A Minutiae-based Fingerprint Matching Algorithm Using Phase Correlation

Transcription

1 A Minutiae-based Fingepint Matching Algoithm Using Phase Coelation Autho Chen, Weiping, Gao, Yongsheng Published 2007 Confeence Title Digital Image Computing: Techniques and Applications DOI Copyight Statement 2007 IEEE. Pesonal use of this mateial is pemitted. Howeve, pemission to epint/ epublish this mateial fo advetising o pomotional puposes o fo ceating new collective wos fo esale o edistibution to seves o lists, o to euse any copyighted component of this wo in othe wos must be obtained fom the IEEE. Downloaded fom Lin to published vesion Giffith Reseach Online

2 Digital Image Computing Techniques and Applications A Minutiae-based Fingepint Matching Algoithm Using Phase Coelation Weiping Chen and Yongsheng Gao School of Engineeing, Faculty of Engineeing and Infomation Technology, Giffith Univesity, Austalia weiping.chen@student.giffith.edu.au, yongsheng.gao@giffith.edu.au Abstact Minutiae-based method is the most popula appoach in fingepint matching. Howeve, most existing methods need to seach fo the best coespondence of minutiae pais o use efeence points (coe and delta points) to estimate the alignment paametes. The poblem of lost minutiae o spuious minutiae always occus duing the minutiae detection pocess. Hence, the coesponding pais o efeence points may not be found unde this condition. This pape poposes a new minutiae-based fingepint matching algoithm using phase coelation. We define a new epesentation called Minutiae Diection Map (MDM). Fist, we convet minutiae sets into 2D image spaces. Then the tansfomation paametes ae calculated using phase coelation between two MDMs to align two fingepints to be matched. The similaity of two fingepints is detemined by the distance between two minutiae sets. Ou appoach does not need to seach fo the coesponding minutiae pais. Expeimental esults show that the poposed appoach pefomed well in matching fingepint minutiae sets, which geatly impoved the economy of stoage space. 1. Intoduction Fingepint has been used as a method of pesonal identification fo ove a centuy. It is widely used in biometic authentication at pesent because of its uniqueness and pemanence. A fingepint consists of idges and valleys. Thee ae two basic featues used in fingepint ecognition, i.e. idge endings and idge bifucations. Othe featues ae also used. Accoding to featues used in fingepint ecognition, automatic fingepint ecognition techniques ae classified into minutiae-based, image-based and idge featue-based appoaches [1]. Ridge featue-based appoach [2] is used when minutiae ae difficult to extact in vey lowquality fingepint images, wheeas othe featues of the fingepint idge patten (e.g., local oientation and fequency, idge shape, textue infomation) may be extacted moe eliably than minutiae, even though thei distinctiveness is geneally lowe. Image-based appoaches [3, 4] use the entie gay scale fingepint images as a template to match against input fingepint images. This appoach needs a lage size of stoage space and fingepint images ae illegal to be stoed in some nations. Minutiae-based appoach attempts to get the similaity degee between two minutiae sets. Howeve, minutiae-based methods may mae the computation moe sophisticated and need to seach fo the best coespondence of minutiae pais o idge pais [5] o use coe o delta minutiae point to estimate the alignment [6]. The poblem of lost minutiae o false minutiae always occus duing the minutiae detection pocess. Hence, the coesponding pais may not be found unde this condition. In this pape, a new epesentation called Minutiae Diection Map (MDM) is intoduced, which is geneated by conveting minutiae point sets into 2D image spaces. The alignment paametes ae calculated using phase coelation between the input MDM and the template MDM. Ou appoach does not need to seach fo the coesponding minutiae pais between the two fingepints. The alignment paametes ae obtained diectly though phase coelation between two MDMs. Phase coelation [7] method povides staightfowad estimation of igid tanslation between two images. It was applied in image-based fingepint ecognition [3, 4]. Howeve, fingepint ecognition is widely applied in embedded system o potable device which equies a small stoage space. Since imagebased algoithms pocess entie fingepint images, thei lage stoage equiement fo all fingepint images limits thei applicability. The poposed minutiae-based appoach, stoes meely a small numbe of minutiae points, which geatly educes the stoage equiement. The pape is oganized as follows: Section 2 gives the definition of phase coelation. Section 3 descibes a fingepint ecognition algoithm using phase coelation, which includes the poposed epesentation /07 $ IEEE DOI /DICTA

3 MDM. Section 4 pesents the expeiment fo evaluating matching pefomance and peliminay esults. Conclusion is dawn in Section Phase Coelation The phase coelation (PC) method is a popula choice fo image egistation because of its obust pefomance and computational simplicity [8]. It is based on the well-nown Fouie shift theoem. Suppose two images f 1 and f 2, which diffe only by a tanslation dx and dy. The elationship between these two images is given by matching algoithm includes two stages: alignment stage and matching stage. In alignment stage, tansfomations including otation and tanslation between two minutiae sets ae calculated and then the input minutia set is aligned to models fo similaity measuement. In this study, we assume thee is no scaling diffeent between two fingepints as they ae usually taen at the same esolution. The similaity between aligned input minutiae set and the template minutiae set is calculated in matching stage. f ( x, y) = f ( x dx, y dy). (1) 2 1 Thei coesponding Fouie Tansfoms F 1 and F 2 ae elated by j 2 π ( udx M + vdy N ) 2 1 F ( u, v) = e F ( u, v). (2) In othe wods, the Fouie magnitudes of the two images ae same while thei phases ae diffeent. This phase diffeence is diectly elated to displacement. The coss-phase spectum (o nomalized coss-phase spectum) P( uv, ) which is epesented by * F1 ( u, v) F2( u, v) j2 π ( udm M + vdn N ) = = e (3) * F1 ( u, v) F2( u, v) P( u, v), * whee F1 ( uv, ) denotes the complex conjugate of F1 ( uv., ) The 2D invese Fouie tansfom of cossphase spectum is given by 1 p( m, n) (, ). MN = j2 π ( um M + vn N ) P u v e (4) u, v p( mn, ) is a delta function. The displacement coodinates ae detemined accoding to the location of the pea in the invese coss-phase spectum space. 3. Fingepint Matching Algoithm Using Phase Coelation In this section, we pesent the poposed the fingepint matching algoithm using phase coelation based on minutiae points. Minutiae ae pominent local idge chaacteistics in fingepint (see Figue 1). Ou Figue 1. Two types of minutiae: idge ending(left) and idge bifucation (ight) [9]. 3.1 The Poposed Repesentation: Minutiae Diection Map Phase coelation can not be used to align two point sets diectly. We pesent a new epesentation called Minutiae Diection Map (MDM) which is geneated by conveting minutiae point sets into a 2D image space. Alignment paametes ae detemined using phase coelation between two MDMs. Let M = (( x, y, α ),, ( x, y, α )) denote the N N N set of N minutiae in a fingepint image. The image size is C R and ( xi, yi, αi) ae the thee featues (spatial position and oientation) associated with the ith minutiae in set M. Define the MDM of set M as M M ( mn, ), m [0, C 1], n [0, R 1]. It contains the angles of minutiae diections at the positions of minutiae points and 0 othewise, which is witten as j cosαi + sin αi m= xi, n= y M i, M ( mn, ), (5) 0 othewise = 234

4 Whee ( x, y, α ) M. The size of the MDM M M i i i is the same as that of the fingepint image. 3.2 Alignment In this stage, alignment paametes (displacements and otation) ae calculated between the template fingepint and the input fingepint. We assume the scaling is constant because the images in most applications ae acquied at the same esolution. Afte conveting minutiae sets into MDMs, the alignment paametes ae estimated using phase coelation. Suppose the possible otation angle is fom θ θ with a angle spacing θ. To evey θ [ θ, θ ], the input minutiae set I is otated into a new input minutiae set I, then convet the otated input minutiae set into an input MDM I M (see Section 3.1). A set of input MDMs to I M is obtained whee = 0,1, 2,, M; M = 2θ θ. The highest coelation pea value v in th invese phase coelation space is calculated by ( dx, dy ) = ag m ax { p ( m, n) } m, n (6) v ( dx, dy ) = p ( dx, dy ), whee p ( mn, ) is the invese phase coelation I between th input MDM M and template MDM T M and = 0,1, 2,, M; M 2θ θ dx, dy is the coodinate of v. If the size of MDM is C R, then m [0, C 1] and n [0, R 1]. A set of highest coelation pea V = v dx, dy,, v dx, dy is thus =. ( ) value { 0 ( 0 0) M ( M M )} obtained, whee (, ) v dx dy is imum invese PC value in V, = 0,1, 2,, M; M = 2θ θ. Displacement ( x, y) between two fingepint images is the ( dx, dy) with imal value of v in set V and otation angle θ is coesponding to index with the imal value of v. Tansfomation paametes ae thus calculated using equations (7). 3.3 Matching θ = θ θ x = dx y = dy (7) The input minutiae set ( I ) is aligned into new set ( I ) based on the tansfomation paametes, which ae calculated in section 3.2. The ovelapping egion is defined accoding to minutiae locations in aligned input ( I ) and template minutiae sets ( T ). Two minutiae subsets T o and I o ae minutiae located in ovelapping aea in template minutiae set ( T ) and aligned input set ( I ) espectively. A A B B B B Let Ax (, y, α ) and Bx (, y, α ) denote two minutiae points in template ( T o ) and aligned input set ( I o ) espectively. The distance between these two points is defined in equation (8). A B 2 A B 2 2 d( A, B) = ( x x ) + ( y y ) + f ( θ ), (8) whee A B A B o α α if α α 180 θ = (9) 0 A B o A B o 360 α α if 180 < α α 360, x and f( x) = W tan( ) (10) 2 W is a weight to be detemined expeimentally in section 4.1. Let To = ( A1, A2,..., Ap) and Io = ( B1, B2,..., Bq) denote two minutiae sets. The distance between T o and I o is calculated using equation (11) to measue the similaity between the template minutiae set (T ) and input minutiae set ( I ). whee o o o o o o ST (, I ) = ( DT (, I ), DI (, T)) (11) 1 o o i j p A Bj Io i T o D( T, I ) = min d( A, B ). (12) If the distance ( ST ( o, I o) ) between two minutiae sets is less than a theshold, we thin two images come fom the same finge; othewise the two images come fom diffeent finges. 235

5 4. Expeiment and Peliminay Results In ou expeiment, we captued fingepints using SecuGen Hamste III (see Figue 2). This scanne employs a high-pefomance and maintenance-fee optical senso. The size of captued fingepint image is (width height). We ceated a fingepint database containing 400 fingepints, which consists of 100 finges and 4 impessions pe finge. Sample impessions ae illustated in Figue 3. Minutiae extaction algoithm [9] is applied to get minutiae sets fo fingepint images. Genuine matching scoes and imposto matching scoes wee calculated using the same stategy as in [10]. In genuine test, each sample is matched against the emaining samples of the same finge to compute the False Non Match Rate (FNMR). In the imposto matching test, the fist sample of each finge is matched against the fist sample of the emaining finges in database to compute the False Match Rate (FMR). The total numbe of genuine tests and imposto tests ae 600 and 4950 espectively. Figue 3. Example impessions of one finge. 4.1 Detemination of W The effect of W in equation (10) was investigated using above database. Figue 4 shows the cuve of equal eo ate (EER) of FMR nd FNMR against the W. The EER deceases geatly fom W=0 to W=80. Between W=80 and W=200, the EER is steady. Then it inceases with the incease of W. Fo the following expeiments, W was set as 170. Figue 2. SecuGen Hamste III fingepint eade Figue 4. The effect of W on the equal eo ate (EER). 236

6 4.2 Peliminay Results In the expeiment, Equal Eo Rate (EER) was used to evaluate the system pefomance of the poposed method. In geneal, the pefomance of a matching algoithm can be depicted by the Equal Eo Rate (EER), which is value whee the FMR (False Match Rate) and FNMR (False Non-Match Rate) ae equal [10]. FNMR and FMR ae computed using equation (13). cad{ ims ims d} FMR( d) = NIRA cad{ gms gms < d} FNMR( d) = NGRA (13) whee gms and ims ae genuine matching scoe and imposto matching scoe espectively. d is the theshold of matching scoe. cad denotes the cadinality of the given set. NGRA is the numbe of genuine matching attempts and NIRA is the numbe of imposto matching attempts. Given a theshold d, FMR( d ) and FNMR( d) denote the pecentage of ims d and the pecentage of gms < d espectively [11]. Figue 5 shows the ROC cuve in log-log scales fo the poposed algoithm. The EER of the poposed algoithm is 2.44%. 5. Conclusion This pape poposes a novel minutiae-based fingepint matching appoach, which utilizes phase coelation to calculate the alignment paametes between two minutiae sets and the similaity is measued between the template minutiae set and the aligned input set. The computation of this poposed method is simple without the need of seaching fo coesponding minutiae pais. In ou algoithm, we only use the locations and diections of spase minutiae points in fingepints, which geatly educes the stoage space, compaing to cuent phase-based fingepint matching techniques [3, 4]. Expeimental esults show that the poposed appoach pefomed well in matching fingepint minutiae sets, which geatly impoved the economy of stoage space. As the FVC2004 fingepint database contains patial impession, we will solve the incomplete/patial fingepint poblem in futue eseach in ode to mae a diect pefomance compaison between the poposed method and those epoted methods in [10]. 6. Refeences [1] D.Maltoni, D.Maio, A.K.Jain, and S.Pabhaa, Handboo of Fingepint Recognition. New Yo: Spinge, [2] A.K.Jain, S.Pabhaa, H.Lin, and S.Pananti, "Filteban-based fingepint matching," IEEE Tansactions on Image Pocessing, vol. 9, pp , [3] K.Ito, H.Naajima, K.Kobayashi, T.Aoi, and T.Higuchi, "A Fingepint Matching Algoithm Using Phase-Only Coelation," IEICE TRANS. FUNDAMENTALS, vol. E87-A, pp , [4] J.Zhang, Z.Ou, and H.Wei, "Fingepint Matching Using Phase-Only Coelation and Fouie-Mellin Tansfoms," pesented at The Sixth Intenational Confeence on Intelligent Systems Design and Applications (ISDA06), [5] A.K.Jain, H.Lin, and R.Bolle, "On-line fingepint veification," IEEE Tansactions on Patten Analysis and Machine Intelligence, vol. 19, pp , Figue 5. ROC cuves of the poposed algoithm. [6] K.C.Chan, Y.S.Moon, and P.S.Cheng, "Fast fingepint veification using subegions of fingepint images," IEEE Tansactions on Cicuits and Systems fo Video Technology, vol. 14, pp , [7] L.G.Bown, "A suvey of image egistation techniques," ACM Computing Suveys, vol. 24, pp ,

7 [8] W. S. Hoge, "A subspace identification extension to the phase coelation method [MRI application]," IEEE Tansactions on Medical Imaging, vol. 22, pp , [9] C.Watson and M. Gais, "Uses guide to NIST Fingepint image softwae2," National Institute of Standads and Technology, [10] R. Cappelli, D. Maio, D. Maltoni, J. L. Wayman, and A. K. Jain, "Pefomance Evaluation of Fingepint Veification Systems," IEEE Tansactions on Patten Analysis and Machine Intelligence, vol. 28, no. 1, Januay [11] D. Maio, D. Maltoni, R. Cappelli, J. L. Wayman, and A. K. Jain, "FVC2000: Fingepint Veification Competition," IEEE Tansactions on Patten Analysis and Machine Intelligence, vol. 24, no. 3, Mach