng (MLERPM) [25], Mult-Keypont Descrptors-Sparse Representaton-based Classfcaton-Gabor Ternary Pattern (MKD-SRC-GTP) [7] and Coherent pont drft (CPD) [26] Results on LFW The Labeled Face n the Wld (LFW) database [12] conssts of labeled faces of 5749 subjects. The mages were obtaned under unconstraned crcumstances, causng large varatons n scale, rotaton, llumnaton and occluson. We evaluated the proposed method on the Vew 2 of the LFW dataset, whch ncludes 6000 pars n total wth half of them matched and the other msmatched. They are separated nto 10 folds wth 600 pars for each fold. In order to obtan partal face mages, we frst appled the Vola-Jones face detector to detect and crop the facal regons of all mages. Then, we randomly transformed those detected holstc facal mages to obtan the arbtrary face patches, where both gallery and probe mages were partal faces wth some facal components cropped out, makng t extremely dffcult to match. We added hgh dmensonal LBP (HDLBP) method [27] wth face algnment by CFAN facal landmark detector and CNN [5] feature wth VGG-16 network nto comparson, whch acheve the state-of-the-art performances on holstc face recognton tasks. Table 1 shows the mean verfcaton rates of dfferent methods. Our TPGM outperforms other baselne methods whch proves ts effectveness, whle HDLBP presents the poorest performance on the partal face recognton task. HDLBP employs CFAN to detect 25 landmarks, yet t does not work on partal faces especally when some facal components are occluded. CNN explots holstc facal mages for representaton through learnng from large amount of outsde data. However, the contents of each partal face mage are dfferent, whch leads to a confusng descrpton. The proposed TPGM drectly matches on the mage pars wthout tranng Table 2. Recognton accuracy (%) of dfferent methods on the AR dataset. Method S1-G S1-S S2-G S2-S CPD MLERPM LAIRPM MKD-SRC-GTP RPSM TPGM procedure and acheves the hghest accuracy on partal face recognton, whch proves ts effectveness and robustness. Iteraton Number and Computatonal Tme: We tested the average teraton number and computatonal tme of the proposed TPGM. Our hardware confguraton comprses of a 2.8-GHz CPU and a 15G RAM. In each experment, the tme complexty vares wth the number of ntal matchng keyponts, where the mean teraton number s 1.4 and the computatonal tme s 0.94s on LFW. The proposed TPGM converges much faster than RPSM, because the geometrc nformaton accelerates the convergence Results on AR The AR database [13] conssts of 126 denttes ncludng 70 males and 56 females. It contans two sessons and there are 13 face mages for each subject n a sesson, where three of them are taken under varous llumnaton condtons, four wth dfferent expressons, three wearng sunglasses and the other three wearng scarves. We evaluated the performance of our proposed approach on the face recognton task where the orgnal mages from the AR dataset were drectly used as the probe set wthout crop or algnment. It s ubqutous n real-lfe applcatons that probe mages and gallery mages are of dfferent sze and are not properly algned. Table 2 shows the recognton accuracy of dfferent methods. We see that our method obtaned the best result, demonstratng the robustness aganst varous scales. MKD-SRC-GTP utlzes Harrs-Laplacan keypont detector [7] whch s senstve to corners, so that a great number of mproper keyponts were detected n har regons, leadng to unstable and dscrmnatve descrptors Results on PubFg PubFg dataset [14] contans mages of 200 people from unconstraned condtons, whch vary n poses, llumnatons, expressons and background. The evaluaton set of 140 people are used for the probe set and the remanng 60 people are regarded as the gallery set. Followng the settngs n [8], we select 5 mages for each subject. The selected dataset well preserves the varaton n poses, llumnatons, expressons and background. 1498

6 Table 3. Average recognton rates (%) of dfferent methods wth dfferent ranks on PubFg. Method rank = 1 rank = 10 rank = 20 SftSurfSILBP CPD MLERPM MKD-SRC-GTP LAIRPM RPSM TPGM We randomly transformed the orgnal mages to obtan partal face patches. We frst rotated each mage randomly from 20 to 20. Then, we cropped the rotated mage to the 0.8 tmes of the orgnal mage sze. Fnally, the cropped mage was randomly scaled rangng from 0.8 to 1.2. We conducted fve-fold testng scheme by randomly splttng the cropped mages nto fve subsets. Besdes the baselne approaches, we also tested on the orgnal SftSurfSILBP where the Lowe s matchng scheme was utlzed for partal face recognton. Table 3 shows that TPGM outperforms other state-of-theart partal face recognton methods on PubFg. Compared wth SftSurfSILBP whch smply apples Lowe s matchng scheme, the proposed TPGM performs a graph matchng procedure to encode the graphcal nformaton and obtans about 18% ncreases n recognton rates, whch demonstrates the effectveness of the proposed TPGM approach. 5. CONCLUSION In ths paper, we have proposed a topology preservng graph matchng (TPGM) method for partal face recognton, where a non-rgd transformaton s estmated encodng the geometrc structure of the graph. Wth the geometrc graph structure, TPGM obtans more accurate and robust correspondence, whch leads to a stronger recognton ablty. Moreover, the proposed TPGM drectly matches on the partal mage pars, whch does not requre large amount of tranng data. The expermental results show the effectveness of TPGM. 6. 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