Fingerprint Enhancement Based on Discrete Cosine Transform

Transcription

1 Fngerprnt Enhancement Based on Dscrete Cosne Transform Suksan Jrachaweng and Vutpong Areekul Kasetsart Sgnal & Image Processng Laboratory (KSIP Lab), Department of Electrcal Engneerng, Kasetsart Unversty, Bangkok, 19, Thaland Abstract. Ths paper proposes a novel fngerprnt enhancement algorthm based on contextual flterng n DCT doman. All ntrnsc fngerprnt features ncludng rdge orentaton and frequency are estmated smultaneously from DCT analyss, resultng n fast and effcent mplementaton. In addton, the proposed approach takes advantage of frequency-doman enhancement resultng n best performance n hgh curvature area. Comparng wth DFT doman, DCT has better sgnal energy compacton and perform faster transform wth real coeffcents. Moreover, the expermental results show that the DCT approach s out-performed the tradtonal Gabor flterng, ncludng the fastest separable Gabor flter, n both qualty and computatonal complexty. Keywords: Fngerprnt Enhancement, Dscrete Cosne Transform Enhancement, Frequency-Doman Fngerprnt Enhancement. 1 Introducton Inevtably, many fngerprnt dentfcaton applcatons are playng an mportant role n our everyday lfe from personal access control, offce tme attendance, to country boarder control. To pursue ths goal, automatc fngerprnt dentfcaton system (AFIS) must be proved to be hghly relable. Snce most automatc fngerprnt dentfcaton systems are based on the mnutae and rdge matchng, these systems rely on good qualty of nput fngerprnt mages for mnutae and rdge extracton. Unfortunately, bad qualty of fngerprnt and elastc dstorton are now major problems for most AFISs especally large database systems. In order to reduce the error accumulated from false accept rate and false reject rate, qualty of fngerprnt must be evaluated and enhanced for better recognton results. Based on flterng domans, most fngerprnt enhancement schemes can be roughly classfed nto two major approaches;.e. spatal-doman and frequency-doman. Flterng n spatal-doman apples convoluton drectly to fngerprnt mage. On the other hand, flterng n frequency-doman need Fourer analyss and synthess. Fngerprnt mage s transformed, then multpled by flter coeffcents, and nverse transformed Fourer coeffcents back to enhanced fngerprnt mage. In fact f employed flters are the same, enhancement results from both domans must be exactly the same by sgnal processng theorem. However, for practcal mplementaton, these S.-W. Lee and S.Z. L (Eds.): ICB 7, LNCS 464, pp , 7. Sprnger-Verlag Berln Hedelberg 7

2 Fngerprnt Enhancement Based on Dscrete Cosne Transform 97 two approaches are dfferent n terms of enhancement qualty and computatonal complexty of algorthms. Practcal performng fngerprnt enhancement based on each doman has dfferent advantage and dsadvantage. For example, most popular Hong s Gabor flters [1], wth orentaton and frequency spatally adaptable, are appled to parttonng fngerprnt mage. However, ths Gabor flter model s based on undrectonal rdge enhancement, resultng n rdge dscontnuty and blockng artfacts around hghly curvature regon. On the other hand, for frequency doman approaches, natural fngerprnt mage s localzed n some frequency coeffcents. Gabor flter can be easly desgned to cooperate wth hgh curvature area. For example, Kame et al. [] ntroduced fngerprnt flter desgn based on frequency doman usng dscrete Fourer transform. Chkkerur et al. [3] appled short tme Fourer transform and took advantage from -dmensonal flter shapng desgn, adapted wth hghly curvature area, resultng n better enhanced results. However, comparng wth spatal-doman approaches, ths scheme suffers from hgh computatonal complexty n Fourer analyss and synthess even though Fast Fourer Transform (FFT) s employed. In order to take advantage from frequency-doman fngerprnt enhancement wth low computatonal complexty, we propose fngerprnt enhancement based on Dscrete Cosne Transform (DCT). The DCT s a untary orthogonal transform wth real coeffcents. It s closely related to the Dscrete Fourer transform (DFT) whch has complex coeffcents. Moreover, t has been known that DCT provdes a dstnct advantage over the DFT n term of energy compacton and truncaton error [4]. Thus s why DCT has been wdely employed n general mage and vdeo compresson standards. Hence, n ths paper, we nvestgated DCT-base fngerprnt enhancement for practcal mplementaton. We expected best enhanced qualty results wth low computatonal complexty. Ths paper s organzed as follows. Secton descrbes several processes n order to mplement enhancement flterng n DCT doman ncludng ntrnsc estmaton and practcal flterng. Secton 3 shows expermental evaluaton. Fnally, secton 4 concludes our works and future research. Proposed Approach The fngerprnt enhancement approach conssts of 4 concatenated processes;.e. dscrete cosne transform of sub-blocks of parttonng fngerprnt, rdge orentaton and frequency parameters estmaton, flterng n DCT doman, and nverse dscrete cosne transform of sub-blocks. The advantages of the proposed approach are as follows. Fngerprnt rdges form a natural snusod mage, whch ts spectrums are packed or localzed n frequency doman. Hence these spectrums can be easly shaped or fltered n ths doman. Moreover, flter can be specally desgned n order to handle hgh curvature rdge area such as sngular ponts. Ths s the great advantage over the spatal-doman flterng approach. Comparng wth dscrete Fourer transform, dscrete cosne transform performs better n term of energy compacton. Moreover, DCT coeffcents are real number comparng wth complex number of DFT coeffcents. Therefore, we can handle DCT coeffcents easer than DFT coeffcents. Besdes, fast DCT

3 98 S. Jrachaweng and V. Areekul requres less computatonal complexty and less memory usage comparng wth fast Fourer transform (FFT). By parttonng fngerprnt nto sub-blocks, the proposed approach utlzes spatally contextual nformaton ncludng nstantaneous frequency and orentaton. Intrnsc features such as rdge frequency, rdge orentaton, and angular bandwdth can be smply analyzed drectly from DCT coeffcents. Each process of the proposed fngerprnt enhancement s explaned as follows..1 Overlappng DCT Decomposton and Reconstructon Conventonal fngerprnt enhancement schemes, applyng wth non-overlappng blocks of parttonng fngerprnt, often encounter wth blockng artfacts such as rdge dscontnuty and spurous mnutae. To preserve rdge contnuty and elmnate blockng artfacts, overlappng block s appled to both DCT decomposton and reconstructon, smlar to the DFT approach n [3]. However, there s no need to apply any smooth spectral wndow for DCT because overlappng area s large enough to prevent any blockng effects, correspondng wth ts energy compacton property.. Intrnsc Parameter Estmaton on DCT Doman Rdge frequency, rdge orentaton, and angular bandwdth can be analyzed from DCT coeffcents drectly. Therefore DCT analyss yelds approprate doman to perform fngerprnt enhancement and provdes flterng parameters as the same tme. Rdge Frequency Estmaton: The rdge frequency (ρ ) s smply obtaned by measurng a dstance between the orgn (,) and the hghest DCT peak of hghfrequency spectrum as followng equaton, ρ (1) = u + v where ( u,v ) s the coordnate of the hghest peak of hgh-frequency spectrum. (a) (b) (c) (d) Fg. 1. Fgure (a) and (c) represent blocks of a fngerprnt model wth dfferent frequency. Fgure (b) and (d) are DCT coeffcents of fgure (a) and (c), respectvely. Note that DC coeffcent s set to zero n order to clearly dsplay hgh-frequency spectrum. Rdge orentaton estmaton: The domnant orentaton of parallel rdges, θ, are closely related to a peak-angle, φ, n DCT coeffcents, where φ s measured counterclockwse (f φ > ) from the horzontal axs to the termnal sde of the hghest spectrum peak of hgh frequency (DC spectrum s not ncluded). However, θ and φ relatonshp s not one-to-one mappng. The rdge orentaton, whch θ vares n the

4 Fngerprnt Enhancement Based on Dscrete Cosne Transform 99 range of to π, s projected nto the peak-angle, whch φ vares n the range of to π/. Relatonshp between θ rdge orentaton n spatal doman and φ peak angle n frequency doman are descrbed n equaton () wth some examples n Fg.. 1 v π φ = tan, φ = θ where θ π u () = = =7 /8 =3 /4 =5 /8 = / =3 /8 = /4 = /8 Fg.. Examples of relatonshp between rdge orentaton n spatal doman and peak-angle n DCT doman, all rdge angles refer to horzontal axs and DC coeffcent s set to zero n order to show hgh-frequency spectrum. (Note that only the top-left quarters of DC coeffcents are zoomed n for clear vew of hgh-frequency peak behavor.) From Fg., rdge orentaton at π-θ has the hghest spectrum peak wth the same locaton as rdge orentaton at θ. However, ther phase patterns are dstngushable by observaton. Therefore addtonal phase analyss s needed to classfy the quadratcs of rdge orentaton n order to correctly perform fngerprnt enhancement. Snce Lee et al. [5] proposed edge detecton algorthm based on DCT coeffcents, our fngerprnt enhancement modfed Lee s approach by modulaton theorem n order to detect quadrant of fngerprnt rdge orentaton. Accordng to Lee s technque, the orentaton quadrant of a sngle lne can be determned by the polartes of two frst AC coeffcents, G 1 and G 1, where G uv s the (a) (b) (c) (d) Fg. 3. Four polarty patterns ndcate (a) a sngle lne orentaton rangng from to π/, (b) a sngle lne orentaton rangng from π/ to π, (c) parallel rdge orentaton rangng from to π/, and (d) parallel rdge orentaton rangng from π/ to π

5 1 S. Jrachaweng and V. Areekul DCT coeffcent at coordnate (u,v), as shown n Fg. 3. In case of a sngle lne, polarty of product of G 1 and G 1 coeffcents ndcates the lne orentaton. If G 1 G 1, ths lne orentaton s n the frst quadrant ( to π/) as shown n Fg. 3(a). On the other hand, f G 1 G 1 <, ths lne orentaton s n the second quadrant (π/ to π) as shown n Fg. 3(b). Ths technque can be appled to detect orentaton of parallel lnes or rdges by modulaton theorem wth the pattern of polartes around the hgh peak DCT coeffcents. To be precse, rdge orentaton n the frst quadrant ( to π/) and rdge orentaton n the second quadrant (π/ to π) can be ndcated by the same polartes of 45 o and 135 o dagonal coeffcents referred to the hghest absolute peak as shown n Fg. 3(c) and (d), respectvely. 5 pxels V 1 3 pxels 5 pxels V 3 pxels Fg. 4. Demonstrate -D perpendcular dagonal vectors, V 1 at 45 o and V at 135 o, referred to the hghest absolute spectrum peak (the center black pxel (negatve value)) In order to dentfy the quadrant and avod nfluence of nterference, two -D perpendcular dagonal vectors, V 1 and V, are formed wth sze of 5 3 pxels, center at the peak poston as shown n Fg. 4. The average drectonal strengths of each vector (S 1, S ) are then computed by equaton (3). Then the quadrant can be classfed and the actual fngerprnt rdge orentaton can be dentfed as shown n equaton (4). S = Max n= 1,,1 V ( u m= + m, v 5 + n) where = 1, (3) π / φ where S1 S θ = (4) π ( π / φ) Otherwse Fnally, the estmated rdge frequency and orentaton of each local regon s formed a frequency feld and an orentaton feld. Then Gaussan flter s appled to smooth both global felds n order to reduce nose effect as [1]. Angular bandwdth estmaton: At the sngularty regon, rdge spectrum s not an mpulse but t spreads bandwdth out. Therefore, the desred flter of each block must be adapted based on ts angular bandwdth. We slghtly modfed the coherence parameter from Chkkerur s concept n [3], called non-coherence factor. Ths noncoherence factor represents how wde rdge orentaton can be n the block that has more than one domnant orentaton. Ths factor s n the range of to 1, where 1 represents hghly non-coherence or hghly curved regon and represents unorentaton regon. The non-coherence factor can be gven by

6 Fngerprnt Enhancement Based on Dscrete Cosne Transform 11 sn( θ ( u v u v j W c, c ) θ (, j )) (, ) NC( uc, vc ) = (5) W W where (u c,v c ) s the center poston of block, (u,v j ) s the th and j th postons of neghborhood blocks wthn W W, and the angular bandwdth, φ BW, can be estmated by the equaton (6) as follows, 1 φ ( u, v ) = sn ( NC( u, v )). (6) BW c c c c. Enhancement Flterng n DCT Doman In DCT doman, flterng process s not smply as n DFT doman [,3], whch requred only coeffcent multplcaton. The Gabor flter n [1] s modfed n order to cooperate wth DCT doman based on Cartesan-form representaton. The enhancement flterng n DCT doman can be separated nto two arthmetc manpulaton;.e. multplcaton and convoluton. 1) Flterng by Multplcaton: The enhancement flter can be expressed n term of product of separable Gaussan functons, smlar to the frequency-doman flterng technque n [] as follows. F ( ρ, φ) = F( ρ, φ) H ( ρ) H ( φ) (7) fd where F(ρ,φ) s DCT coeffcents n polar-form representaton, drectly related to DCT coeffcents, F(u,v), n rectangular-form representaton. F fd (ρ,φ) s DCT coeffcents of the flterng output. The H f (ρ) flter, whch performs the rdge frequency flterng n Gaussan shape, s gven by f d 1 ( ρ ρ ) H ( ρ ρ =, σ ρ, Z) exp, ρ = u + v ; ρ mn ρ ρ max f Z σ ρ (8) where ρ and σ ρ are the center of the hgh-peak frequency group and the flterng bandwdth parameter, respectvely. The ρ mn and ρ max parameters are mnmum and maxmum cut-off frequency constrants, whch suppress the effects of lower and hgher frequences such as nk, sweat gland holes, and scratches n the fngerprnt. The Z s a flterng normalzaton factor, dependng on flterng energy result. The H d (φ) flter, whch performs the rdge orentaton flterng, s gven by ( φ φ ) exp where φ φ φ,, ) = BW φ φ σ φ φ BW σ (9) φ 1 Otherwse H d ( where the φ s the peak orentaton for bandpass flter, σ φ s the drectonal bandwdth parameter, and φ BW, the angular bandwdth, s gven by equaton (6).

7 1 S. Jrachaweng and V. Areekul ) Flterng by Convoluton: Snce the θ and π-θ rdge orentaton coeffcents are projected nto the same DCT-doman regon. Therefore, both drectonal coeffcents stll reman from the prevous flterng. In order to truncate napproprate drectonal coeffcents, two dagonal Gabor flters are exploted by convoluton operaton. The fnally enhanced DCT coeffcents are gven by F Enh ( u, v) = F ( u, v) H ( u, v) (1) fd where F Enh (u,v) s enhanced DCT coeffcents n rectangular-form. F fd (u,v) s the prevous result of enhanced DCT coeffcents n rectangular-form, by converted from F fd (ρ,φ) n polar-form. The quadrant correcton flter, H q (u,v), s gven by q ( u + v) π ( u + v) cos exp σ q H q ( u, v ) = ( ) u v π ( u v) cos exp σ q where θ π / Otherwse (11) where σ q s the quadratc parameter and cos(nπ/) only has three values -1, and -1. Indeed, ths convoluton operaton requres low computaton because most of bandpass fltered coeffcents are truncated to zero from the prevous operaton. In case of hghly curved rdges, the transformed coeffcents are projected nto wdely curved subband of DCT doman as shown n Fg. 5. R1 R θ1 θ θ Spatal Doman θ 1 DCT Doman Fg. 5 Hghly curved rdges n spatal and frequency (DCT) doman. Sgnal s localzed n wdely curved subband, whch can be classfed nto the prncpal regon (R 1 ) and the reflecton regon (R ). From Fg. 5, we approxmate the orentaton range from θ 1 to θ by non-coherence factor from the equaton (6). The curved subband can be classfed nto two regons;.e. prncpal regon (R 1 ) and reflecton regon (R ). The prncpal regon (R 1 ) contans only one dagonal component (45 o or 135 o ) as mentoned before. The 45 o or 135 o dagonal components are the phase pattern of the orented rdges n the range of o to 9 o or 9 o to 18 o, respectvely. The reflecton regon (R ) composes of both of 45 o and 135 o dagonal components from the reflecton property of DCT coeffcents. Then the convoluton s appled only n the prncpal regon.

8 Fngerprnt Enhancement Based on Dscrete Cosne Transform 13 3 Expermental Evaluaton The expermental results have been evaluated on publc fngerprnt database FVC Db3a [6] (1 users, 8 mages each) n term of enhancement qualty, matchng performance, and computatonal complexty. The fngerprnt mage s parttoned nto blocks of pxels, and a smple segmentaton scheme usng mean and varance s employed. Fve fngerprnt enhancement flterng types are evaluated as follows; Tradtonal Gabor flterng wth non-quantzed orentaton (TG)[1], Separable Gabor flterng wth non-quantzed orentaton (SG)[7], Separable Gabor flterng wth 8-quantzed orentaton (SG8)[8], Short-Tme Fourer Transform approach (STFT)[3], and proposed approach (DCT). In the spatal doman approaches, the dscrete Gabor flters are the same 5 5 fxed-wndow sze. Note that the separable Gabor flter [7,8] was mplemented on the fly usng a set of pror created and stored flters. Moreover, symmetrc of -D Gabor flter [1] was also exploted n ths process. These flterng schemes accelerated executon speed of the tradtonal Gabor enhancement process as fast as possble. For the STFT [3] and the DCT approaches n frequency doman, fngerprnt mage s also parttoned nto blocks but each block s transformed wth 3 3 overlapped wndow to reduce blockng artfacts. Note that the probablty estmaton n [3] s not ncluded. In order to compare the performance of varous enhancement algorthms, three evaluaton methodologes are used;.e. the goodness ndex [1] of mnutae extracton, the matchng performance, and the average executon tme. Frst, the goodness ndex (GI) from [1] s employed to measure the extracted mnutae quantty from each fngerprnt enhancement algorthm. In ths case, we needed to manually mark mnutae of all fngerprnts n FVC Db3a. The goodness ndex s gven by GI = r = q [ M L S ] r = 1 q T 1, (1) where r s the number of wndows n the nput fngerprnt mage, q represents the qualty factor of th wndow (good = 4, medum =, poor = 1) whch estmated by parttonng and thresholdng of the dryness factor (mean varance of block) and the smudgness factor (mean / varance of block). M represents the number of mnutae par, whch match wth human expert n a tolerance box n the th wndow. L and S represent the number of lost and spurous mnutae n the th wndow, respectvely. T represents the number of mnutae extracted by experts. Second, enhancement results are tested wth our mnutae matchng verfcaton algorthm based on Jang s concept of [9], and the equal error rate (EER) s reported. Fnally, the average executon tme of fngerprnt enhancement process s measured for FVC Db3a (mage sze 3 3 pxels) on Pentum M 1.5GHz wth 376Mb RAM. Note that executon tme ncludes flter parameter estmaton (frequency and orentaton), transform (f requred), and flterng process. However, segmentaton process s not ncluded and we used the same segmentaton process for all comparson schemes. The objectve test results are summarzed n Table 1. Contradct to our belef; overall executon tme of DCT approach s faster than the separable Gabor

9 14 S. Jrachaweng and V. Areekul Table 1. Summary of the performance comparson among varous fngerprnt enhancement algorthms over FVC Db3a Fngerprnt Database, Pentum M 1.5GHz, 376Mb RAM Fngerprnt Enhancement Algorthm Average Goodness Index (GI) [1] Our Matchng (% EER) Executon Tme (Second) TG [1] SG [7] SG8 [8] STFT (modfed from [3]) DCT (Proposed Approach) (a 1) #_5 (b 1) SG[7] (GI=.59) (c 1) STFT[3] (GI=.63) (d 1) DCT (GI=.7) (a ) #4_4 (b ) SG[7] (GI=.19) (c ) STFT[3] (GI=.3) (d ) DCT (GI=.3) (a 3) #17_7 (b 3) SG[7] (GI=.18) (c 3) STFT[3] (GI=.47) (d 3) DCT (GI=.68) Fg. 6. (a) Orgnal fngerprnt #_5, #4_4 and #17_7 from FVC Db3a, (b) Enhanced results from SG[7], (c) Enhanced results from STFT modfed from [3], (d) Enhanced results of our proposed DCT based method flterng wth 8-quantzed orentaton. We nvestgated n depth and we found that even though separable -D convoluton alone s faster than both FFT and Fast DCT analyss and synthess, the fngerprnt ntrnsc parameter estmaton was slow ths approach down snce these parameters are evaluated n frequency doman. Fg. 6 shows enhancement results for subjectve tests wth GI values for objecttve tests. Note that the qualty of enhanced fngerprnts s mproved based on

10 Fngerprnt Enhancement Based on Dscrete Cosne Transform 15 frequency-doman flterng, especally n hghly curved rdges. Overall of FVC, DB3a database, both STFT and DCT based performed very well around hghly curved area wth slghtly dfferent results around sngular pont area. 4 Concluson and Future Research In concluson, ths paper proposes a novel fngerprnt enhancement approach based on dscrete cosne transform (DCT). The enhancement takes advantage of flterng real DCT coeffcents wth hgh-energy compacton n frequency-doman. Hence flterng can be specally desgned to cooperate hghly curvature area resultng n less dscontnuty and blockng artfacts comparng wth spatal-doman flterng. For future research, we wll conduct exhaustve experments based on all FVC databases n order to prove the effcent of DCT-based fngerprnt enhancement. To acheve ths goal, all mnutae n all FVC databases need to be manually marked. We wll also explot orentaton adaptve flter n DCT Doman n the near future. Acknowledgments. Ths work was partally supported by Department of Electrcal Engneerng, Kasetsart Unversty, Thaland Research Fund (TRF) through the Royal Golden Jublee Ph.D. Program (Grant No.PHD/17/549), and the Commsson on Hgher Educaton through the TRF Research Scholar (Grant No. RMU4987). References 1. Hong, L., Wang, Y., Jan, A.K.: Fngerprnt Image Enhancement: Algorthm and Performance Evaluaton. IEEE Trans. on Pattern Analyss and Machne Intellgence (8), (1998). Kame, T., Mzoguch, M.: Image Flter Desgn for Fngerprnt Enhancement. In: Proc. ISCV 95, pp (1995) 3. Chkkerur, S., Cartwrght, A.N., Govndaraju, V.: Fngerprnt Enhancement Usng STFT Analyss. Pattern Recognton 4, (7) 4. Rao, K.R., Yp, P.: Dscrete Cosne Transform: Algorthms, Advantages, Applcatons. Academc Press, Boston, MA (199) 5. Lee, M., Nepal, S., Srnvasan, U.: Role of edge detecton n vdeo semantcs. In: Proc. Pan- Sydney Workshop on Vsual Informaton Processng (VIP). Conferences n Research and Practce n Informaton Technology, Australa (3) 6. Malton, D., Mao, D., Jan, A.K., Prabhakar, S.: Fngerprnt Verfcaton Competton. Database Avalable: Handbook of Fngerprnt Recognton. Sprnger, Hedelberg (3) 7. Areekul, V., Watchareerueta, U., Suppasrwasuseth, K., Tantaratana, S.: Separable Gabor flter realzaton for fast fngerprnt enhancement. In: Proc. Int. Conf. on Image Processng (ICIP 5), Genova, Italy, pp. III-53 III-56 (5) 8. Areekul, V., Watchareerueta, U., Tantaratana, S.: Fast Separable Gabor Flter for Fngerprnt Enhancement. In: Zhang, D., Jan, A.K. (eds.) ICBA 4. LNCS, vol. 37, pp Sprnger, Hedelberg (4) 9. Jang, X., Yau, W.Y.: Fngerprnt Mnutae Matchng Based on the Local and Global Structures. In: Proc. Int. Conf. on Pattern Recognton (15 th ), vol., pp ()