A 3D Feature Descrptor Recovered from a Sngle 2D Palmprnt Image Qan Zheng,2, Ajay Kumar, and Gang Pan 2 Abstract Desgn and development of effcent and accurate feature descrptors s crtcal for the success of many computer vson applcatons. Ths paper proposes a new feature descrptor, referred to as DoN, for the 2D palmprnt matchng. The descrptor s extracted for each pont on the palmprnt. It s based on the ordnal measure whch partally descrbes the dfference of the neghborng ponts normal vectors. DoN has at least two advantages: ) t descrbes the 3D nformaton, whch s expected to be hghly stable under commonly occurrng llumnaton varatons durng contactless magng; 2) the sze of DoN for each pont s only one bt, whch s computatonally smple to extract, easy to match, and effcent to storage. We show that such 3D nformaton can be extracted from a sngle 2D palmprnt mage. The analyss for the effectveness of ordnal measure for palmprnt matchng s also provded. Four publcly avalable 2D palmprnt databases are used to evaluate the effectveness of DoN, both for dentfcaton and the verfcaton. Our method on all these databases acheves the state-of-the-art performance. INTRODUCTION AUTOMATED personal dentfcaton usng bometrcs characterstcs s one of the most crtcal and challengng tasks to meet growng demand for strngent securty. There s ever growng need to develop more accurate and effcent bometrcs matchng technologes. Therefore our goal n ths work has been to desgn, develop and evaluate more accurate, compact and faster matchng algorthms for the palmprnt dentfcaton. In the context of advancements n the matchng of 2D palmprnts, ths paper ntroduces new algorthm to further mprove feature extracton and matchng technques for the contactless palmprnt dentfcaton. Our key contrbutons are three-folds: ) we present a new palmprnt feature whch s effcent and effectve for 2D palmprnt matchng; 2) we show that such feature descrbes the 3D nformaton and t can be extracted from a sngle 2D palmprnt mage; 3) our feature s based on the ordnal measure and we show that the ordnal measure s powerful for palmprnt matchng. Our method acheves the state-of-the-art performance on four publcly avalable 2D palmprnt databases. Besdes, extra experments are well desgned to verfy our arguments on contrbuton 2) and 3). The paper s organzed as follows: we frst ntroduce the DoN feature and explan ts recovery from a sngle 2D mage n Sec. 2; the effectveness of the ordnal measure s ascertaned n Sec. 3; fnally, the expermental results are reported n Sec. 4. 2 DON FOR PALMPRINT MATCHING In ths secton, the DoN feature s frstly ntroduced. We then llustrate that how such feature whch descrbes 3D nformaton can be recovered from a sngle 2D mage. Fnally, Department of Computng, The Hong Kong Polytechnc Unversty, Hung Hom, Kowloon, Hong Kong; 2 Department of Computer Scence, Zhejang Unversty, Hangzhou, Chna.. The mplementaton of proposed method s publcly made avalable [] the extracton of DoN from the 2D palmprnt mage and the feature matchng between two palmprnt templates are ntroduced. 2. DoN: Dfference of Vertex Normal Vectors For the better descrpton of the feature, we buld Cartesan coordnates for each acqured palmprnt mage, mage plane formng x-y plane, wth the normal of mage surface N representng z-axs, as shown n Fg.. Each pont/pxel p on the mage plane s one-to-one correspondng to a vertex v on palmprnt surface. Let n = (x, y, z ) denote the normal vector of vertex v. Suppose pont p has two neghborng regons R and R 2, ts DoN feature DoN() s DoN() = τ( z j z j ), () j R j R 2 where τ( ) s the sgn functon whch s defned as {, α <, τ(α) =, α. The DoN feature for p descrbes the dfference between the z-component of normal vectors from ts two neghborng regons. Accordng to (), two key ssues n recoverng the DoN feature of pont p are: ) how to obtan z value for each pont from ts neghborng regons (Sec. 2.2); 2) how to dentfy the neghborng regons of pont p (Sec. 2.3). 2.2 3D Feature from a Sngle 2D Image We address the frst problem by ntroducng the Lambertan Model n our analyss. The Lambertan Model has also been utlzed by Basr and Jacobs [2] to prove that the Lambertan objects appear close to a 9D lnear subspace. Ths concluson was evaluated for face recognton problem and excellent performance was acheved [2]. In ths paper, we further explore Lambertan Model for the contactless palmprnt matchng. (2)
2 Presented Palm Palmrpnt Image Fg. : The 2D palmprnt mage s essentally the projecton of the palmprnt surface. The drecton of llumnaton L s always from the front sde of the palmprnt magng. Accordng to the Lambertan Model, the pxel value I() of pont p on mage I s jontly determned by reflectance k d, llumnaton ntensty l d, llumnaton drecton vector L, and pont normal vector n, I() = k d l d Ln. (3) For dfferent ponts on the same palmprnt mage, k d, l d, and L can be consdered as the same. Gven a pont p, the dfference between the ponts ntensty from ts neghborng regon R and R 2 s j R I(j) I(j). We can substtute these two components n sgn functon τ and defne D() as follows, D() = τ( I(j) I(j)). (4) j R 2 j R Usng (3), (4) can be rewrtten as D() = τ(k d l d L( j R j R 2 n j n j )) j R 2 = τ(l( n j n j )). j R j R 2 D() s determned by the angle between llumnaton vector L and vector ( j R n j j R n 2 j ). For the smplcty, let X = x x, j R j R 2 Y = y y, j R j R 2 Z = z z, j R and let L = (a, b, c), we have j R 2 (5) (6) D() = τ( X a + Y b + Z c). (7) It may be noted that palmprnt mages are always acqured under frontal llumnaton. Therefore, under the Cartesan coordnate n Fg., we have c >. When Zc k > Xa k + Y b k s satsfed, D() s determned by the sgn of Z,.e., D() = τ( X a + Y b + Z c) = τ( Z c) = τ( Z ). (8) Accordng to the descrpton n Sec. 2., τ( Z ) represents the DoN feature DoN() we plan to recover. (8) llustrates that the 3D nformaton DoN() can be recovered from a sngle 2D mage. When constrant Zc k > Xa k + Y b k s satsfed, we can use avalable texture-level nformaton to recover the 3D shape nformaton. Wthout loss of generalty, for the sample case when X a > Y b, the constrant can be rewrtten as c a c a > 2 X Z. (9) s determned by the llumnaton durng the magng whch cannot be always controlled. One feasble way to meet the constrant n (9) s to ensure the rght sde 2 X Z as small as possble. We show that the proper partton for the neghborng regons can be used to acheve ths goal whch s ntroduced n next secton. For the smplcty, the partton for each pont on the palmprnt are set to be the same. Therefore the feature extracton usng DoN can be acheved by usng a convoluton operaton followed by a sgn functon. The partton of the neghborng regons on palmprnt mages s then replaced by the dvson of regons on the spatal flter. The spatal regons correspondng to the operatng flter s dvded nto two subsets, say R and R 2 n an M N sze spatal flter. All the entres n regon R are set as and the entres n regon R 2 are set as -. Extendng τ to matrx operaton, the DoN feature matrx or template F for mage I can be computed as follows: F = τ(f I), () () s a computatonally smpler operaton and s used to recover the 3D nformaton from a sngle 2D mage I n our approach. 2.3 Parttonng Local Regons The second problem outlned n Sec. 2. s to decde the neghborng regons. We acheve ths goal by parttonng the local regons on the spatal flter as dscussed above. Consderng the fact that bnarzed feature template s generated from the (contactless magng) nosy mages, the operator or the flter should be desgned n such a way that the postve and negatve flterng results from multple pxels are evened out. Ths mples that the sum of all the entres n the flter should be zero and the spatal dstrbuton of or - n the flter be symmetrc and orderly. On the other hand, as we dscussed above, such dvson should ensure the rght sde of the constrant n (9) be as small as possble. We now brefly revst the characterstcs of the palmprnt surface. Human palm surface s a complex 3D textured surface consstng of many rdges, wrnkles and lnes [3], [4]. The spatal extents of these key elements are dfferent from each other. Generally rdges represent the smallest element whle the wrnkles are larger than rdges, and the lnes are the most remarkable features n a typcal palmprnt database. All these key elements share the shape lke a valley. The valley typcally represents a symmetrcal shape whose symmetry axs
3 s the valley bottom. A 3D palm surface can be seen as a combnaton of several such symmetrcal unts. Such unts dstrbute rregularly on palmprnt surface. We utlze these propertes of such unts to make the rght sde n (9) as small as possble, that s, make X approxmate to zero and Z be a large value. If the neghborng regons partton s desgned to be contnuously connected and n patches, t s expected that j R x, j R x 2, thus ther dfference X. Ths s for two reasons: ) the symmetrc unts are over x-y plane and such partton ensures the surface symmetry for the regons. When the pont normal vectors are added, the azmuth components have large chance to be nearly cancelled out or elmnated (Fg. 2); 2) the x-y plane s almost a flat plane, whch ndcates that the x-component for most of ponts are excepted to be zero. The value of Z s excepted be large for two reasons, ) j R z tself s large value snce each z s a postve value, whch s manly determned by the sze and the length of valley; 2) j R z s excepted to be dfferent from j R z 2 due to the rregular dstrbuton of the valley unt on the palmprnt surface. 2 X Therefore, for the palmprnt mage, Z s more lkely to have small value and satsfy the constrant n (9). Fg. 2 llustrates the summaton result of normal vectors from the ponts on a typcal palm lne. Y Z X Palmprnt surface Small regon of palmprnt Cross sec on ofbluelne Normal vectors summa on Fg. 2: For a small regon on palmprnt, f we add the normal vector of each pxel pont, the summaton result wll almost be vertcal. Ths fgure llumnates the summaton of ponts on arbtrary palm lne. Fg. 3 llustrates some canddate flters. Fg. 3 -(c) show three such spatal dvsons wth the cross or number of parttons ncreasng from left to rght. Fg. 3 (d)-(f) llustrate spatal dstrbuton of values for the three dfferent drectons of a subset when the cross number s fxed to 2. The ncrease n the number of cross n parttons s expected to help n suppressng the photometrc dstortons by balancng the fltered results from the postve and negatve values. However, too many crosses wll make the flter rotatonally senstve. Ths wll also ntroduce asymmetry by reducng the symmetrcal property of the small regons on palmprnt, whch wll make the argument j R x, j R x 2 unrelable or nvald. Besdes, too many crosses wll also make Z. Ths can further pose lmtatons n meetng the constrant n (9). It may be noted that the symmetrcal unts (such as rdges, wrnkles and lnes) representng domnant palmprnt features are expected to have some wdth. The drecton of ntersecton (c) (d) (e) (f) Fg. 3: Dfferent colors represent dfferent subsets n a flter. In -(c) the crossng n the flter ncreases from to 3 whle n (d)-(f) the drectons of flters are vared when the crossng s fxed to 2. Fg. 4: The feature code of palmprnt. Orgnal gray level mage. The feature code. boundary (center or whte lne on flter n Fg. 3) also has wdth. In order to ensure the symmetry, the whte lne n the flter confguraton should be located orthogonal or parallel to the domnant symmetrcal unts. The expermental results n Sec. 4.2 also support these arguments. Accordng to prevous analyss, the flter of Fg. 3 s selected to construct the feature extractor or the flter. Ths flter can be defned as follows: > j f,j = < j otherwse. () where, j s the ndexes,, j [ B, B]. The flter sze s (2B + ) (2B + ). Fg. 4 shows a typcal palmprnt ROI mage and ts encoded features. 2.4 Template Denosng and Matchng Our analyss n prevous sectons suggests that the constrant n (9) may not be satsfed for some cases. Ths can be due to two key reasons: ) n some of the extreme locatons, there s stll a chance that Z, and 2) when porton of the valleys appears on the boundary or edges of the flter, the response from the small regons wll no longer be symmetrcal. In order to allevate the unrelable codes or features resultng from the nose or extreme cases as dscussed above, we ncorporate a denosng strategy durng matchng. The morphologcal operatons,.e., openng operaton and closng operaton, are performed on the feature templates, and the weghted sum of three scores s computed as the fnal matchng score. The morphologcal operatons are adopted for two reasons, ) the nosy perturbatons due to the lmtatons of the feature extractor are expected to be dscretely dstrbuted
4 n the feature templates and 2) the feature template s bnary and has spatal contnuty. It should be noted that ths step does not ncrease the feature template sze. Gven two feature template F and F 2, the matchng dstance s computed by the weghted sum of three scores, ds(f, F 2 ) = w S(F, F 2 ) + w 2 S( F, F 2 ) + w 3 S( F, F 2 ), (2) where F and F are the results after applyng closng and openng operatons on feature template F. S(F, F 2 ) s defned as S(F, F 2 ) = Γ(F F 2 &M(F )&M(F 2 )), (3) Γ(M(I )&M(I 2 )) where and & are XOR and AND operaton, Γ(F) computes the number of non-zero value n matrx F, M(I) s the mask matrx ndcatng the vald regon on palmprnt mage I. It s defne as {, background M(I)(, j) = (4), otherwse. We use horzontal and vertcal translatons between two matched templates to mprove algnment. In all our experments, the best match score among these algnments s used as the fnal match score. 3 ANALYSIS ON PALMPRINT MATCHING The DoN feature for each pont on the mage can have only two values. Therefore, t s necessary to analyss whether ths feature can be powerful enough for the accurate palmprnt matchng. The DoN feature s a knd of ordnal measure. In the lterature, Snha [5] beleved that ordnal measure can only be used for smple detecton or classfcaton task and t should be mpossble usng ordnal measure alone to solve complex object recognton problems. Ths concern arses from the nature of ordnal measure whch loses some numercal nformaton. Sun et al. [6], [7] demonstrated that the ordnal measure can play a defnng role for the complex rs recognton and palmprnt recognton problems. They acheved sgnfcant performance mprovement over competng methods. However, they essentally used three features to ncrease the dscrmnaton of the ordnal measure and the dscrmnaton usng only one feature based on ordnal measure was not nvestgated. Besdes, they acheved most of the success from desgnng the feature extractor,.e., usng dervaton of Gaussan flter, and dd not provde much analyss for the role played by the ordnal measure. In ths secton, we demonstrate that a sngle feature based on ordnal measure can be very powerful for the palmprnt matchng. In the palmprnt matchng, feature or template of a palmprnt mage s usually a feature matrx [6], [8], [9], [], [], [2]. Each entry on the matrx s an encoded feature code. Dstance between two templates s defned as the sum of dstances between such codes. Hammng dstance s usually employed to measure the codes dstance as the codes are often bnarzed. In ordnal measure, the number of encodng classes for each code s 2 whle n [9] or [8], the encodng classes s 6. For smplcty, the number of encodng classes s represented by λ n the followng analyss. Let us consder the smlarty between two palmprnt templates beng matched. If these two palmprnt mages belong to the same subject, we refer them as ntra-class matchng dstance or genune matchng dstance. Smlarly, f these templates belong to dfferent subjects, we refer them as nterclass matchng dstance or mposter matchng dstance. In order to smplfy the analyss, dstance between two codes s assumed to be zero f they are equal, otherwse one. For a 28 28 palmprnt template, the dmenson of ts feature vector s 6384. Consderng the spatal dependence of palmprnt regon, t s qute reasonable to assume that the ntrnsc dmenson of a sngle palmprnt feature vector, let us denote here by M, s much smaller than 6384,.e., M 6384. For the convenence of llustratons, we can consder a certan value for M, say. Consderng the nter-class matchng attempts, whether the codes on the templates are matched or msmatched can be consdered as a random event. Ths s because two palmprnts are from dfferent subjects and are unknown. Therefore, we assume 2 that the dstrbuton of nter-class matchng dstance D nter follows Bnomal dstrbuton D nter B(n nter, p), (5) where n nter s the number of trals n the Bnomal dstrbuton whch s the same as M, p s the success probablty. The relaton between λ and p can be expressed as p = λ. (6) Fg. 5 shows the nter-class dstance dstrbutons when n ter =, λ s 6 and 2 respectvely. Ths fgure llustrates the nter-class palmprnt matchng scores for the deal cases,.e., when features are robust and free from magng varatons, wth the changes n λ. Probablty Densty.35.3.25.2.5..5 λ=2 λ=6 4 5 6 7 8 9 Matchng Dstance Probablty Densty.4.3.2. nter class ntra class, ω=.8 ntra class, ω=.9 ntra class, ω=.95 6 7 8 9 Matchng Dstance Fg. 5: Typcal matchng dstance dstrbuton for dfferent λ. When p = 5, the nter-class dstance dstrbuton and three ntra-class 6 dstance dstrbuton wth dfferent ω. Consderng the ntra-class matchng attempts, among all the codes pars, we call the codes par as relable when both of partcpatng matchng codes are encoded n the rght class 3, otherwse the pars are consdered as unrelable. For a relable codes par, the matchng dstance should certanly be zero. For an unrelable par, the matchng dstance stll have chance to be 2. Analyss of rs codes usng mllons of matchng scores presented by Daugman [3] also justfes ths assumpton. 3. Rght class descrbes the actual depth nformaton.
5 zero. Therefore, the ntra-class matchng dstance between two templates s effectvely determned by the number of unrelable codes pars. For the unrelable pars, whether these respectve codes are matched or not can also be consdered as a random event. Ths s because the unrelable codes are manly caused by nose and msalgnment whose exact nfluence unknown. Representng the number of unrelable pars as ωm, where ω s the unrelable pars rate ( < ω < ), we assume ntra-class matchng dstance D ntra follows the Bnomal dstrbuton D ntra B(n ntra, p), (7) n ntra s number of trals, whch s equal to the unrelable pars number ωm, p s the success probablty. The relatonshp between p and λ s the same as for nter-class dstance dstrbuton. When λ = 6, M =, several ntra-class dstance dstrbutons wth dfferent ω as well as the nter-class dstance dstrbuton are shown n Fg. 5. From ths fgure, we can observe that when ω becomes larger, whch means the number of unrelable pars s large, the overlappng area between ntra-class and nter-class dstance dstrbutons also becomes larger. It s known that n order to acheve accurate dentfcaton, least overlap between the ntra-class and nterclass matchng dstance dstrbuton s desrable. The lkelhood of an unrelable par beng generated can be estmated as θ = ( p)( p). (8) It may be noted that the ω also represents the expected rate of unrelable code pars. Therefore t s qute reasonable to assume that ω s proportonal to θ,.e., ω θ. (9) Gven two λ, the relaton between ther correspondng p, p 2, ω, and ω 2 can be expressed as ω = ( p )( p ) ω 2 ( p 2 )( p 2 ). (2) When two λ are 6 and 2, p s 5 6 and p 2 s 2 respectvely, gven ω =.95,, accordng to (2), the correspondng ω 2 =.73,.76. Fg. 6 and show these dstrbuton wth ω =.95, respectvely. Probablty Densty.4.3.2. nter class, λ=2 nter class, λ=6 ntra class, λ=2 ntra class, λ=6 2 4 6 8 Matchng Dstance Problty Densty.35.3.25.2.5..5 nter class,λ = 2 nter class,λ = 6 ntra class,λ = 2 ntra class,λ = 6 4 6 8 Matchng Dstance Fg. 6: If ω =.95, the nter-class and ntra-class dstance dstrbuton wth λ = 2 and λ = 6 respectvely. If ω =, the nter-class and ntra-class dstance dstrbuton wth λ = 2 and λ = 6 respectvely. We can observe from Fg. 6 that under the same condton, the overlappng area between nter-class and ntra-class dstance dstrbutons for λ = 2 s always smaller than that for λ = 6. No overlap means the nter-class dstance s always larger than ntra-class dstance, whch results n good performance. Note that λ = 2 means the feature template s bnary, t s expected that bnary representaton for feature s more effectve. The analyss presented n ths secton theoretcally argues the effectveness of ordnal measure for palmprnt matchng. Ths argument s further supported by our expermental results on 2D palmprnt databases n Sec. 4.4. 4 EXPERIMENTAL VALIDATION AND RESULTS In ths secton, we frstly evaluate the performance from our method on four publcly avalable 2D palmprnt databases. Three competng methods, [8], [9], and Ordnal Code [6] are mplemented 4 for the comparatve performance. To facltate far comparson wth pror work, dfferent protocols are adopted for dfferent databases. The computaton complexty s also compared. In order provde detaled analyss on our method, the performance from our method usng dfferent flters (Fg. 3) as well as wthout denosng strategy s also reported. To demonstrate the robustness of our feature to the llumnaton changes, the experment from a face database wth sgnfcant llumnaton changes s also reported. Besdes, a fast verson of, namely Fast-, whch s based on the ordnal measure, s employed to support the arguments we made n Sec. 3. 4. Expermental Results from Proposed Method 4.. PolyU Contactless 2D/3D Palmprnt Database Ths contactless palmprnt database [5] s acqured from 77 dfferent subjects (rght hand). There are 2 samples from each subject wth 2D mages and depth mages. It also provdes segmented palmprnt mages of 28 28 pxels. Our experments are performed on full 2D part of ths database. The 2D mages n ths database are acqured under poor (ambent) llumnaton condtons. In our experment, the frst 5 samples of each subject are enrolled as tranng set. The rest 5 are as the test set. There are 885 samples for tranng/gallery and 885 samples for testng/probe. The ROC, CMC curves as well as the EER are used to evaluate the performance. The poor or ambent llumnaton n ths database, along wth contactless magng, makes t most challengng among other databases. Fg. 7 llustrates the ROC and CMC curves. Table provdes the EER and average rank-one recognton accuracy. It can be observed that the proposed method acheves outperformng results over the other methods for both the verfcaton and dentfcaton. 4..2 IITD Palmprnt Database The IITD touchless palmprnt database [6] provdes contactless palmprnt mages from the rght and left hands of 23 subjects. There are more than 5 samples for each rght hand or left hand. Ths database provdes 5 5 pxels segmented palmprnt mages. 4. The three methods are mplemented by us. All of the results usng the verson of our mplementaton acheve smlar or slghtly better than those reported n the authors paper [8], [9], [4], wth same protocol and same datasets. The mplementaton as well as the parameters can be found on [].
6 Genune Acceptance Rate.96 Ordnal Code 4 2 Recognton Rate 9 8 7 6 5 4 3 Ordnal Code 2 4 6 8 Rank Fg. 7: The ROC curves and CMC curves of dfferent methods from the PolyU 2D/3D contactless palmprnt database. TABLE : The EER and rank-one recognton rate (accuracy) of dfferent methods from PolyU 2D/3D palmprnt database. Method Compettve Code Ordnal Code EER (%).22.64.68.33 Accuracy (%) 99.77 99.2 99.77 The protocol s exactly the same as n []. All the 3 rght hand palmprnt mages are used for our experments. For each subject, one mage for testng and the rest for tranng. The average performance s reported. The ROC, EER and CMC are used to ascertan the performance. Fg. 8 llustrates the ROC and CMC curves. Table 2 presents the EER and average rank-one recognton accuracy. The EER and rankone recognton rate from our method acheves outperformng results. TABLE 2: The EER and rank-one recognton rate (accuracy) of dfferent methods from the IITD palmprnt database. Method Compettve Code Ordnal Code EER (%).68.88..25 Accuracy (%) 99.5 99. 98.85 98.92 4..3 PolyU Palmprnt Database The PolyU palmprnt database [7] contans 7752 palmprnt mages from 386 dfferent palms. These mages were automatcally segmented to 28 28 pxel. In ths database, there are several mages whch are poorly algned due to ther rotatonal varaton. In our experments, we used the same protocol as reported n [8]. Only the frst sample of each ndvdual s used to construct the tranng set. Then, the tranng set s enlarged by rotatng each mage n tranng set at -9, -6, -3, 3, 6 and 9 respectvely. Consequently, there are seven tranng samples for each of the palms from database. Fg. 9 llustrates the comparatve ROC and CMC curves. Table 3 summarzes the EER and rank-one recognton accuracy from dfferent methods. The results from our method and the Ordnal Code are superor than those from the other two methods. Note that the performance from our method s observed to be slghtly better than that of Ordnal Code. The reason for the performance mprovement not beng sgnfcant, for ths PolyU palmprnt database, s that the Ordnal Code s specal case of our feature. Ths palmprnt database s a contact-based database acqured under controlled or very good llumnaton condton. The drecton of llumnaton vector L s almost parallel to z-axs (Fg. ). In ths case, the left sde Genune Acceptance Rate.96 Ordnal Code 4 2 Recognton Rate 8 6 4 2 Ordnal Code 2 4 6 8 Rank Fg. 8: The ROC curves and CMC curves of dfferent methods from the IITD palmprnt database. Genune Acceptance Rate 5 5 5 5 Ordnal Code Recognton Rate 95 9 85 8 2 4 6 8 Rank Ordnal Code Fg. 9: The ROC curves and CMC curves of dfferent methods from the PolyU palmprnt database. of the constrant n (9) s large enough to make t s satsfed. Accordng to our prevous analyss, the Ordnal Code method s essentally the dfference between the weghted combnaton of the pont normal vectors. Even f the flter s not carefully desgned, the constrant n (9) s excepted to hold good. Note that the feature sze of Ordnal Code s three tmes larger than ours, whle our method outperforms Ordnal Code. TABLE 3: The EER and rank-one recognton rate (accuracy) of dfferent methods from PolyU palmprnt database. Method Compettve Code Ordnal Code EER (%).33.89.76.38 Accuracy (%) 99.95 99.76 4..4 CASIA Palmprnt Database The CASIA palmprnt database contans 5239 palmprnt mages from 3 ndvduals. It s the largest publcly avalable palmprnt database n terms of the number of ndvduals. In ths database, the ndvdual s the same as the ndvdual 9 and therefore these two classes were merged nto one class. The th mage from the left hand of ndvdual 27 s also msplaced to the rght hand. The 3rd mage from left hand of ndvdual 76 s a dstorted sample whose qualty s very poor. These two samples can also be automatcally detected by our palmprnt segmentaton program []. We elmnated these two mages n our experment. Therefore all our experments wth ths database used 5237 mages belongng to 6 dfferent palms. We segmented and scaled the resultng mages n the database to 28 28 pxels. In our experments, the total number of resultng matches s 3,692,466, whch ncludes 2,567 genune and 3,689,899 mposter matches. Fg. llustrates the ROC and CMC results from the proposed method,, compettve code and Ordnal Code.
7 Genune Acceptance Rate.96.94.92.9.88 Ordnal Code 5 Fg. : The ROC curves from the CASIA palmprnt database. Table 4 summarzes EER acheved from these methods. Our method sgnfcantly outperforms competng three methods. TABLE 4: The EER(%) comparson from CASIA palmprnt database. Method Compettve Code Ordnal Code EER.53..76.79 4..5 Computatonal Complexty Table 5 lsts the computatonal tme for our method,, and Ordnal Code. The matchng speed of our method s the fastest among other methods. The feature extracton speed of our method s much faster than the, Ordnal Code and margnally slower than for. However, the matchng speed of our method s more than 22 tmes faster than that for the. TABLE 5: Feature extracton and matchng tme (ms) of dfferent methods. Method Feature Extracton Matchng..54.3.2 Compettve Code 4..54 Ordnal Code 3.2.54 Note: The expermental envronment s: Wndows 8 Professonal, Intel(R) Core(TM) 5-32M CPU@2.5GHz, 8G RAM, VS 2. 4.2 Addtonal Expermental Results In ths secton, we nvestgate the nfluence of usng dfferent flter confguratons as well as the denosng strategy for the palmprnt matchng performance. We use four publcly avalable databases employed n earler experments, wth ther descrbed protocols, to ascertan the performance from other flter confguratons. The weght rato and flter sze have been emprcally selected to acheve the llustrated performance. The EER results usng the dfferent flter confguratons n Fg. 3 are shown n Fg.. The expermental results valdate our analyss presented n Sec. 2.3, regardng the expected nfluence n the performance from the varatons n the number of cross and the drectons of the dfferent subset. The flter we selected acheves the best performance as llustrated. The results for the three competng methods are also shown n the fgure. All the other flter results are also not sgnfcantly nferor because they are ordnal measures and they can stll extract robust codes or feature n ther respectve templates. Ths fgure also llustrates the results wthout usng the denosng strategy,.e., employng ds(f, F 2 ) = S(F, F 2 ). nstead of (2), to compute the matchng dstance. As can be observed from the results, even wthout employng the denosng strategy, our feature can also acheve competng performance wth the state-of-the-art methods reported n the lterature. It should be noted that wthout denosng strategy, the matchng speed s three tmes faster. EER(%) 3.5 3 2.5 2.5.5 PloyU 2D/3D IITD PolyU CASIA /(d),ours (c) (e) (f) w/o denosng Ordnal Code Fg. : Comparatve performance usng EER from dfferent flter confguratons for four palmprnt databases. 4.3 Experment on Yale Face Database In ths experment, Extended Yale Face Database B [8] s employed. These experments are not ntended to nvestgate our feature on face surface, but we just want to evaluate the effectveness of our feature to support the arguments that our feature s ndeed descrbng the 3D shape nformaton whch s nsenstve to llumnaton changes. We choose Extended Yale Face Database B to acheve the goal for three reasons: ) There are only few palmprnt mages acqured under extreme lghtng condtons. The face data, whose surface s almost flat, s smlar to palmprnt surface. 2) Ths database s acqured under extreme llumnaton varatons. 3) The face data n ths database doesn t have any vew or expresson varatons. The Extended Yale Face Database B contans 38 subjects and each subject s wth 64 llumnaton condtons. The cropped faces wth the resoluton of 68 92 are also provded. In our experment, the most neutral lght sources (A+E+) mages are used as the gallery, and all the other frontal mages are used as probes (n summary, 38 mages consttute the tranng set and 2376 mages as test set). Ths database s used to evaluate the dentfcaton performance. We do not desgn addtonal flters accordng to the geometrcal propertes of the face surface but smply use the same dvson strategy as for the palmprnt. Besdes, the denosng matchng strategy s not employed to underlne our feature s robustness to the extremely varyng llumnaton condtons. The rank-one recognton result s 99.3% whch s the stateof-the-art performance. Table 6 provdes the comparson wth another two state-of-art methods on ths database. The results demonstrate that our feature s also robust to the llumnaton varatons.
8 TABLE 6: Identfcaton rate comparson wth the state-of-the-art methods from the Extended Yale Face Database B. Method PP+LTP/DT [9] G LDP [2] Rank- rate (%) 99.3 99. 97.9 4.4 Expermental Results from Fast- The experments n ths secton are used to verfy the effectveness of ordnal measure for the 2D palmprnt matchng. Frstly, we smplfy the to generate bnary representaton feature. As reported n [9], the uses sx flters to generate sx pre-templates. In the smplfed verson, two of the sx flters (the orentaton of these two flters are orthogonal) are used to generate two ntermedate pre-templates and subsequently bnary template s generated as the fnal feature. The rest of mplementaton of the s the same as n [9]. Ths method s referred [2] to as Fast-. Fg. 2 llustrates the ROC for the Fast- and on four 2D palmprnt databases usng the same protocols as reported above. It can be observed that the performance of smplfed/ordnal approach s superor to that of orgnal one. Therefore t s reasonable to conclude that ordnal measure s not only faster but also more accurate whch valdates our analyss n Sec. 3. Genune Acceptance Rate Genune Acceptance Rate 5 5 5 5 5 5 Fast 4 2 5 (c) Fast Genune Acceptance Rate Genune Acceptance Rate.96.96.94 Fast 4 2 Fast 5 Fg. 2: The ROC curves for Fast- and from PolyU Contactless 2D/3D database, IITD palmprnt database, (c) PolyU 2D palmprnt database and (d) CASIA 2D palmprnt database. 5 CONCLUSIONS Ths paper has proposed a new feature whch s based on ordnal measure. Ths feature recovers 3D shape nformaton of the surface whle t s extracted from pxel level nformaton n the contactless mages. The feature extracton and matchng s very effcent and the mplementaton s smple whch emphaszes on ts practcalty. The template sze from ths feature s also very small whle t acheves excellent performances on many databases. (d) The proposed feature s sutable to be combned [3] wth other features to further mprove the performance. There are two key reasons: ) t has lower storage requrements whle beng effcent to recover/extract and match, and most mportantly t s effectve n achevng accurate performance, 2) most of 2D feature mentoned n prevous sectons extract the texture nformaton whle our feature s recoverng 3D shape nformaton, whch means t s lkely to have less redundancy than the other features. Despte promsng results, there are several aspects of proposed approach that requre further consderaton. The mpact of non-lambertan surface and non-lnear palm deformatons, n the feature recovery and matchng, requres further study and analyss. REFERENCES [] Weblnk for downloadng codes for all algorthms n ths paper, avalable from: http://www4.comp.polyu.edu.hk/ csajaykr/2dto3d.htm. [2] R. Basr and D. W. Jacobs, Lambertan reflectance and lnear subspaces, Patt. Anal. Mach. Intell., IEEE Trans. on, vol. 25, no. 2, pp. 28 233, 23. [3] A. Kumar and C. Kwong, Towards contactless, low-cost and accurate 3d fngerprnt dentfcaton, Pattern Analyss and Machne Intellgence, IEEE Transactons on, vol. 37, no. 3, pp. 68 696, 25. [4] D. Malton, D. Mao, A. K. Jan, and S. Prabhakar, Handbook of fngerprnt recognton. Sprnger Scence & Busness Meda, 29. [5] P. Snha, Qualtatve representatons for recognton, n Bologcally Motvated Computer Vson. Sprnger, 22, pp. 249 262. [6] Z. Sun, T. Tan, Y. Wang, and S. Z. L, Ordnal palmprnt representon for personal dentfcaton [representon read representaton], n Comp. Vs. Patt. Recogn., 25. CVPR 25. IEEE Computer Socety Conf. on, vol.. IEEE, 25, pp. 279 284. [7] Z. Sun and T. Tan, Ordnal measures for rs recognton, Patt. Anal. Mach. Intell., IEEE Trans. on, vol. 3, no. 2, pp. 22 2226, 29. [8] W. Ja, D.-S. Huang, and D. Zhang, Palmprnt verfcaton based on robust lne orentaton code, Patt. Recogn., pp. 54 53, 28. [9] A.-K. Kong and D. Zhang, Compettve codng scheme for palmprnt verfcaton, n Patt. Recogn., 24. ICPR 24. Proc. of the 7th Inter. Conf. on, vol.. IEEE, 24, pp. 52 523. [] A. Kumar and S. Shekhar, Personal dentfcaton usng multbometrcs rank-level fuson, Systems, Man, and Cybernetcs, Part C: Applcatons and Revews, IEEE Trans. on, vol. 4, no. 5, pp. 743 752, 2. [] V. Kanhangad, A. Kumar, and D. Zhang, A unfed framework for contactless hand verfcaton, Info. Fore. Sec., IEEE Trans. on, vol. 6, no. 3, pp. 4 27, 2. [2] D. Zhang, W.-K. Kong, J. You, and M. Wong, Onlne palmprnt dentfcaton, Patt. Anal. Mach. Intell., IEEE Trans. on, vol. 25, no. 9, pp. 4 5, 23. [3] J. Daugman, The mportance of beng random: statstcal prncples of rs recognton, Patt. recogn., vol. 36, no. 2, pp. 279 29, 23. [4] D. N. Bhat and S. K. Nayar, Ordnal measures for mage correspondence, Patt. Anal. Mach. Intell., IEEE Trans. on, vol. 2, no. 4, pp. 45 423, 998. [5] The Hong Kong Polytechnc Unversty Contact-free 3D/2D Hand Images Database (Ver.), avalable onlne. [6] IIT Delh Touchless Palmprnt Database (Ver.). (25, Jun. ). [onlne], avalable from: http://web.td.ac.n/ ajaykr/database Palm.htm. [7] PolyU Palmprnt Palmprnt Database [onlne], The Hong Kong Polytechnc Unversty, http://www.comp.polyu.edu.hk/ bometrcs/. [8] K.-C. Lee, J. Ho, and D. J. Kregman, Acqurng lnear subspaces for face recognton under varable lghtng, Patt. Anal. Mach. Intell., IEEE Trans. on, vol. 27, no. 5, pp. 684 698, 25. [9] X. Tan and B. Trggs, Enhanced local texture feature sets for face recognton under dffcult lghtng condtons, Image Proc., IEEE Trans. on, vol. 9, no. 6, pp. 635 65, 2. [2] B. Zhang, Y. Gao, S. Zhao, and J. Lu, Local dervatve pattern versus local bnary pattern: face recognton wth hgh-order local pattern descrptor, Image Proc., IEEE Trans. on, vol. 9, pp. 533 544, 2. [2] Q. Zheng, A. Kumar, and G. Pan, Suspectng less and achevng more: new nsghts on palmprnt dentfcaton for faster and more accurate matchng, Info. Fore. Sec., IEEE Trans. on, 25.