A fingerprint identification algorithm by clustering similarity

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1 Scence n Chna Ser. Informaton Scences 005 Vol.48 No A fngerprnt dentfcaton algorthm by clusterng smlarty TIAN Je, HE Yulang, CHEN Hong & YAN Xn Center for Bometrc Research and Testng (CBRT), Key Laboratory of Complex Systems and Intellgence Scence, Insttute of Automaton, Chnese Academy of Scences, raduate School of the Chnese Academy of Scences, Bejng , Chna Correspondence should be addressed to Tan Je (emal: tan@doctor.com; je.tan@mal.a.ac.cn) Receved November 30, 004 Abstract Ths paper ntroduces a fngerprnt dentfcaton algorthm by clusterng smlarty wth the vew to overcome the dlemmas encountered n fngerprnt dentfcaton. To decrease mult-spectrum noses n a fngerprnt, we frst use a dyadc scale space (DSS) method for mage enhancement. The second step descrbes the relatve features among mnutae by buldng a mnuta-smplex whch contans a par of mnutae and ther local assocated rdge nformaton, wth ts transformaton-varant and nvarant relatve features appled for comprehensve smlarty measurement and for parameter estmaton respectvely. The clusterng method s employed to estmate the transformaton space. nally, mult-resoluton technque s used to fnd an optmal transformaton model for gettng the maxmal mutual nformaton between the nput and the template features. The expermental results ncludng the performance evaluaton by the nd Internatonal Verfcaton Competton n 00 (VC00), over the four fngerprnt databases of VC00 ndcate that our method s promsng n an automatc fngerprnt dentfcaton system (AIS). Keywords: dyadc scale space (DSS), mnuta-smplex, mult-resoluton, comprehensve smlarty. DOI: /04yf Introducton Automatc fngerprnt dentfcaton system (AIS) has been wdely used and t conssts of fngerprnt enhancement and matchng. ngerprnt enhancement s to recover the topology structure of rdges and valleys from the corrupted mage durng capture because of mpresson, sn, and reader etc. Most of fngerprnt enhancement algorthms are based on orentaton feld estmaton, such as Ln et al. s [1] abor flter method. These methods have a defect that a local bad-qualty regon needs to be enhanced whle estmatng ts local orentaton feld. As a result, the orentaton feld s unrelable and the enhancement s compromsed. ngerprnt matchng s to obtan the maxmal mutual nformaton between the nput

2 438 Scence n Chna Ser. Informaton Scences 005 Vol.48 No and the template features. It generally conssts of extractng feature, modellng relatve structure, algnment, and therefore obtanng the maxmal smlarty between two fngerprnts. ngerprnt matchng nvolves a wde range of algorthms wth dfferent technques. These schemes are based predomnantly on local landmars, exclusve global features as well as comprehensve fngerprnt features. The mnutae-based matchng methods [,3] are wdely used n memory-lmted AISs because they need less memory expense and havng tme savng advantages. However, mnutae cannot characterze overall pattern of a fngerprnt, and t s hard to further mprove ther performance. The exclusve global feature-based technques [4,5] match the global patterns of the fngerprnt texture by algnng the nput global features and calculatng the maxmum mutual global nformaton between two fngerprnts. In these methods, however, the central pont should be determned wth a relable accuracy and t s dffcult to deal wth dstorton n fngerprnts. Comprehensve feature-based technques [6,7] are also seen as a hybrd matchng method by fusng mnutae, local features and global features. Local features help accelerate the algnment of the unregstered mnuta patterns n dfferent szes. lobal features are used to overcome the shortness of mnutae and local features n bad qualty fngerprnts. Wth the reasonable tme and memory expenses, comprehensve feature-based technques outperform the above mentoned matchng methods. In addton, they combne varous classfers for fngerprnt matchng. Wth the advanced hardware technology, these approaches have become popular for ther good performance n acceptable memory expense n recent years. Ths paper ntroduces an dentfcaton algorthm by clusterng smlarty wth the vew to overcome the dlemmas encountered n fngerprnt matchng process. We frst employed Cheng et al. s dyadc scale space (DSS)-based enhancement method [8] for a fngerprnt s often affected by mult-spectrum noses. Mnutae and local rdge nformaton are combned, and mnuta-smplex s bult to descrbe a nd order relatve structure among mnutae. By the second step, the transformaton space s estmated n terms of a clusterng method, and mult-resoluton technque [9] s employed to obtan an optmal transformaton model. nally, the global smlarty s calculated by accumulatng all local smlarty by usng plus rule. Expermental results show that our method s promsng n an AIS. ngerprnt enhancement based on DSS In computer vson, scale-space theory s often used for mage segmentaton and edge extracton. Those are consdered as the object s outlne. ngerprnt mage has ts own characterstcs, such as the flow-le pattern, whch means rdges are alternated wth valleys. In our algorthm, a fngerprnt s frst decomposed nto a seres of mages to reduce noses n dfferent scales. All the enhanced mages are combned to get a more credble mage. Each tme we reduce the nose to some extent, and wth several teratons, the fnal enhanced mage was obtaned.

3 A fngerprnt dentfcaton algorthm by clusterng smlarty Lnear scale space Scale-space theory provdes a canoncal framewor for modelng vsual operaton at multple scales. The scale-space representaton L: R R R of a two-dmensonal mage f s defned as one-parameter famly of functons obtaned by convolvng f wth aussan ernel: Lxyt (, ; ) = f( xy, ) gt ( xy,, θ ); (( xcosθ) + ( ysnθ) ) g (,, ) t t x y θ = e, π t (1) where the parameter t s called scale parameter and θ s the drecton of the pxel (x, y) n f. Although fngerprnts are non-sotropc, we use the lnear scale-space to detect the feature because the rdge s a lne n local regon. And the convoluton s along the rdge drecton, as the flter s adapted to rdge drecton. Equvalently, these famly mages can be generated by the soluton to the dffuson equaton: wth ntal condton L(x, y; 0)= f(x, y). 1 T 1 t L= L= ( + )L () x y In scale-space, wth the ncrease of the scale, the number of the detals decreases and the nose s successvely suppressed gradually. The feature of the mage n large scale exsts n the mage of small scale as well, whle the wea sgnal wll dsappear n the large scale space. Those features exstng n the mage of large scale are global structure. Usng a seres of scales σ 1, σ,, σ n0 to flter the mage f, the scale-spaces are denoted as L σ (n 0 1) wth scale σ. We defne the detals between two scales as ( ) D = L L ; n 1 1. σ σ Let D 0 = f L σ 1, we obtan the scale-space representaton and ts detals, and construct them to enhance the mage f:. Pre-processng wth DSS n 1 = 0 (3) f = L + D. (4) σ n There are two problems n fngerprnt enhancement by usng scale-space theory. One s how to select dfferent scales, and the other s how long the seres s. We dscuss the problem as follows. Analogcal to the wavelet, we use the dyadc scale to decompose a fngerprnt. The scale s selected as σ = (n 0 1), and t s called dyadc, the scale-space s nown

4 440 Scence n Chna Ser. Informaton Scences 005 Vol.48 No as DSS. The length of the seres s decded by n 0. We defne the mean wdth of fngerprnt as w, calculated wth Ln et al. s method [1], and n 0 = log (w). We get the smoothed mage of the fngerprnt mage f by usng DSS (n 0 1), = f. Wth formulas (3) and (4), the detal mage, D (n 0 1 0), s obtaned. The effect of the nose s reduced n the mage L σ. The gray values reflect the rdge value. And D contans the nformaton, so does, but at the stage of the nformaton s lost. L σ L σ L σ+ 1 Because of the nose n D, we smooth t wth scale +1, that s, L σ L σ = D g. Let E 1 be the mage obtaned through the scale 1. The mage E at the scale s calculated wth formulas (5) and (6): 0, t 0, E 1(, j) Lσ (, j) L (, ) ; 1 σ j + E(, j) = 55, t = 0 or E 1 (, j) ( Lσ (, j) + L (, )); 1 σ j (5) + 55 ( E 1(, j) L (, j) L (, j) ), t 0, E 1 1( t - σ + σ, j ) ( L σ (, j ) + L (, j ) ), + 1 σ where L σ ( ) Lσ (, j) + L (, ) 1 1(, ), (, ) (, ) 55, σ j E j L j L j + σ + 1 σ + t = 55 Lσ (, j) L (, j), otherwse. + 1 σ Because the gray value n the L σ + 1 s credble. Then we compare the gray value of +1 g (6) s smoothed to reduce the nose, the gray value L σ +1 wth L σ and get the result mage whch s affected by noses. The nose s reduced through ths step tme by tme. Snce a fngerprnt may be corrupted by nose durng capture because of mpresson, sn, reader, etc., Luo et al. s nowledge-based fngerprnt enhancement method [10] s used to reduce the effects. And arna s mnuta extracton method [11] s appled to detect mnutae n the thnned fngerprnt. 3 Mnutae matchng usng clusterng method In our matchng, fngerprnt s matched to fngerprnt wth the followng steps. We frst ntroduce mnuta-smplex, a relatve structure among mnutae, for ts good trade-off between performance and memory expense. Then we roughly match mnutasmplex, calculate the local smlarty, and estmate the transformaton model and ts correspondng space n terms of clusterng. nally, we search for an optmal transformaton model usng mult-resoluton technque to obtan the maxmal mutual nformaton between two fngerprnts. 3.1 eature analyss wth clusterng method A fngerprnt feature s produced wth weght p (1 p 0) for t s nterrupted by

5 A fngerprnt dentfcaton algorthm by clusterng smlarty 441 noses or bad qualty. In our study, we estmate the dstrbuton of these features n terms of -means clusterng method [1]. (N) Let X={X = ( x () 1,, x ) T ; X 1} denote a feature set. Assume that all features n X are ndependent, and the elements of each feature are also ndependent. Then analyze the dstrbuton of all features X X wth the followng steps: Step 1. Set X s represented wth X () ={x () ; X 1, N 1} and X={X (1),, X (N) }. Let x () denote the th element of a feature. To buld the hstogram of x (), H(x () ) (N 1) wth formula (7). H(x () ) represents the dstrbuton of x (). ( ) ( ) H x = ( ) ( ) { j; xj = x } Σp Step. To flter H(x () ) wth formula (8) to reduce the effects of noses on the dstrbuton of x. j p j. (1 cos( xπ / d)) f( x) = ; 1 x d + 1. (8) Step 3. To calculate the confdence nterval of x () under a confdence. Theoretcally, x () most probably happens where H(x () ) s maxmal, that s, H(u )=max{h(x )}. However, u s affected by noses so that we use a confdence nterval U =[u λ σ, u +λ σ ] nstead of a pont where u and σ are the mean and standard devaton of x () respectvely. And λ (λ >0) s an emprcal threshold. There s a probablty that x () wll happen n the nterval U s φ (λ ) 1. It s dffcult to obtan the varance u and σ. Therefore, we ndrectly estmate them by the followng steps. We frst fnd the maxmum of H(x () ) to obtan u, that s, to fnd a ste x () = u ± λ σ where H(x () λ ( ) )= exp max{ H ( x ) }. Then we estmate the confdent nterval U wth the confdence φ (λ ) 1. We algn λ accordng to confdence λ and ts confdent nterval. If λ = ln =1.38, exp =0.5, ts correspondng con- fdence and confdence nterval are and U =[u 1.38σ, u +1.38σ ]. Step 4. To calculate the confdence nterval of feature X. or the confdence nterval of all x (), and ther correspondng confdence nterval U, the confdence nterval of feature X s S={x () U ; N 1}(λ 1 =λ = =λ N =λ). If a feature s outsde S, t s unmportant. If an estmated space wth λ s far greater than a preset space, the feature set X s consdered as a dsorder set. (7)

6 44 Scence n Chna Ser. Informaton Scences 005 Vol.48 No ngerprnt representaton n our method A comprehensve mnuta ncludes ts mnutae and ts local assocated rdge nformaton. Let M ={ M = ( x,, α, y l j β,, ϕ j ) T ; M 1, L j 1} denote the comprehensve mnutae set of fngerprnt. A comprehensve mnuta M s repre- sented by a feature vector ( x, y, α, where 1) y x and are the coordnates; ) l j β,, ϕ j ) T ( M 1, L j 1), α s the tangent drecton at β s the local grey varance of a area whose centre s type of the mnuta wth ts local grey varaton snce the type of, endng or bfurcatng, s corrupted by noses; 4) M to the jth sampled pont on the rdge begnnng at the jth sampled pont. All ( l j, ϕ j denotes the drecton from l j M M M ; 3). We replace the M, and denotes the dstance from M to ϕ j ) represent the rdge nformaton assocated wth the mnutae; 5) M denotes the number of mnutae n fngerprnt and L the number of sampled ponts on a rdge. A fngerprnt s represented by relatve structures among mnutae. Let E ={ ; E 1} denote all relatve structures, where E s the sze of set E. eatures of E can be decomposed nto transformaton-nvarant feature vector varant feature vector C V V and transformaton accordng to ther relatvty wth transformaton. Let E C V C ={ }, V ={ }, and ={, }. or an optmal transformaton T, t s possble to obtan the maxmal mutual nformaton between fngerprnts and, that s, the maxmal mutual nformaton between all V and V. Ther relaton s descrbed by T (V V ) T=H(V V ), H( ) s the functon of V V. In our study, a mnuta-smplex s employed to descrbe a nd-order relatve structure among mnutae. Compared wth mnuta-trplet [3], mnuta-smplex has good trade-off between performance and expense. Mnuta-smplex s bult as follows. or each par of mnutae d( M, and M and M j )= ( x xj ) +( y yj ) M j C E ( M, j 1) n M, f ther dstance satsfes d l d ( M, j M ) d h, M j are connected as a mnuta-smplex descrbed by a feature vector composed of r e ndex features (, ), transformaton-nvarants (, l 1 transformaton-varants ( θ, ϕ t 1, ϕ t, α 1, α )(L t 1) where r e u v M β, β,, ), and 1) Index features and denote the seral numbers of two mnutae assocated

7 A fngerprnt dentfcaton algorthm by clusterng smlarty 443 E r e wth,.e. = and =j. l 1 ), u v β, β, and descrbe the transformaton-nvarant relatve features of E. They are rrelevant wth rotaton and translaton, where 1 β = β, β = β j, u = α θ, v = α j θ. 3) l =d( M, M j ), θ, ϕ t 1, ϕ t, α 1 and α (L t 1) represent the transformaton-varant relatve features of t 1). Let E ={ E E where y θ = arctan x y j x j ; ϕ t 1 = ϕ t and ϕ t= ϕ jt (L ; E 1} denote all smplexes n fngerprnt where E s the sze of set E. E represents the global characterstcs of fngerprnt more accurately than the mnuta set M. E s much smaller than M because many mnuta pars do not satsfy d l d(m, M j ) d h. d l and d h are two emprcal thresholds dependent on sensors. Let dv={dv =(dθ, dx, dy ) T } denote the bas set of all transformaton-varant relatve features of mnuta-smplexes, where dv s a vector descrbng bases of transformaton-varants of the th mnuta-smplex wth formula (9). dx dy = 1 = 1 dx =, dy =, L L dθ + dα + dϕ + dϕ dθ = L = 1 = 1 = 1. (9) 3.3 Transformaton space estmaton In our study, affne transformaton s employed to model H( ) for ts good matchng performance. Compared wth eng et al. s [13] method, -clusterng method s employed n our wor to estmate the transformaton space. Let H( ) denote all transformaton models n fngerprnt matchng. H( ) s understood as the functon of dv=v V, that s, H( )={H θ ( ), H x ( ), H y ( )}. In our study, matchng s performed n the polar system and center ponts of fngerprnts and are calculated n advance. One of the most challengng tass n matchng s to estmate an optmal nterval of rotaton transformaton parameter wth the followng steps:

8 444 Scence n Chna Ser. Informaton Scences 005 Vol.48 No Step 1. To calculate dv. or an nput mnuta-smplex correspondng template E n dv are calculated wth formula (9). E m ( E m 1) and ts ( E n 1), ther transformaton-varant feature bases Step. To test all elements n dv. dv s nvald f s not equal to. Consderng the nose n matchng, s matched to n terms of tolerance devaton, and ther smlarty s denoted wth S(, ) wth formula (10). S(, ) s also seen as the weght of dv. In formula (10), ε s a threshold ndcatng the tolerance devaton of transformaton-varant relatve features. 0, Cm Cn ε; SC ( m, Cn ) = Cm Cn 1,otherwse. ε (10) Step 3. To estmate rotaton-transformaton nterval. or dv and ts correspondng S(, ), the dstrbuton H θ ( ) and confdence nterval of transformaton θ can be estmated wth the clusterng method descrbed above. Step 4. To calculate the ntal rotaton transformaton model. or the transformaton space S and the dstrbuton of rotaton transformaton parameter H θ ( ), an ntal transformaton model θ 0 s calculated wth formula (11) n terms of geometrc means. u θ and σ θ can be calculated wth the scheme descrbed above when λ θ =1.38. θ = 0 u + λσ θ θ θ uθ λσ θ θ u + λσ θ θ θ u λσ θ θ θ θ H ( θ ) θ H ( θ ). (11) To evaluate the performance of the ntal rotaton-parameter, an experment was performed over 0 fngerprnts randomly selected from the fngerprnt databases of VC00 (the nd Internatonal ngerprnt Verfcaton Competton n 00 [14] ). or fngerprnt, ts transformed fngerprnt was produced by rotatng wth an angle θ (15 θ 15 ), wth reference to ts central pont. And rotaton parameters θ between and were estmated from ther H θ ( ). The result s shown n g. 1. The mean of the absolute errors θ θ was To evaluate the performance of H θ ( ), a par of fngerprnts were selected from the same fnger, as shown n g. (a), whle two other pars of fngerprnts were selected from two dfferent fngers respectvely, see g. (b) and (c). The two fngerprnts of

9 A fngerprnt dentfcaton algorthm by clusterng smlarty 445 g. 1. Performance of estmatng ntal rotaton-parameter. g.. Performance of H θ ( )s of three pars of fngerprnts. (a) shows two fngerprnts from the same fnger whle (b) and (c) dsplay two pars of fngerprnts from two dfferent fngers.

10 446 Scence n Chna Ser. Informaton Scences 005 Vol.48 No the second par are smlar. g. (a), (b) and (c) show that the H θ ( ) of the frst par s of normal dstrbuton whle two other H θ ( )s are of random dstrbuton caused by msmatches produced by spurs or deformaton although the second H θ ( ) s more regular than that of the thrd one. 3.4 ngerprnt matchng ngerprnt matchng s to fnd the maxmal mutual nformaton between nput and template features wth an optmal transformaton model. Our matchng method conssts of the followng steps: Step 1. To estmate the transformaton space n matchng two fngerprnts and descrbed n the prevous secton and to get an ntal transformaton model T 0 wth formula (11). Step. To calculate the smlarty between mnuta par M and M j wth formula (1) where Ω ={ ; ( =) or ( =)} and Ω ={ ; ( = j) or ( = j)}. m E m r m e m j E n SM (, M ) = SC (, C ). (1) j m n E Ω, E Ω n m j All the smlarty of mnuta pars s sorted n descendng order of value. We select the frst K mnuta pars as the center pont canddates of fngerprnts and respectvely. Let {(( x 0, y0 ), ( x 0, y 0 )); K 1} denote the set of these mnuta pars. Step 3. or ntal transformaton model T 0 and the center pont canddate set, to calculate the global smlarty between fngerprnts and. 1) To obtan a transformaton model T usng mult-resoluton technque n space S. ) To select a center pont par ( x 0, y0 ) and ( x 0, y 0 ) (K 1) as the center ponts of fngerprnts and respectvely. 3) To transform all mnutae n M and M nto the respondng polar systems wth the transformaton model T wth reference to ther center ponts respectvely. 4) To valdate S(, ). If the two algned mnutae assocated wth E m are located wthn the bounded boxes [15] centred at the two algned mnutae assocated wth respectvely, mnutae-smplexes and are assumed to be smlar, then, E n E m S(, ) s vald. Otherwse, they are consdered as nvald and S(, ) s deleted from the matchng result set. 5) To estmate the smlarty between transformaton-varants of and by matchng the algned transformaton-varant relatve features of and, whch E n r n E m e n E m E n E n

11 A fngerprnt dentfcaton algorthm by clusterng smlarty 447 m ϕ m1 means vector ( θ +θ, ϕ m1 p+θ, m p+θ, α +θ, α m +θ ) s matched to vector n ( θ, φ n1p, ϕ n p, α n1, α n ) where θ s the rotaton parameter of T. Let S () ( V m, V n ) denote the smlarty between the two vectors calculated wth formula (10), all local matchng results S(, ) are tested and two new smlarty sets S () (, ) and V m V n S () (, ) are produced. 6) To calculate the global smlarty between two fngerprnts and n terms of plus rule wth formulas (13) and (14) wth transformaton model T and centered pont par (( x 0, y0 ), ( x 0, y 0 )). In formula (13), n s, n l, e s, and e l are emprcal thresholds. (, ;, ) ( ( ( )(, ) ( )(, )); ) S f S n n ( ) = ( )( ) LM s l flm S Vm Vn + S Cm Cn es, el, (13) 0, x < δs, x δs flm ( x; δs, δl ) =, δs x< δl, δl δs 1, x δl. (14) 7) If S () (, ) ρ, the matchng s over; otherwse, go to step 3-(). The matchng s looped K tmes untl every center pont par n {(( x 0, y0 ), ( x 0, y 0 )); K 1} s tested. 8) To contnue step 3-(1) to fnd a new transformaton model T +1 from the space S by usng mult-resoluton technque. If the matchng s looped more than P tmes, the matchng s over. And max{s () } s thought as the fnal global smlarty between fngerprnts and. 4 Results Experments were performed over the fngerprnt databases of VC00 [14] nstead of data sets of the US Natonal Insttute of Standards and Technology (NIST) [16 18] for these fngerprnt databases of the 1st Internatonal ngerprnt Verfcaton Competton n 000 (VC000 [19] ) and VC00 are more sutable for evaluatng a matchng method n applcaton [19]. And our method was evaluated by VC00 and t raned the seventh. 4.1 Results of enhancement The performance of the enhancement algorthm was evaluated over the four fngerprnt databases of VC00. g. 3 llustrates four typcal examples of the enhancement performance. In g. 3, (a-1), (b-1), (c-1) and (d-1) are the 3rd fngerprnts of the four

12 448 Scence n Chna Ser. Informaton Scences 005 Vol.48 No g. 3. Performance of our enhancement method based on DSS over the fngerprnts of VC00. fngerprnt databases of VC000 respectvely; (a-), (b-), (c-) and (d-) represent ther orentaton feld mages; (a-3), (b-3), (c-3) and (d-3) ndcate ther bnary mages; and (a-4), (b-4), (c-4) and (d-4) show ther thnned mages. The average tme of en-

13 A fngerprnt dentfcaton algorthm by clusterng smlarty 449 hancement are 0.41, 0.34, 0.91 and 0.6 s respectvely; experments on enhancement were conducted on a Pentum III450 MHz machne by usng wndows 000. The results confrm that the enhancement method outperforms other methods [1]. 4. Results of matchng Our matchng performance was evaluated over the four fngerprnt databases of VC00 as shown n g. 4 and Table 1, whch were provded by VC00. g. 4. ROCs of our matchng method over the four fngerprnt databases of VC00, provded by VC00. Database Table 1 Performance ndces of the four fngerprnt databases of VC00, provded by VC00 EER (%) EER* (%) MR100 (%) MR1000 (%) ZeroMR (%) ZeroNMR (%) AV enroll tme (s) AV match tme (s) DB1_a DB_a DB3_a DB4_a

14 450 Scence n Chna Ser. Informaton Scences 005 Vol.48 No Concluson and dscusson Ths paper ntroduces a matchng algorthm by clusterng smlarty wth the novel ponts: DSS enhancement and transformaton space estmaton n terms of clusterng method. The outstandng performance of ths method confrms t s promsng n an AIS. However, ths method s senstve to the bad-qualty fngerprnts. They affect the relablty of mnutae, rotaton parameter, center ponts, and therefore affect matchng performance. urther nvestgaton wll be carred out to mprove our method by mnmzng false match whch occasonally occurs under the condton of large deformaton and very poor-qualty fngerprnts [0]. 1) lobal pattern and features and a hybrd matchng technque wll be nspected to reduce the senstvty of poor qualty fngerprnt for t s hard for mnuta-based matchng method [1] and therefore mprove the performance of the proposed method over these bad qualty fngerprnts. ) The technque that employs a mult-resoluton search strategy to calculate the optmal transformaton s studed as well. Acnowledgements Ths wor was supported by the Project of Natonal Scence und for Dstngushed Young Scholars of Chna (rant No ), the Natonal Natural Scence oundaton of Chna (rant No ), and the Project for Young Scentsts und of Natonal Natural Scence oundaton of Chna (rant No ). References 1. Ln, H., Wan, Y.., Jan, A. K., ngerprnt mage enhancement: algorthm and performance evaluaton, IEEE Transactons on Pattern Analyss and Machne Intellgence, 1998, 0(8): [DOI]. old, S., Rangarajan, A., A graduated assgnment algorthm for graph matchng, IEEE Transacton on Pattern Analyss and Machne Intellgence, 1996, 18(4): [DOI] 3. Jang, X. D., Yau, W. Y., ngerprnt mnutae matchng based on the local and global structures, n Proceedngs of the 15th Internatonal Conference on Pattern Recognton (eds. Sanfelu, A. et al.), Bercelona: IEEE CS-Press, 000, : Jan, A. K., Prabhaar, S., Ln, H. et al., lterban-based fngerprnt matchng, IEEE Transacton on Image Processng, 000, 9(5): [DOI] 5. Sujan, V. A., Mulqueen, M. P., ngerprnt dentfcaton usng space nvarant transforms, Pattern Recognton Letters, 00, 3(5): [DOI] 6. Luo, X. P., Tan, J., A mnuta matchng algorthm n fngerprnt verfcaton, n Proceedngs of the 15th Internatonal Conference on Pattern Recognton (eds. Sanfelu, A. et al.), Bercelona: IEEE CS-Press, 000, 4: Ross, A., Jan, A. K., Resman, J., A hybrd fngerprnt matcher, Pattern Recognton, 003, 36(7): [DOI] 8. Cheng, J.., Tan, J., ngerprnt enhancement wth dyadc scale-space, Pattern Recognton Letters, 004, 5: [DOI] 9. Huttenlocher, D.., Rucldge, W. J., A mult-resoluton technque for comparng mages usng the Hausdorff dstance, n Proceedngs of IEEE Conference of Computer Vson and Pattern Recognton, IEEE CS-Press, 1993, Luo, X. P., Tan, J., Knowledge based fngerprnt mage enhancement, n Proceedngs of 15th Internatonal Conference on Pattern Recognton (eds. Sanfelu, A. et al.), Bercelona: IEEE CS-Press, 000, 4: arna, A., Kovacs-Vajna, Z. M., Leone, A., ngerprnt mnutae extracton from seletonzed bnary mages,

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