An Efficient Algorithm for Fingercode-Based Biometric Identification

Transcription

1 An Efficient Algorithm for Fingercode-Based Biometric Identification Hong-Wei Sun, Kwok-Yan Lam, Ming Gu, and Jia-Guang Sun School of Software, Tsinghua University, Beijing , PR China {lamky, guming, Abstract. With the emerging trend of incorporating biometrics information in e-financial and e-government systems arisen from international efforts in anti-money laundering and counter-terrorism, biometric identification is gaining increasing importance as a component in information security applications. Recently, fingercode has been demonstrated to be an effective fingerprint biometric scheme, which can capture both local and global details in a fingerprint. In this paper, we formulate fingercode identification as a vector quantization (VQ) problem, and propose an efficient algorithm for fingercode-based biometric identification. Given a fingercode of the user, the algorithm aims to efficiently find, among all fingercodes in the database of registered users, the one with minimum Euclidean distance from the user s fingercode. Our algorithm is based on a new VQ technique which is designed to address the special needs of fingercode identification. Experimental results on DB1 of FVC 2004 demonstrate that our algorithm can outperform the full search algorithm, the partial distance search algorithm and the 2-pixel-merging sum pyramid based search algorithm for fingercode-based identification in terms of computation efficiency without sacrificing accuracy and storage. Keywords: Biometric security, fingercode; fingerprint matching; vector quantization. 1 Introduction In the face of strong needs arisen from counter-terrorism and anti-money laundering requirements, new theories and technologies are being developed recently to address key issues related to the identification needs of financial and government systems. With the emerging trend of incorporating biometrics information in e-financial and e-government systems arisen from international efforts against terrorist financing and for effective border control, biometric identification is gaining increasing importance as a component in security applications. Recently, fingercode has been demonstrated to be an effective fingerprint biometric scheme [1]. Unlike minutiae-based matching algorithms, fingercode captures both local and global details in a fingerprint; thus overcoming some of the major problems of minutiae-based matching. Fingercode-based matching is based on the squared Euclidean distance between two corresponding fingercodes. A fingerprint matching system may operate in one of the two modes: verification mode (1:1 matching) and identification mode (1:n matching). When R. Meersman, Z. Tari, P. Herrero et al. (Eds.): OTM Workshops 2006, LNCS 4277, pp , c Springer-Verlag Berlin Heidelberg 2006

2 470 H.-W. Sun et al. operating in the verification mode, it either accepts or rejects a user s claimed identity. Whereas, a fingerprint matching system operating in the identification mode establishes the identity of the user without a claimed identity information. This research focus on the identification mode of fingercode-based matching. The fingerprint matching system firstly computes the fingercodes of all registered users and stores them as fingerprint templates in the user database. The identification process then finds the minimum of the squared Euclidean distance between the user s fingercode and all the templates in the database. By comparing this minimum distance with a predefined threshold, the system determines whether the user s fingercode belongs to some registered user in the database. If so, it establishes the identity of the user based on the nearest template. However, fingercode-based identification is a computation-intensive process as it needs to compute and compare the squared Euclidean distance between the user s fingercode and all stored templates. To enhance the performance of fingercode-based identification, we formulate the identification process as a vector quantization (VQ) problem, and devise an efficient VQ algorithm to find the template with minimum Euclidean distance from the user s fingercode. We observed that the fingercode matching process is very similar to the encoding process in VQ [2,3], which is an efficient technique for low-bit-rate image compression. Many efficient algorithms have been developed to enhance the VQ encoding process [4,5,6]. These methods typically use the statistical features of a vector to estimate the Euclidean distance and reject most of the unlikely codewords without computing the actual Euclidean distances. Our algorithm also adopted this principle to accelerate the matching process for the fingercode-based identification system. Nevertheless, not all VQ techniques can be applied directly to fingercodebased matching. VQ techniques designed for image compression use a small codebook, 512 codewords typically. Besides, the dimension of vectors representing image blocks is also small, typically 16 dimensions. Whereas, the dimension of fingercode is of several hundred and the codebook size is determined by the number of registered users in the template database. Thus it is important to have a VQ technique which does not require storage space or pre-computed data set proportional to the dimension of the vectors or the codebook size. This paper presents a new fingercode identification algorithm based on VQ. The fingercode biometric scheme is introduced in Section 2. In Section 3, we explain the fingercode-based biometric identification and formulate the problem as a VQ encoding process. The new fingercode identification algorithm will bedescribedindetailinsection4which is followed by a presentation of the experimental results in Section 5. The paper is concluded in Section 6. 2 Fingercode Biometric Scheme Fingercode has been demonstrated to be an effective fingerprint biometric scheme, which can capture both local and global details in a fingerprint [1]. The fingercode-based matching algorithm uses a bank of Gabor filters to capture both

3 An Efficient Algorithm for Fingercode-Based Biometric Identification 471 local and global details in a fingerprint as a fingercode, which is represented by a fixed-length vector. The fingercode scheme divides the fingerprint image of a user into a number of sectors, applies Gabor filters to transform the image in each sector; then obtains a real value from each sector by computing the average absolute deviation from the mean for each sector. This results in a k-dimensional real vector where k is the number of sectors on the fingerprint. The fingercode generation process [1] can be summarized by the following: Step 1: Locate a reference point and determine the region of interest for the fingerprint image. The reference point of a fingerprint is defined as the point of maximum curvature of the concave ridges in the fingerprint image [7]. For fingercode encoding, [1] located the reference point based on multi-resolution analysis of the orientation fields of the fingerprint image. The use of reference point helps address the translation invariance of fingercodes. Step 2: Tessellate the region of interest around the reference point. The region of interest is divided into a series of B concentric bands and each band is subdivided into k sectors. In our experiments, we use four bands (B =4) and each band is segmented into sixteen sectors (k = 16), thus resulting in a total of 16 4 = 64 sectors; Step 3: Normalize the region of interest in each sector to a constant mean and variance. Let I(x, y) denotes the gray value at pixel (x, y), M i and V i, the mean and variance of the gray values in sector S i,andn i (x, y), the normalized gray value at pixel (x, y). For all the pixels in sector S i,the normalized image is defined as: M 0 + V0 (I(x,y) M i) 2 V N i (x, y) = i if I(x, y) >M i M 0 V0 (I(x,y) M i) 2 otherwise where M 0 and V 0 are the desired mean and variance values, respectively. The normalization process removes the effects of sensor noise and gray level deformation due to the finger pressure differences; Step 4: Filter the region of interest in eight different directions using a bank of Gabor filters to produce a set of eight filtered images. Properly tuned Gabor filters can remove noise, preserve the true ridge and valley structures, and provide information contained in a particular orientation in the image. The typically used even symmetric Gabor filter [1] has the following general form in the spatial domain: G(x, y; f,θ) =exp{ 1 2 [x 2 δx 2 + y 2 δy 2 ]} cos(2πfx ) x = x sin θ + y cos θ y = x cos θ y sin θ where f is the frequency of the sinusoidal plane wave along the direction θ from x-axis, and δ x and δ y are the space constants of the Gaussian envelope along x and y axes, respectively. V i

4 472 H.-W. Sun et al. Step 5: For each filtered output, compute the average absolute deviation from the mean (AAD) of gray values in individual sectors in filtered images to form the fingercode. In our experiments, sixty-four features of each of the eight filtered images provide a total of 512 (64 8) features. Hence the fingercode of the user is represented by a collection of eight (8 filters) 64-dimensional real vectors. The translation invariance of the fingercode is established by the reference point. To achieve approximate rotational invariance, the features in the fingercode are cyclically rotated. The fingercode is firstly rotated cyclically to generate five templates corresponding to five rotations (0, ±22.5, ±45 ) of the original fingerprint image. The original fingerprint image is then rotated by an angle of and its fingercodes are generated by computing another five templates corresponding to five rotations. Thus, the database contains ten templates for each fingerprint. To perform fingercode biometric verification, a user s fingercode is generated from his fingerprint image which is then matched against the stored fingercodes of the claimed identity. In this mode, fingercode matching is based on the Euclidean distance between the two corresponding fingercodes. The final matching distance score is taken as the minimum of the ten scores, i.e. matching of the input fingercode with each of the ten templates. This minimum score corresponds to the best alignment of the two fingerprints being matched. 3 Fingercode-Based Biometric Identification When performing fingercode identification, a user supplies his fingerprint (query fingerprint) to the system without a claimed identity. The identification system then compares the supplied fingerprint with all the stored templates in order to determine the identity of the user. The fingerprint identification system thus firstly computes the fingercodes of all registered users and stores them as fingerprint templates in the database. The fingercode identification process finds the minimum squared Euclidean distance between the fingercode of the query fingerprint and all the templates in the database. By comparing this distance with a predefined threshold, the system determines whether the query fingerprint matches some fingercode template in the database, and establishes the identity of the user. Since the database stores ten templates for each fingerprint, if the full search (FS) algorithm is used, the matching process needs to compute the squared Euclidean distance between the fingercode of the query fingerprint and each of the templates in the database, thus it is computation-intensive. To enhance the efficiency of fingercode-based biometric identification, we formulate the identification process as a VQ problem. In essence, the identification system needs to search through the fingercode database for the fingercode which is nearest (in terms of Euclidean distance) to the query fingerprint. This search problem is similar to the encoding process in VQ.

5 An Efficient Algorithm for Fingercode-Based Biometric Identification 473 VQ is a mapping Q of a k-dimensional Euclidean space R k into certain finite subset C of R k,wherec is the codebook with size N and each codeword c i = {c i1,c i1,,c ik } in C is k-dimensional. The codeword searching problem in VQ is to assign one codeword to the input test vector such that the distance between this codeword and the test vector is the smallest among all codewords. Given one codeword c i = {c i1,c i2,,c ik } and the test vector x = {x 1,x 2,,x k }, the squared Euclidean distance can be expressed as d 2 (x, c i )= k j=1 (x j c ij ) 2. In the fingercode identification system, since a fingercode typically has several hundred dimensions, and there are 10 templates for each fingerprint, the searching process is computation-intensive if the FS algorithm is used. From the above equation, each distance calculation needs k multiplication and 2k 1 additions. To encode the input vector, the FS method [2] computes the squared Euclidean distances between the input vector and each codeword and determines the best-matched one c w by d 2 (x, c w )=min ci C d 2 (c i,x). To encode each input vector, the FS method needs N distance computations and N 1 comparisons. In other words, it must perform kn multiplications, (2k 1)N additions and N 1 comparisons, which is time-consuming. In order to accelerate the VQ encoding process, many fast methods [4,5,6] have been proposed. These methods use an estimate of the Euclidean distance to quickly determine whether a codeword can be eliminated thus the actual Euclidean distance need not be computed. Suppose the running minimum for the input vector x is d min, if the estimation for the Euclidean distance between x and current codeword c i is larger than d min and the corresponding real Euclidean distance is larger than the estimation, then we can safely reject c i and avoid computing the actual Euclidean distance. For example, the partial distance search (PDS) algorithm [4] uses the following rejection test t j=1 (x j c ij ) 2 d 2 min, for any t<k. If the partially calculated squared Euclidean distance from dimensions 1 to t is greater than the running minimum d min, this codeword can be rejected without calculating the actual one in k dimensions. As another example, the subvector (SV) method divides x and c i into the first and second subvectors as x f = {x 1,x 2,,x k/2 }, x s = {x k/2+1,x k/2+2,,x k }, c i,f = {c i1,c i1,,c ik/2 }, c i,s = {c i(k/2+1),c i(k/2+2),,c ik }, respectively [5]. The sums, means and the variances of x and c i are defined as S x = k j=1 x j, S ci = k j=1 c k ij, M x = S x /k, M ci = S ci /k, V x = j=1 (x j M x ) 2, V ci = k j=1 (c ij M ci ) 2. Similarly, the partial sums of each subvector are defined as S x,f = k/2 j=1 x j, S x,s = k j=k/2+1 x j, S ci,f = k/2 j=1 c ij, S ci,s = k j=k/2+1 c ij. The SV method uses the following 3-step rejection test flow. If any inequality holds, it rejects c i as the nearest codeword. Step 1. (S x S ci ) 2 kd 2 min. Step 2. (S x S ci ) 2 + k(v x V ci ) 2 kd 2 min. Step 3. (S x S ci ) 2 2(S x,f S ci,f) [(S x S ci ) (S x,f S ci,f)] (k/2)d 2 min.

6 474 H.-W. Sun et al. In order to realize recursive computation in a memory efficient way, 2PM SPasshowninFigure1wasproposedin[6]forcodewordsearchinVQ.A hierarchical rejection rule is set up as d 2 (x, c i )=d 2 u(x, c i ) 2 (u v) d 2 v(x, c i ) 2 (u 1) d 2 1 (x, c i) 2 u d 2 0 (x, c i). The squared Euclidean distance (i.e. the test function) at the v th level of the hierarchy for v [0,u]isd 2 v (x, c i)= 2 v m=1 (S x,v,m S ci,v,m) 2 where S x,v,m is the m th pixel at the v th level for x and S ci,v,m similarly defined for c i.fora k-dimensional vector, u =log 2 k. L0 (top level) L1 L2 Summing L3 L4 m n Lu (bottom level) Fig. 1. A 2-pixel-merging sum pyramid Thus, at any v th level for v [0,u], if the inequality 2 (u v) d 2 v (x, c i) d 2 min holds, then c i can safely be rejected at the v th level. 4 Efficient Fingercode Identification Based on VQ Due to the fundamental distinction between the fingercode identification system and the image compression system, not all VQ techniques can be applied directly to fingercode searching. The major differences include: (1) Codebook size in image compression is fixed, typically 512; whereas, fingercode stored in database is very large and depends on the number of registered users in the system. (2) Image vector dimension is small, typically 16; whereas fingercode vector dimension is much larger, e.g in our examples. Thus a good fingercode identification system should adopt a VQ technique which does not require storage space or pre-computed data set proportional to the dimension of the vectors or size of the user population. Based on the above analysis, we firstly investigate some suitable fast VQ encoding methods and evaluate their performance for fingercode identification. In this study, we use benchmarking data set DB1 from FVC 2004 [8] for our experiments. There are a total of 100 fingers and 8 impressions per finger (800

7 An Efficient Algorithm for Fingercode-Based Biometric Identification 475 impressions) in this database. We use the first impression of each finger to test the performance of the PDS method [4], the SV method [5] and the 2PM SP method [6]. We then use the other 700 impressions as the registered fingerprints, compute 10 fingercodes for each impression and store them as the templates, which results in = 7000 templates. In the first experiment (Fig. 2), we used the first 1000 templates in the database to simulate a fingerprint identification system with a small population. In the second experiment (Fig. 3), we used all the 7000 templates in the database, which simulate a fingerprint recognition system with a larger population. FS PDS SV 2PM SP Execution time Number of users Fig. 2. Performance comparison for small number of users FS PDS SV 2PM SP Execution time Number of users Fig. 3. Performance comparison for large number of users From Figures 2 and 3, it is clear that the PDS and 2PM SP methods are more efficient and scalable for fingercode identification. Note that both the PDS and 2PM SP schemes do not require additional storage space proportional to the user population size or vector dimensionality. Our new scheme is based on and enhanced from these two methods. We propose an efficient search algorithm to find the minimum squared Euclidean distance, which combines the PDS algorithm [4] and the 2PM SP algorithm [6]. Since there will be more levels for fingercodes than the vectors in VQ and using the first several levels can hardly reject enough fingercodes, so we propose

8 476 H.-W. Sun et al. a new scheme, namely the truncated 2PM SP, for the fingercode identification system. To achieve the improvement, the truncated 2PM SP scheme begins the computation of the squared Euclidean distance at the s th level instead of the 0 th level, and at the s th level, we introduce PDS algorithm. The truncated 2PM SP algorithm consists of the following five steps: Step 1: Convert each template in the database to an m n matrix as shown in Figure 4 (m = 16, n = 32 in our experiment). 0º 157.5º 0º 22.5º 45º 67.5º 90º 112.5º 135º 157.5º Fig. 4. Convert each template in the database to an m n matrix Step 2: Construct the truncated 2PM SP by computing the pyramid from the bottom level to the s th level for each matrix computed in Step 1 (s =5in our experiment). If there are N users, and 10 templates for each user in the database, 10N truncated 2PM SP are constructed. That is, each template in the database is associated with one truncated 2PM SP. Step 3: For the query fingercode x, the truncated 2PM SM of x is constructed. Select the first template c 1 in the database to be the current template closest to the query fingercode x. Compute and temporarily store the running minimum d 2 min = d2 (x, c 1 )andd 2 v,min =2(u v) d 2 min for v [s, u]. Step 4: Foranyothertemplatec i in the database, execute the rejection tests from the s th level to the bottom level. At the s th level, if the partially calculated squared Euclidean distance is greater than the running minimum d 2 s,min, this template can be rejected. If c i goes through all the rejection tests and arrives the bottom level, then recompute and store the running minimum d 2 min = d2 (x, c i )andd 2 v,min =2(u v) d 2 min for v [s, u]. Step 5: If there is no more candidate template, the current so far bestmatched template is the real best-matched one, and if d 2 min is less than the predefined threshold, the index of this template is used to establish the identity of the user. 5 Experimental Results Our algorithm is compared with the PDS and 2PM SP algorithms through experiments. In our experiments, we use the same parameters as in Section 4. The improvement ratio in terms of execution time required in the proposed algorithm

9 An Efficient Algorithm for Fingercode-Based Biometric Identification 477 Table 1. Comparison of average online execution time per query fingercode Number of Number of T PDS T 2PM T T 2PM R 1 R 2 users templates (s) (s) (s) % % PDS 2PM SP T2PM SP Execution time Number of users Fig. 5. Performance comparison for large user population TPDS TT2PM over the PDS and 2PM SP algorithms are denoted by R 1 = T PDS 100 T2PM TT2PM and R 2 = T 2PM 100 respectively. Here T PDS, T 2PM and T T 2PM denote the average online execution time of the 100 tested fingercodes required in the PDS algorithm, the 2PM SP algorithm and the proposed algorithm, respectively. Table 1 illustrates the respective performance comparisons where the time unit is denoted by s. As can be seen from Table 1, our algorithm performs more efficiently than both the PDS algorithm and the 2PM SP algorithm. More importantly, experimental results also illustrate the scalability of our algorithm since our algorithm performs well even with large user population as shown in Figure 5. Furthermore, our algorithm outperforms the FS algorithm, the PDS algorithm and the 2PM SP based search algorithm for fingercode identification in terms of computation efficiency and yet without sacrificing accuracy and storage. (2PM SP requires k memories for a k-dimensional vector [6]). 6 Conclusions In this paper, we proposed an efficient fingercode identification technique based on an improved VQ encoding algorithm. The new algorithm finds the minimum squared Euclidean distance by combining the partial distance search and the

10 478 H.-W. Sun et al. 2-pixel-merging sum pyramid in VQ encoding. Because of the test structure of the truncated 2PM SP algorithm, our algorithm is more efficient than both the PDS and basic 2PM SP algorithms. Experimental results on DB1 of FVC 2004 [8] demonstrated that our algorithm can outperform the full search algorithm, the partial distance search algorithm and the 2-pixel-merging sum pyramid based search algorithm for fingercode-based fingerprint matching in terms of computation efficiency without sacrificing accuracy and storage. Acknowledgement. This research was partly funded by the Chinese National Science Foundation (Project Number: ), P. R. China and the Biometric Cryptography project of PrivyLink Pte Ltd (Singapore). References 1. A.K. Jain, S. Prabhakar, L. Hong, S. Pankanti. Filterbank-based fingerprint matching, IEEE Trans on Image Processing, 2000, 9(5): Y. Linde, A. Buzo, R. M. Gray. An algorithm for vector quantizer design, IEEE Trans on Comm, 1980, 28(1): N.M. Nasrabadi, R.A. King. Image coding using vector quantization: a review, IEEE Trans on Comm, 1988, 36(8): C. Bei, R.M. Gray. An Improvement of the Minimum Distortion Encoding Algorithm for Vector Quantization, IEEE Trans on Comm, 1985, 33(10): Z. Pan, K. Kotani, T. Ohmi. Improved fast encoding method for vector quantization based on subvector technique,2005 IEEE International Symposium on Circuits and Systems, 2005: Z. Pan, K. Kotani, T. Ohmi. A memory-efficient fast encoding method for vector quantization using 2-pixel-merging sum pyramid,2004 IEEE Int l Conf on Acoustics, Speech and Signal Processing, 2004, 3: X.D. Jiang, M.H. Liu, A.C.C. Kot. Reference Point Detection for Fingerprint Recognition, the 17 th Int l Conf on Pattern Recognition, 2004, 1: FVC The 3rd International Fingerprint Verification Competition,