Fingerprint Verification Based on Invariant Moment Features and Nonlinear BPNN

Transcription

1 800 International Journal o Control, Autoation, and Systes, vol. 6, no. 6, pp , Deceber 008 Fingerprint Veriication Based on Invariant Moent Features and Nonlinear BPNN Ju Cheng Yang and Dong Sun Park* Abstract: A ingerprint veriication syste based on a set o invariant oent eatures and a nonlinear Back Propagation Neural Network (BPNN) veriier is proposed. An iage-based ethod with invariant oent eatures or ingerprint veriication is used to overcoe the deerits o traditional inutiae-based ethods and other iage-based ethods. The proposed syste contains two stages: an o-line stage or teplate processing and an on-line stage or testing with input ingerprints. The syste preprocesses ingerprints and reliably detects a unique reerence point to deterine a Region-o-Interest (ROI). A total o our sets o seven invariant oent eatures are extracted ro our partitioned sub-iages o an ROI. Matching between the eature vectors o a test ingerprint and those o a teplate ingerprint in the database is evaluated by a nonlinear BPNN and its perorance is copared with other ethods in ters o absolute distance as a siilarity easure. The experiental results show that the proposed ethod with BPNN atching has a higher atching accuracy, while the ethod with absolute distance has a aster atching speed. Coparison results with other aous ethods also show that the proposed ethod outperors the in veriication accuracy. Keywords: Absolute distance, BPNN, ingerprint atching, ingerprint veriication, invariant oent eatures, neural network. 1. INTRODUCTION Aong all the bioetric indicators, ingerprints have one o the highest levels o reliability and have been extensively used by orensic experts in criinal investigations. Fingerprint veriication has eerged as one o the ost reliable eans o bioetric authentication due to its universality, distinctiveness, peranence and accuracy. Various approaches o ingerprint veriication syste have been proposed in the literature. Two ain categories or ingerprint veriication are inutiaebased ethods [8,10] and iage-based ethods [1,7,9, Manuscript received Noveber 6, 007; revised October 30, 008; accepted Noveber 3, 008. Recoended by Guest Editor Phill Kyu Rhee. This work was supported by Hankuk University o Foreign Studies Research Fund o 008. Ju Cheng Yang is with the Departent o Coputer Science and Engineering, Hankuk University o Foreign Studies, Yongin, , Korea, and he is also with the School o Inoration Technology, Jiangxi University o Finance and Econoics, Nanchang, Jiangxi, , P. R. China, and was with the Division o Electronics & Inoration Engineering, Chonbuk National University, Jeonju, Jeonbuk , Korea (e-ails: yangjucheng@ gail.co, yangjucheng@hotail.co). Dong Sun Park is with the Division o Electronics & Inoration Engineering, Chonbuk National University, Jeonju, Jeonbuk , Korea (e-ail: dspark@chonbuk. ac.kr). * Corresponding author ]. The ore popular and widely used techniques, inutiae-based ethods, use a eature vector extracted ro the ingerprints and stored as sets o points in a ulti-diensional plane. A eature vector ay contain eatures o inutiae such as positions, orientations and types. It essentially consists o inding the best alignent between eatures o inutiae in teplates and those in ingerprints under veriication. The disadvantages o inutiae-based ethods are that they ay not utilize the rich discriinatory inoration available in the ingerprints and it ay have a high coputational coplexity [14]. Iage-based ethods use dierent types o eatures ro the ingerprint ridge patterns such as local orientation and requency, ridge shape and texture inoration. The eatures ay be extracted ore reliably than detecting inutiae ro ingerprints. Aong various iage-based atching ethods, a Gabor ilter based ethod [7] and its iproved version [16] show relatively high perorance coparing to previous works. In order to iprove the atching accuracy even or rotated inputs, they used an approxiated approach by representing each ingerprint with ten associated teplates with dierent angles. Hence these ethods inherently require a larger storage space and a signiicantly high processing tie as well as the perorance degradation ro the approxiation. Tico et al. [17] propose a transor-based ethod

2 Fingerprint Veriication Based on Invariant Moent Features and Nonlinear BPNN 801 using Digital Wavelet Transor (DWT) eatures, while Aornraksa et al. [1] propose using Digital Cosine Transor (DCT) eatures. The transor ethods show a high atching accuracy or inputs identical to one in its own database. However, these ethods have not considered the invariance to an aine transor to deal with dierent input conditions. Another ethod with the integrated Wavelet and Fourier-Mellin Transor (WFMT) [9] uses ultiple WFMT eatures to deal with the variability o input ingerprint iages. This ethod, however, is not suitable or all types o ingerprint iages by choosing a core point as a reerence point. In our previous work [19], the ingerprint veriication using invariant oents with the learning vector quantization neural network is proposed. We use a ixed-size ROI to extract seven invariant oents as a eature vector. However, this ethod ay not deal with the cases that a reerence point is located near the ri o the ingerprint iage, and the eatures or the whole ROI ay not consider the eect o non-linear distortions. To overcoe the shortcoings o these ethods, in this paper, a ingerprint veriication syste based on a set o invariant oent eatures and a nonlinear BPNN is proposed. A ingerprint iage is irst preprocessed to enhance an original iage by Short Tie Fourier Transor (STFT) analysis []. The algorith siultaneously estiates all the intrinsic properties o the ingerprints to enhance the ingerprint iage copletely. In addition, it is also capable o connecting broken ridges and separating erged ridges, and this can iprove a reliable detection o unique reerence point. A unique reerence point or all types o ingerprints, including partial ingerprints, is to align a teplate to an input ingerprints beore extracting eatures and it is deterined by the coplex iltering ethods [1,15]. The coplex ilter is applied to ridge orientation ield iage to detect the position o a reerence point with the axiu curvature. The orientation o this point is deterined by using the Least Mean Square (LMS) orientation estiation algorith [5], which estiates the orientation ield using the gradient at each pixel and soothes it with a Gaussian window. Invariant oents are one o the principal approaches used in iage processing to describe the texture o a region. The seven oents used in this paper are invariant to translation, rotation, and scale changes [4], so they are able to handle the various input conditions. To signiicantly reduce the eects ro noise and non-linear distortions, and thus better preserves the local inoration, we use our sets o seven invariant oent eatures extracted ro our partitioned sub-iages o ROI. An ROI is a region centered with a reerence point in an enhanced ingerprint iage with its orientation ield. The invariant eatures ro our regions adjusted by its orientation ield can iprove the tie-consuing alignent o transoration and rotation occurred at other ethods [7,16]. A BPNN is adopted to veriy the identiication o an input ingerprint by easuring siilarity between eature vectors o test ingerprint iages and those o teplate iages. The nonlinear neural network veriier is trained to deterine whether the input atches to a teplate in a database. Using a nonlinear BPNN as a veriier ay provide the lexible syste with high atching accuracy. For a coparison study, an absolute distance easure which weights each eleent with the axiu o the each two input vectors is also used to evaluate the veriication syste in atching accuracy. The absolute distance is siple and ast and hence it has an advantage in atching speed. Coparing with soe noted ethods, our proposed ethod perors better o accuracy, too. The paper is organized as ollows: the ingerprint veriication syste is briely reviewed in Section. In Section 3, the proposed veriication syste with eature extraction and atching ethods are explained in details. Experiental results are shown in Section 4. Finally, conclusion rearks are given in Section 5.. INVARIANT MOMENTS ANALYSIS Moent eatures can provide the properties o invariance to scale, position, and rotation [4]. We used oent analysis to extract invariant eatures ro partitioned sub-iages in an ROI. This section gives a brie description o the oent analysis. For a -D continuous unction (x,y), the oent o order (p + q) is deined as pq + + = p q x y ( x, y) dxdy or p, q= 0, 1,, (1) The central oents are deined as p q µ pq = ( x x) ( y y) ( x, y) dxdy () where x = and y = I (x,y) is a digital iage, then () becoes ( ) p q µ pq = x x ( y y) ( x, y), (3) x y

3 80 Ju Cheng Yang and Dong Sun Park and the noralized central oents, denotedη deined as pq, are µ pq p+ q η pq =, where γ = + 1, γ µ 00 or p+q =,3,. (4) A set o seven invariant oents can be derived ro the second and third oents proposed by Hu [6]. As the equations shown below, Hu derived the expressions ro algebraic invariants applied to the oent generating unction under a rotation transoration. They consist o groups o nonlinear centralized oent expressions. The result is a set o absolute orthogonal oent invariants that can be used or scale, position, and rotation invariant pattern identiication. = + φ1 η0 η0, φ = ( η0 η0) + 4 η11, φ3 = η30 η1 + η1 η03 φ4 = ( η30 + η1) + ( η1+ η03), ( 3 ) (3 3 ), φ = ( η 3 η )( η + η )[( η + η ) ( η1 + η03) ] + (3 η η )( η + η )[3( η + η ) ( η1 + η03) ], 6 = ( 0 0)( )[ ( η30 + η1) ( η1 + η03) ] φ η η η η + 4 η11( η30 + η1 )( η1 + η03), φ = (3 η η )( η + η ) η30 + η1 η1 + η03 [( ) 3( ) ] + (3 η η )( η + η ) η30 + η1 η1 + η03 [3( ) ( ) ]. 3. PROPOSED FINGERPRINT VERIFICATION SYSTEM (5) The ingerprint veriication syste contains two stages: the o-line stage and the on-line stage, as shown in Fig. 1. In the o-line stage, ingerprint iages o the dierent individuals to be veriied are irst processed by a eature extraction odule and then the extracted eatures are stored as teplates in a database or later use. In the on-line stage, a ingerprint iage o an individual to be veriied irst processed by a eature extraction odule; the extracted eatures are then ed to a atching odule with one s identity ID, which atches the against Fig. 1. Overview o the ingerprint veriication syste. Fig.. Flowchart o the whole ipleentation schee o the ingerprint veriication syste. one s own teplates in the database. Both stages contain the sae eature extraction odule, which consists o our ain steps as depicted as shown in Fig. : STFT enhanceent, deterination o reerence point, deterination o ROI and partition, and invariant oent analysis. At the last part o the whole veriication syste, the atching is ipleented with absolute distance or BPNN STFT enhanceent The irst step is to enhance the ingerprint iage using STFT analysis []. The perorance o a ingerprint atching algorith depends critically upon the quality o the input ingerprint iage. While the quality o a ingerprint iage ay not be objectively easured, it roughly corresponds to the clarity o the ridge structure in the ingerprint iage, and hence it is necessary to enhance the ingerprint iage. Since the ingerprint iage ay be thought o as a syste o oriented texture with non-stationary properties, traditional Fourier analysis is not adequate to analyze the iage copletely as the STFT analysis does. The algorith or iage enhanceent consists o two stages as suarized below: Stage 1: STFT analysis 1. For each overlapping block in an iage, generate and reconstruct a ridge orientation iage by coputing gradients o pixels in a block, and a ridge requency iage through obtaining the FFT value o

4 Fingerprint Veriication Based on Invariant Moent Features and Nonlinear BPNN 803 the block, and an energy iage by suing the power o FFT value;. Soothen the orientation iage using vector average to yield a soothed orientation iage, and generate a coherence iage using the soothed orientation iage; 3. Generate a region ask by thresholding the energy iage; Stage : Enhanceent 4. For each overlapping block in the iage, the next our sub-steps are applied. a. Generate an angular ilter Fa centered on the orientation in the soothed orientation iage with a bandwidth inversely proportional to coherence iage; b. Generate a radial ilter Fr centered on requency iage; c. Filter a block in the FFT doain, F=F Fa Fr; d. Generate the enhanced block by inverse Fourier transor IFFT(F); 5. Reconstruct the enhanced iage by coposing enhanced blocks, and yield the inal enhanced iage with the region ask. 3.. Deterination o reerence point In the second step, we deterine the reerence point ro the enhanced iage. The reerence point is deined as the point o the axiu curvature on the convex ridge [11], which is usually located in the central area o ingerprint. The reliable detection o the position o a reerence point can be accoplished by detecting the axiu curvature using coplex iltering ethods [1,15]. They apply coplex ilters to ridge orientation ield iage generated ro original ingerprint iage. The reliable detection o reerence point with the coplex iltering ethods as suarized below: 1. For each overlapping block in an iage; a. Generate a ridge orientation iage with the sae ethod in STFT analysis; b. Apply the corresponding coplex ilter h= ( x+ iy) g( x, y) centered at the pixel orientation in the orientation iage, where and g( xy, ) = exp{ (( x + y ) /( σ ))} indicate the order o the coplex ilter and a Gaussian window, respectively; c. For = 1, the ilter response o each block can be obtained by a convolution, h* O( x, y ) = t t g( y) (( xgx ( )) Oxy (, )) + igx ( ) (( ygy ( ) O ( xy, ))), where Oxy (, ) represents the pixel orientation in the orientation iage;. Reconstruct the iltered iage by coposing iltered blocks. It is worth to ention that the ulti-resolution ethod [15] can overcoe the orientation iled (a) (b) Fig. 3. (a) Original ingerprint (size 96x560) (b) deterined reerence point. estiation error or the poor quality iages. In this algorith, however, since ingerprint iages are enhanced irst, the orientation ields ro the enhanced iages are accurate enough or reerence point deterination. So we just apply the coplex ilters on the orientation ield o the enhanced iage to increase the processing speed. The axiu response o the coplex ilter in the iltered iage can be considered as the reerence point. Since there is only one output, the unique output point is taken as the reerence point. The LMS orientation estiation algorith [5] is used to deterine the orientation o reerence point. It is entioned that we use a pixel-wise ethod to instead the block-wise ethod as in [5]. Then, i we know the precise position o the reerence point, we can deterine its orientation accurately by the LMS orientation estiation algorith. Thereore the 0 0 position and the orientation ( θ0 [0,180 ) ) in the enhanced iage becoe those o a reerence point. An exaple o the experients with an original ingerprint is shown in Fig. 3(a). The deterined reerence point is shown in Fig. 3(b). We can see the deterined result is accurate both in position and orientation Deterination o ROI and partition The third step is to crop the ingerprint iage based on the reerence point into an ROI. In order to speed up the overall process, we use only a predeined area (ROI) around the reerence point at the center or eature extraction instead o using the entire ingerprint. The center o the cropped iage centers the position o the reerence point and parallels the orientation o the reerence point. Figs. 4(a) and (b) deonstrate the eature extraction ro ROIs centered

5 804 Ju Cheng Yang and Dong Sun Park Table 1. Seven invariant oents with the dierent sub-iages o the original ingerprint iage (IM= Invariant Moent, S=sub-iages). IM(Log) S1 S S3 S4 φ φ φ φ φ φ φ (a) (b) Fig. 4. (a) (b) deonstrate the eature extraction ro ROIs centered on the deterined reerence point o an input ingerprint and a teplate one, respectively. Fig. 5. Method or partitioning the ROI into 4 subiages. on the deterined reerence point o two input ingerprints o a person, respectively. Since the ROIs centered on the sae area around the reerence point, the eatures are assured to be extracted, and they are invariant to rotation and translation. The size o the ROI can be experientally deterined. In this paper, a size o ROI is used. In order to reduce the eects o noise and nonlinear distortions, the ROI is partitioned into our saller sub-iages (4 quadrants) in an anticlockwise sequence as depicted in Fig. 5. So each sub-iage has a size o Invariant oent eatures At the ourth step, we apply the invariant oent analysis introduced in Section on each sub-iage respectively. For each sub-iage, a set o seven invariant oents is coputed, so our sets o invariant oents o the sub-iages are extracted as eatures to represent a ingerprint. Let [ φ k1, φ k, φ k7 ] ( k= 1 or, 3, 4) as a set o invariant oents, the total eature vectors are the cobination o the 4 sets o invariant oents V=[ φ 11, φ 1, φ 17, φ 1, φ, φ 7, φ 31, φ 3, φ 37, φ 41, φ 4, φ 47 ]. The length o the total eature vectors is 8. An exaple o these invariant oent values is listed as in Table Matching Matching with absolute distance Absolute distance is used to easure the siilarity between the eature vectors o the input ingerprint with those o the teplates ingerprint stored in the database. Let V 1 = { a1, a,..., an} and V = { b1, b,..., bn} (n=8) denote the eature vectors o the two ingerprints to atched, T denotes the thresholds used in the atching process. The dierence vector Vd o the two ingerprint eature vectors is calculated as in (6). V d a1 b1 a b an bn =,... (6) ax( a1, b1) ax( a, b) ax( an, bn) We deine the absolute distance o the two atching vectors as in (7). R n ai bi = i= 1 ax( ai, bi ) (7) Then the inal decision o atching result is deterined by (8). accept i R < T (8) reject i R T In this equation the thresholds T varies according to the quality o the ingerprint iages. The quality o ingerprint iages can be varied depending on sensors, thus the threshold should be adjusted on a speciic sensor. According to the experient, the better the ingerprint iage is, the larger T should be. In this paper, T is deterined experientally and set to 1.0.

6 Fingerprint Veriication Based on Invariant Moent Features and Nonlinear BPNN Matching with BPNN Instead o using the distance easures, a set o three-layer BPNNs are used to veriy a atching between eature vectors o input ingerprint and those o a teplate ingerprint. The nuber o the BPNN is the sae with the veriying persons. The structure o the BPNNs consists o input layer, one hidden layer and output layer. For each input ingerprint and its teplate ingerprint, we copute axiu, iniu and average eleents o the input vector V 1, the teplate vector V and the dierence vector V d as the input o the BPNNs. The axiu values are V d ax, V V ax, the iniu values are V in, 1ax, 1in, V V in, and the average values are V, 1 avg, d davg V V. Since the output is to judge whether avg the input ingerprint is atch or non-atch according to the identity ID, we can take the atching process as a two-class proble. There are 9 input eatures and output classes, so the input layer neurons and the output layer neuron are 9 and 1 respectively. The nuber o the hidden layer neurons is obtained epirically. In order to train the BPNN with a atch or non-atch case, we label the class values as 1 or 0. That is, 1 eans the atch and 0 eans non-atch. So the desired output values can be distributed intelligently by the BPNN. In the training (o-line) stage, a set o { V d ax, V V ax, V in, V in, V, V 1, V 1ax, avg d davg avg } are ed to the corresponding BPNN with indicating their corresponding class. The eatures are coputed ro the training data, each contains two eature vectors o the input ingerprint and teplate ingerprint as well as a dierence vector o the. While, in the testing (on-line) stage, a set o { V d ax, V V ax, V d in, V 1in, V in, V 1, V } are ed to the BPNN to 1ax, davg, V avg avg produce the output values. Siilarly, the eatures are coputed ro the testing data, each contains two eature vectors o the test ingerprint and the corresponding teplate ingerprint with the querying ID as well as a dierence vector o the. The eleent o the output values C n is restricted in the range o [0, 1]. With the thresholds T l and T h, the atching result can be described as in (9). accept i Cn Th (9) reject i Cn < Tl In this equation, the thresholds, T h and T l are the thresholds o accept and reject respectively. In the experients, T l was set to and T h was set to EXPERIMENTAL RESULTS The ingerprint iage database used in this experient is the FVC00 ingerprint database set a [0], which contains our distinct databases: DB1_a, DB_a, DB3_a and DB4_a. The resolution o DB1_a, DB3_a, and DB4_a is 500 dpi, and that o DB_a is 569 dpi. Each database consists o 800 ingerprint iages in 56 gray scale levels (100 persons, 8 ingerprints per person). For those reerence points o the ingerprint iages were near or on the border o the ingerprint iages due to the sall sensor sizes, the ROIs would be ailed to acquire or coputing the eatures, so we chose to replace the eatures using the average two eatures ro the ront and next ipressions o the current ipressions, the siilar process can be extended to those containing ore rejected ipressions. In the experients o absolute distance atching, the average o the training saples per person was taken as the teplate ingerprint. The teplate eature vector o each person was coputed ro all the average eature vectors o the training ingerprints o the person. Training patterns were selected on the irst 6 ingerprints o per person (6/8=75%) in each database, while all the 8 ingerprints o per person in each database were used or testing. That is, 600 (800 75%=600) patterns in each database was used or training, and tests were perored on all 800 patterns. In the experients o BPNN atching, 100 BPNNs each with 9 input layer neurons and 1 output layer neuron was trained on the 600 o patterns in each database, and test was perored on all patterns, too. So the training data contained 100 6=600 atch saples and 99 6=594 non-atch saples, totally 1194 saples or each BPNN. And the testing data contained 800 test saples. The training data and testing data were noralized by dividing the axiu values o each colun into (0, 1] beore training and testing network to avoid non-convergence. The training paraeters were decided by experients. Learning rate was set to 0.01, epoch was 5000, and ean absolute error was Experientally, the optial nuber o hidden layer neurons was deterined to 15. The perorance evaluation protocol used in FVC00 is adopted in the experients [13]. The Equal Error Rate (EER), revised EER (EER*), Reject Enroll (REJEnroll), Reject Match (REJMatch), Average Enroll Tie (AETie) and Average Match Tie (AMTie) are coputed on the our databases. To copute the False Acceptance Rate (FAR) and the False Reject Rate (FRR), the genuine atch and ipostor atch were perored. For genuine atch, each test ipression o each person was copared

7 806 Ju Cheng Yang and Dong Sun Park with the teplate o the sae person. Since there are 100 persons, the nuber o atches was 100 8=800. For ipostor atch, the test ipression o each person was copared with the teplate o other persons. The nuber o atches was =7900. The FRR and FAR are deined as ollows: Nuber o rejected genuine clais FRR = 100%, Total nuber o genuine accesses (10) Nuber o accepted iposter clais FAR = 100%. Total nuber o iposter accesses (11) The EER is used as a perorance indicator. The EER indicates the point where the FRR and FAR are equal. The tests were executed on Pentiu IV 1GHz achines. The perorances o our proposed ethod with two atching ethods over the our databases o FVC00 were shown in Tables and 3, respectively. Fro the tables, we can ind that the average EER values o absolute distance atching and that o BPNN atching over our databases are 4.91% and 3.69%, respectively. And the average enroll tie o absolute distance atching and those o BPNN atching over our databases are 0.43 and 0.77 seconds, and the average atch tie are 0.10 and 0.19 seconds, respectively. So BPNN atching has a higher atching accuracy, while absolute distance atching has a aster atching speed. It is because that training the BPNN is uch tie consuing. For evaluating the recognition rate perorance, the Receiver Operating Characteristic (ROC) is used as another perorance indicator. An ROC is a plot o Genuine Acceptance Rate (GAR=1-FRR) against FAR. In order to exaine and prove the perorance o the proposed ethod, a nuber o experients coparing perorance to other renowned ethods were carried out on the FVC00 database. Three atching ethods, proposed in reerences [1,9], and [16], were selected or coparison. (1) Method o Aornraksa [1]: the ingerprint atcher uses DCT eatures with the sae paraeters as in their paper. () Method o Jin [9]: the ingerprint atcher uses WFMT raework with our ultiple training WFMT eatures. (3) Method o Sha [16]: This is the Gabor ilter based ethod with the sae paraeters as in their paper. For the experients in the proposed ethod, the size o an ROI and the partitioned sub-iages are identical with those introduced in the previous subsection. The BPNN is used as the atching ethod in this experient. Fig. 6 shows the ROC curves o the ethods o Aornraksa, Jin, Sha and along with our proposed ethod on databases FVC00 DB1_a. For the Table. Perorances o the proposed ethod with the absolute distance atching over the our databases o FVC00. database EER EER* REJ Enroll REJ Match AE Tie AM Tie DB1_a 3.35% 3.35% 0.00% 0.00% 0.37sec 0.08sec DB_a 6.1% 6.1% 0.00% 0.00% 0.44sec 0.10sec DB3_a 5.78% 5.78% 0.00% 0.00% 0.3sec 0.05sec DB4_a 4.8% 4.8% 0.00% 0.00% 0.57sec 0.17sec Average 4.91% 4.91% 0.00% 0.00% 0.43sec 0.10sec Table 3. Perorances o the proposed ethod with BPNN atching over the our databases o FVC00. database EER EER* REJ Enroll REJ Match AE Tie AM Tie DB1_a.73%.73% 0.00% 0.00% 0.59sec 0.15sec DB_a 3.6% 3.6% 0.00% 0.00% 0.64sec 0.19sec DB3_a 4.94% 4.94% 0.00% 0.00% 0.85sec 0.16sec DB4_a 3.81% 3.81% 0.00% 0.00% 0.98sec 0.5sec Average 3.69% 3.69% 0.00% 0.00% 0.77sec 0.19sec Fig. 6. ROC curves coparing the recognition rate perorance o the proposed ethod with the ethods o Aornranksa, Jin and Sha on database FVC00 DB1_a. Table 4. The GAR(%) under a FAR(%) value o 0.8% o the proposed ethod coparing with the ethod o Aornraksa, Jin, and Sha over the our databases o FVC00. Methods DB1_a DB_a DB3_a DB4_a Average Method o Aornraksa 91.4% 85.7% 8.1% 9.6% 87.9% Method o Sha 9.7% 88.9% 85.3% 93.% 90.0% Method o Jin 94.3% 9.4% 90.6% 94.9% 93.1% Our proposed ethod 96.4% 95.8% 94.% 97.3% 95.9%

8 Fingerprint Veriication Based on Invariant Moent Features and Nonlinear BPNN 807 experients, as shown in the igure, since the curve o the proposed algorith is above those o the other three ethods, it eans that the atching accuracy o the proposed algorith is greater than the others. Table 4 illustrates the average GAR(%) under a FAR(%) o 0.8% with the ethods o Aornranksa, Jin, Sha and our proposed ethod are 87.9%, 90.0%, 93.1% and 95.9% respectively over the our databases o FVC00. It shows that the average GAR(%) o our proposed ethod is ore than.8% higher than any other ethods. 5. CONCLUSIONS In this paper, a ingerprint veriication syste based on invariant oent eatures and nonlinear BPNN is proposed. A preprocessing enhanceent with the STFT analysis akes the algorith highly robust to poor-quality ingerprint iages and iproves the atching accuracy. Under the help o the enhanceent, the reerence point can be reliably and accurately deterined with the coplex iltering ethods and LMS orientation estiation algorith. Using the invariant oent analysis on sub-iages, the extracted eatures have bound the eects o noise and non-linear distortions, while utilizing the invariant ability to the aine transorations o eatures to handle various input conditions. Matching the ingerprints is ipleented by two easures: absolute distance and BPNN. The axiu, iniu and average eleents o the vectors o input ingerprint, teplate ingerprint and the dierence vectors o the are used as the BPNN inputs. As an excellent nonlinear classiier, the BPNN can iprove the whole atching perorance. The experiental results show that both absolute distance and BPNN can be used or ingerprint veriication. The BPNN atching has a higher atching accuracy, while the absolute distance atching has a aster atching speed. Thereore, we can choose dierent atching ethods or dierent application cases. Copared with soe noted ethods, we ind that our proposed ethod also perors uch better in atching accuracy. Further work should be proceeded to iprove robustness and reliability o our proposed ethod. REFERENCES [1] T. Aornraksa and S. Tachaphetpiboon, Fingerprint recognition using DCT eatures, Electronics Letters, vol. 4, no. 9, pp. 5-53, 006. [] S. Chikkerur, A. N. Cartwright, and V. Govindaraju, Fingerprint enhanceent using STFT analysis, Pattern Recognition, vol. 40, no.1, pp , 007. [3] L. Fausett, Fundaentals o Neural Networks Architecture, Algorith and Application, Prentice Hall, [4] R. C. Gonzalez and R. E. woods, Digital Iage Processing, nd Edition, Prentice Hall, 00. [5] L. Hong, Y. Wang, and A. K. Jain, Fingerprint iage enhanceent: Algorith and perorance evaluation, Transactions on Pattern Analysis and Machine Intelligence, vol. 1, no. 4, pp , [6] M. K. Hu, Visual pattern recognition by oent invariants, IRE Trans. on Inoration Theory, vol. 8, pp , 196. [7] A. K. Jain, S. Prabhakar, L. Hong, and S. Pankanti, Filterbank-based ingerprint atching, IEEE Trans. on Iage Processing, vol. 9, pp , 000. [8] X. Jang and W. Y. Yau, Fingerprint inutiae atching based on the local and global structures, Proc. o Int. Con. on Pattern Recognition, vol., pp , 000. [9] A. T. B. Jin, D. N. C. Ling, and O. T. Song, An eicient ingerprint veriication syste using integrated wavelet and Fourier-Mellin invariant transor, Iage and Vision Coputing, vol., no. 6, pp , 004. [10] J. Liu, Z. Huang, and K. Chan, Direct inutiae extraction ro gray-level ingerprint iage by relationship exaination, Proc. o Int. Con. on Iage Processing, vol., pp , 000. [11] M. Liu, X. D. Jiang, and A. Kot, Fingerprint reerence-point detection, EURASIP Journal on Applied Signal Processing, vol. 005, no. 4, pp , 005. [1] M. Liu, X. D. Jiang, and A. Kot, Fingerprint retrieval by coplex ilter Responses, Proc. o Int. Con. on Pattern Recognition, HongKong, pp , 006. [13] D. Maio, D. Maltoni, R. Cappelli, J. L. Wayan, and A. K. Jain, FVC00: Second ingerprint veriication copetition, Proc. 16th Int l Con. Pattern Recognition, vol. 3, pp , 00. [14] D. Maltoni, D. Maio, A. K. Jain, and S. Prabhakar, Handbook o Fingerprint Recognition, Springer, Berlin, 003. [15] K. Nilsson and J. Bigun, Localization o corresponding points in ingerprints by coplex iltering, Pattern Recognition Letters, vol. 4, pp , 003. [16] L. F. Sha, F. Zhao, and X. O. Tang, Iproved ingercode or ilterbank-based ingerprint atching, Proc. o Int. Con. on Iage Processing, vol., pp , 003. [17] M. Tico, P. Kuosanen, and J. Saarinen, Wavelet doain eatures or ingerprint recognition, Electronics Letters, vol. 37, no.1, pp. 1-, 001.

9 808 Ju Cheng Yang and Dong Sun Park [18] J. C. Yang and D. S. Park, A ingerprint veriication algorith using tessellated invariant oent eatures, Neurocoputing, vol. 71, no. 10-1, pp , 008. [19] J. C. Yang, S. Yoon, and D. S. Park, Applying learning vector quantization neural network or ingerprint atching, Lecture Notes in Artiicial Intelligence (LNAI 4304), Springer, Berlin, pp , 006. [0] Ju Cheng Yang received the B.S. degree ro South-central University or Nationalities, China in 00, and the M.S. and Ph.D. degrees ro Chonbuk National University, South Korea in 004 and 008. He did his post-doc at the Advanced Graduate Education Center o Jeonbuk or Electronics and Inoration Technol ogy-bk1 (AGECJEIT-BK1), Chonbuk National University, South Korea. His research interests include iage processing, pattern recognition, bioetrics, coputer vision and artiicial intelligence. He has published over 0 papers in related international conerences and journals. He has served as editors o any journals such as Inoration Technology Journal and Journal o Applied Sciences and reviewers any conerences such as VISAPP 06, ICNC 06- FSKD 06, IPCV 08. He is a eber o IEEE. Dong Sun Park is a Proessor in Chonbuk National University, South Korea. He received the B.S. in Korea University, South Korea and the M.S., Ph.D. degrees in University o Missouri, USA. His research area is iage processing, pattern recognition, coputer vision and artiicial Intelligence. He has published lots o papers in the international conerences and journals. He is an Association Meber o IEEE Coputer Society.