FINGERPRINTS are the flow-like ridges present on human

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1 1100 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 15, NO. 5, MAY 2006 Fingerprint Registration by Maximization of Mutual Information Lifeng Liu, Tianzi Jiang, Jianwei Yang, and Chaozhe Zhu Abstract Fingerprint registration is a critical step in fingerprint matching. Although a variety of registration alignment algorithms have been proposed, accurate fingerprint registration remains an unresolved problem. We propose a new algorithm for fingerprint registration using orientation field. This algorithm finds the correct alignment by maximization of mutual information between features extracted from orientation fields of template and input fingerprint images. Orientation field, representing the flow of ridges, is a relatively stable global feature of fingerprint images. This method uses the statistics and distribution of global feature of fingerprint images so that it is robust to image quality and local changes in images. The primary characteristic of this method is that it uses this stable global feature to align fingerprints, and that its behavior may resemble the way humans compare fingerprints. Experimental results show that the occurrence of misalignment is dramatically reduced and that registration accuracy is greatly improved at the same time, leading to enhanced matching performance. Index Terms Biometrics, fingerprints, matching, minutia, mutual information (MI), orientation field, registration. I. INTRODUCTION FINGERPRINTS are the flow-like ridges present on human fingers. Fingerprint-based personal identification has been used for a very long time [14]. Owning to their distinctiveness and stability, fingerprints are the most widely used biometric features. Nowadays, most automatic fingerprint identification systems (AFIS) are based on matching minutiae, which are local ridge characteristics in the fingerprint pattern. The two most prominent minutiae types are ridge ending and ridge bifurcation. Based on the features that the matching algorithms use, fingerprint matching can be classified into image-based and graph-based matching. Image-based matching [2] uses the entire gray scale fingerprint image as a template to match against input fingerprint images. The primary shortcoming of this method is that matching may be seriously affected by some factors such as contrast variation, image quality variation, and distortion, which are inherent properties of fingerprint images. The reason for such limitation lies in the fact that gray scale values of a fingerprint image are not stable features, and may change Manuscript received April 28, 2004; revised April 3, This work was supported in part by the Natural Science Foundation of China under Grants and , in part by the National Key Basic Research Projects of China (973) under Grant 2002CB312104, and in part by Watchdata Digital Company. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Hassan Foroosh. L. Liu is with the Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada ( lliu@ucalgary.ca). T. Jiang and C. Zhu are with the National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing , China ( jiangtz@nlpr.ia.ac.cn; J. Yang is with the Fangzheng Company, Beijing , China. Digital Object Identifier /TIP among different impressions. Another shortcoming is the large size of template required to store the whole gray scale image. In addition, in some nations it is illegal to store fingerprint images due to the possibility of invasion of privacy. Bazen et al. have proposed a correlation-based algorithm using regions of gray scale fingerprint images to match fingerprints [3]. This method is difficult to handle large rotation and may fail when surroundings of minutiae are similar. Another image-based approach, i.e., matching by entire ridge structure is invariant to the brightness variations but is very sensitive to image quality. Jain et al. have proposed an innovative image-based fingerprint matching algorithm [12]. This method first detects a reference point and then tessellates the fingerprint around this point. Afterwards, a bank of Gabor filters (oriented in eight directions) is used to construct a feature vector, called FingerCode. Thus, matching between two fingerprint images reduces to finding the Euclidean distance between two FingerCodes. The salient advantage of this method is that it can be highly efficient in matching aquery fingerprint againsta very large database because it uses index/retrieval mechanics. However, it is impossible to locate the reference point precisely each time, and sometimes the reference point cannot be detected at all due to poor image quality or only partial finger presented in the image. These shortcomings limit the application of this method for reliable identification. In a similar method, Ross et al. have used Gabor filters to extract ridge feature map and fingerprint matching is achieved by comparing ridge feature maps of two fingerprint images [21]. However, no rotation offset is considered in this work. A hybrid fingerprint matcher is presented which combines minutiae and ridge flow information to represent and match fingerprints [20]. In this method, fingerprint images are first aligned using minutiae and then matching is carried out by combining both minutiae and ridge feature map matching, which is essentially minutiae-based matching and alignment will be affected by the accuracy of minutiae extraction. Graph-based matching [7], [9] represents the minutiae in the form of graphs. The high computational complexity of graph matching hinders its implementation. To reduce the computational complexity, matching the minutiae sets of template and input fingerprint images can be done with point pattern matching. Several point pattern matching algorithms have been proposed and commented in the literature [10], [11], [16], [22], [24]. Point pattern matching is generally intractable due to the lack of knowledge about the correspondence between two point sets. To address this problem, Jain et al. proposed alignment-based minutiae matching algorithms [10], [11]. Two sets of minutiae are first aligned using corresponding ridges to find a reference minutiae pair, one from the input fingerprint /$ IEEE

2 LIU et al.: FINGERPRINT REGISTRATION BY MAXIMIZATION OF MI 1101 and another from the template fingerprint, and then all the other minutiae of both images are converted with respect to the reference minutiae. Afterwards, the aligned point patterns are compared to give a matching result. Jiang et al. also proposed an improved method [13], using minutia together with its neighbors to find the best alignment. To address nonlinear deformation of fingerprint images, nonrigid registrations of minutiae using thin-plate splines are implemented [1], [4]. Both of the approaches may fail when the correct alignment cannot be recovered in fingerprint images with poor quality. This paper proposes a novel fingerprint registration algorithm, in which the best alignment of two fingerprint images, template and input, is achieved by maximization of mutual information (MI) between features extracted from their orientation fields. The orientation field of a fingerprint image, a relatively stable feature independent of fingerprint capture devices and image contrast variation, represents the intrinsic nature of the fingerprint images and can be generally estimated reliably. When humans compare fingerprints, we may use global structures like ridge flows to find the correspondence of two fingerprints. Our registration method emulates this behavior. Experimental results show that our algorithm achieves good registration and verification performance. The rest of this paper is organized as follows. Section II gives the definitions of entropy and MI. In Section III, our feature extraction method is briefly described. Section IV is devoted to our registration algorithm. Experimental results on fingerprint databases are described in Section V. Summary and discussions are outlined in the last section. II. ENTROPY AND MUTUAL INFORMATION A. Entropy Entropy is a statistical measure that summarizes randomness. Given a discrete random variable, its entropy is defined by where is the sample space and is the member of it. represents the probability when takes on the value. We can see in (1) that the more random a variable is, the more entropy it will have. B. Conditional Entropy, Joint Entropy and MI Conditional and joint entropy relate the predictability of two random variables. Conditional entropy and joint entropy are defined as (1) (2) (3) Conditional entropy measures the randomness of when is given, and joint entropy measures the randomness of and. With the increase of, gets more dependent on. However, conditional entropy by itself is not a measure of dependency. A small value of implies either is small or is less dependent on. When and are independent, (2) and (3) can be expressed using and MI between two random variables is defined as (4) (5) Because conditional entropy can be expressed in terms of marginal and joint entropies We can get two equivalent expressions for MI (6) (7) (8) (9) MI measures the statistical dependency between two random variables. The physical meaning of MI is the reduction in entropy of given. This is best demonstrated in the (8). In (8), is the entropy of, computed on the probability distribution of. denotes the conditional entropy, which is based on the conditional probability. When interpreting entropy as a measure of uncertainty, (8) translates to the amount of uncertainty about minus the uncertainty about when is known. In other words, MI is the amount by which the uncertainty about decreases when is given. Viola et al. proposed [26] that registration could be achieved by maximization of MI. Registration using MI is widely used in medical image registration, and it has achieved excellent results for rigid registration. To provide overlap invariance, Studholme et al. have proposed normalized MI (NMI) [23] (10) This measure evaluates the ration of the joint and marginal entropies so that any change in uncertainty of the image values and, therefore, the marginal entropies, will not result in a change in the alignment measure. In this paper, we apply NMI to finerprint registration. The details will be detailed in Section IV. III. FEATURE EXTRACTION In feature extraction, we extract the orientation field of template and input fingerprint images. Orientation field is a reliable feature of fingerprint images, which can be used for fingerprint enhancement, minutiae extraction and matching.

3 1102 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 15, NO. 5, MAY 2006 Fig. 1. Fingerprint image and its mean directions in different blocks. The size of each block is A. Normalization and Segmentation To increase the estimation accuracy of the orientation field, we first normalize fingerprint images using the algorithm described in [8] to adjust the contrast of images. Then, we extract region of interest from the normalized images. B. Orientation Field Estimation Fingerprint images, which can be regarded as oriented texture patterns, are flow-like images consisting of valleys and ridges. The orientation field of a fingerprint image represents the directionality of ridges in the image. Singular points, important features of fingerprint images which are frequently used in fingerprint classification, are the points in a fingerprint where the orientation field is discontinuous and varies significantly. So the orientation field of a fingerprint image can be regarded as an intrinsic nature. Rao et al. proposed an algorithm to estimate the orientation of texture images [17]. Rao s algorithm consists of three main steps: 1) divide the input fingerprint image into blocks of size (16 16 in our experiments); 2) compute the gradients and at each pixel in each block; 3) estimate the local orientation of each block using the following equation: (11) where and are the gradient magnitudes in and directions, respectively. Finally, is normalized into the range of We use a sliding window technique to efficiently extract every pixel s direction in the entire fingerprint image [28]. Due to the noise and corrupted ridge structures in the images, the orientation field may not always be estimated correctly. We perform low-pass filtering on the estimated orientation field [8]. C. Direction Feature Extraction After the orientation field is estimated, we calculate direction features. During fingerprint template enrollment, we divide the whole fingerprint image into blocks and the mean of directions in each block is computed. All the directions of computed blocks are stored as features for registration described later. Fig. 1 shows a fingerprint and its mean directions in different blocks. IV. FINGERPRINT REGISTRATION USING MI Registration or alignment is a process through which the correct transformation is determined. Registration using MI is a method of maximization of similarity measures. It uses MI as the similarity measure and aligns images by maximizing MI between them under different transformations. In our method, orientation fields of two fingerprint images are regarded as two random variables. Then, MI is used to measure the similarity or correlation between these two random variables. MI describes the uncertainty in estimating the orientation field at a certain location given another orientation field. The more similar or correlated the orientation fields are, the more MI they have. The definitions of entropy and NMI have been given in Section II. Here we use NMI between template and input s direction features to align the fingerprints. In our registration algorithm, we assume that distortion is not very large. Since distortion in fingerprint images is usually nonlinear and difficult to represent, a complex and time-consuming nonrigid registration is required if one wants to remedy distortion exactly. But in most circumstances, this is not necessary if distortion is not very large because minutiae matching can usually compensate for some distortions. Registration by maximization of MI can also tolerate certain distortions, so this approach can be used for general purpose. If distortion is large, this method is not appropriate. Given a similarity transformation (for positive angles being clockwise rotations), the orientation field of the input fingerprint image can be converted to the template image coordinate system using the following equation: (12)

4 LIU et al.: FINGERPRINT REGISTRATION BY MAXIMIZATION OF MI 1103 Fig. 2. Graphic representation of transformation and search space. (a) Orientation field of input fingerprint image is superposed on imaginary template orientation field. (b) Search space. where is the coordinates in the orientation field of the input fingerprint image, is the transformed coordinates in the template image coordinate system, and,, are translations in directions, and rotation, respectively. Then, the transformed orientation field image is superposed on the template image. The resultant image is divided into blocks in the same way as was the template image during enrollment [see Fig. 2(a)]. The mean direction of each overlapped block can be computed by the same way as calculating the mean direction of the template image. When the number of overlapped blocks is less than one-third (selected based on experimental results) of the entire valid direction blocks in the template image, the transformation is discarded because too small an overlapped size usually means a false registration, and as a result some images from the same fingers may not be aligned. This is reasonable because when the overlapped area is small, there is insufficient evidence to determine whether the two images are from the same finger or images from different fingers are accidentally aligned. Besides, the computation of MI also requires that there are adequate samples to correctly estimate distributions. The mean direction ranges from 90 90, inclusive. For convenience of expression, we convert this to 180, inclusive. In order to estimate NMI, the continuous direction needs to be evenly discretized and the continuity between 0 and 180 should be reserved Fig. 3. Estimation of joint distribution. the template of a certain block falls into the range of and the corresponding transformed input mean direction falls into the range of, then the element of joint probability adds one. After all the overlapped blocks are examined, we can get the joint and marginal probability distributions using the following equations: (13) where is the number of discrete directions. Having discretized both the template and transformed input mean directions, we can define joint probability of an overlapped block (see Fig. 3). For example, if the mean direction of (14)

5 1104 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 15, NO. 5, MAY 2006 Fig. 4. Result of coarse and fine registration. (a) Template fingerprint image. (b) Input fingerprint image. (c) Result of coarse registration. (d) Result of fine registration. then the NMI of a given transformation can be estimated using (1), (3), and (10). We have put forward an approach to estimate NMI between mean directions of template and input fingerprint images given a transformation. Now, we need to search the parameter space to find the maximal NMI so that the best registration between two fingerprints can be obtained. Fig. 2(b) shows the three-dimensional (3-D) searching space of rotation and translation of and. Although the parameter space is not very large, it is still time-consuming to search the whole parameter space pixel-wisely (in our experiments, we set ranges of these parameters to make majority of images fall into these ranges). To resolve the contradiction between processing time and accuracy, we use a hierarchical approach: coarse and fine registration. In coarse registration, we search the parameter space with a relatively large step to find the maximal NMI, indicating an approximate alignment. Then in fine registration, we find the best transformation in the subspace around the parameters found in the coarse registration. The best transformation with maximal NMI can usually be found using this strategy. But it should be noticed that, if the searching step is too large, the algorithm may be trapped in local maxima and the best registration cannot be found. If the searching step is too small, the computational requirements will be heavy. So this is a tradeoff between efficiency and accuracy. V. EXPERIMENTAL RESULTS We have tested our novel fingerprint registration algorithm on the databases from Universit di Bologna, Italy (DB-b) and FVC2002 DB2 Set A database (DB2_A). DB-b contains 168 fingerprint images from 21 different fingers with eight images per finger. The size of these images is DB2_A consists of 800 images from 100 different fingers with eight images per finger. The size of these images are A. Registration 1) Registration Using Proposed Algorithm: In our experiments, we use both databases to test our registration algorithm. We set different ranges of rotation and translation of and for each database to make majority of images fall into these ranges. Each image is aligned with all the others in the same database, so a total of ( ) registrations for DB-b and ( ) for DB2_A are performed. We use a three-level hierarchical registration. The size of the window used to compute mean direction is 8 8. The number of discretized mean direction is 9, 18, and 36. Fig. 4 shows the result of coarse and fine registration. Fig. 5 shows some registration results of different image qualities. In this figure, images with certain rotation, translation, noises and scars are correctly aligned. We observed that when is large, for example in our experiments, the errors of misalignment dramatically increased, while they are stable when is decreased to 18 and 9 in our experiments. One reason for this phenomenon is that when gets larger, the mean direction is discretized more accurately and more sensitive to orientation field estimation. As a result, small changes in mean direction may greatly affect its distribution. Another reason is that the number of mean direction samples is too few to estimate distribution correctly. Thus, when is large, registration is much more sensitive to image quality, resulting in an estimation of orientation field with reduced accuracy. On the other hand, if is small, misalignments will decrease but so will registration accuracy. After manually checking registration results, we find that there are several reasons for false alignment. The most prominent one is that the size of overlapped area is too small. It is required that enough samples be present for the MI method to correctly estimate distribution of orientation field. So when there are an inadequate number of samples, it is less possible for the MI method to find the correct alignment. Many images in DB2_A contain a very small fraction of the finger so that they cannot be correctly aligned, which accounts mostly for the not very good registration results of DB2_A. A second reason for false alignment is poor image quality. Although registration using MI can tolerate some noises, the correct result cannot be obtained when a large part of orientation field cannot be estimated correctly. The third reason is distortion. When distortion is not very large or only exists in a small portion of an image, our method can find relatively good registration (some parts of the images may not align well due to distortion). When distortion is very large or exists in a large portion of an image, correct registration cannot be achieved. Finally, some images

6 LIU et al.: FINGERPRINT REGISTRATION BY MAXIMIZATION OF MI 1105 Fig. 5. Some registration results using proposed algorithm: column (a), (b), and (c) are template images, input images, and registration results. are occasionally not aligned due to the coarse-to-fine registration mechanism because sometimes registration results may be trapped at local maxima during coarse registration and global maxima cannot be found. Fig. 6 shows an example of incorrect registration by proposed method as a result of distortion. When a human compares fingerprints, he may first use the global pattern to find the correct correspondence and then use the local structures to perform matching. Proposed registration algorithm resembles this behavior, it uses the global orientation field to find correspondence between fingerprints (see Fig. 7). Fig. 8 shows normalized distributions of NMI for same and different fingers in DB-b ( and ). From this figure, we can find out that we may discriminate some fingerprint images by setting threshold of NMI. Table I lists the NMI statistics of database DB-b. A joint probability distribution of orientation fields of a pair of correctly registered fingerprint images is illustrated in Fig. 9. In this figure, each value in the probability table is the number of occurrences of the orientations

7 1106 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 15, NO. 5, MAY 2006 Fig. 6. Incorrect registration by proposed method. (a) Template image. (b) Input image. (c) Registration result. Fig. 7. image. Registration result that is similar to human s comparison. (a) Template image. (b) Input image. (c) Superposed gray scale image. (d) Superposed thinned combination of template and input orientation fields and the corresponding probability can be obtained by dividing the total number of occurrences of all the possible combinations. From this figure we can see that for a pair of correctly registered fingerprint images, the diagonal elements of the joint probability table are predominant. In comparison of different similarity measures, we also use normalized chi-square as association measure to measure relationship between orientation fields of fingerprint images. We use the same features of orientation fields and regard these features as samples of the entire orientation field. Then, normalized chi-square of these samples is used to find the relationship between two orientation fields. The same search strategy is utilized to find the best transformation which gives the minimal normalized chi-square indicating the closest relationship. 2) Registration Using Pixel Correlation: For comparison, we also use pixel correlation to register fingerprint images. We use the following equations to calculate correlation coefficient of two gray scale fingerprint images for a certain transformation: (15) where is the correlation coefficient of variable and, are standard deviations of and, respectively. The value of is between 1 and 1. If there is no relationship between the two variables then and if there is a perfect match,. If there is a perfect inverse relationship, where one set of variables increases while the other decreases, then.infingerprint image registration, the closer the coefficient is to 1, the more possibly the images are registered. We use the same range of rotation and translation as we do in the proposed registration method. We also use the same search strategy to find the maximal correlation coefficient. Fig. 8. Joint probability distribution of a pair of registered orientation fields of two fingerprint images. The numbers in the joint probability distribution table indicate the times of occurrences. 3) Comparison of Results: Table II lists the numbers of misalignment of same fingers for different parameters using proposed registration method with both MI and normalized chi-square as similarity measures. The number of misalignment using pixel correlation is also listed in the same table. Fig. 10 shows a registration comparison result of proposed method and pixel correlation method. From this figure, we can see that the proposed method can register the images more accurately. From

8 LIU et al.: FINGERPRINT REGISTRATION BY MAXIMIZATION OF MI 1107 TABLE I REGISTRATION STATISTICS OF MAXIMAL NORMALIZED MUTUAL INFORMATION (NMI) FOR DATABASE DB-B thinned [5]. Then, minutiae are detected [10] and postprocessed [6]. In experiments for matching, we use two algorithms based on [18]. Minutiae-based algorithm uses the method described in [18] to align and match fingerprint images solely using detected minutiae. Our algorithm uses the proposed registration algorithm and the same minutiae matching method as in minutiae-based one. Here we briefly introduce the minutiae matching method that we used. We first use transformation parameters obtained from orientation field registration to convert minutiae of input image to template image coordinate system by similarity transformation. Then, we can pair input and template minutiae using tolerance box. If two minutiae fall into the same tolerance box, they are defined as paired minutiae. If paired minutiae have similar directions, they become matched. How to establish the tolerance box is detailed in [18]. Our algorithm follows its scheme but we build it along each minutia s direction instead of doing so along the coordinate axes because the deformation of fingerprints often appears along the directions of ridges (see Fig. 12). The matching score is computed according to the following equation: (16) Fig. 9. Normalized distributions of NMI for same fingers and different fingers of DB-b (W =8, n =18). TABLE II ERRORS OF REGISTRATION these results we can see that proposed algorithm with MI as similarity measure is superior to proposed registration method with normalized chi-square as association measure and pixel correlation registration in the reduction of false registrations. Generally, our proposed algorithm can align two fingerprint images more accurate than pixel correlation method. From all of these experimental results, proposed algorithm is very accurate and robust to image quality. B. Matching We also test verification results using minutiae matching after the orientation field registration on DB-b. A block diagram of our matching algorithm is show in Fig. 11. To extract minutiae, fingerprint images are enhanced [29], binarized [25], and where,, and represent the number of matched minutiae, the number of minutiae extracted from the input fingerprint, and the number of the minutiae recorded in the template. Finally, we can judge whether two fingerprint images are matched by setting thresholds of matching score. We set both the width and height of elastic box to 10, and the largest difference of minutiae direction to. We also set and in the registration of proposed method. Fig. 13 shows an example in which proposed method correctly registered fingerprint images while the minutiae-based method gave the false registration result. The receiver operating characteristic curves (ROCs) of the tests for both algorithms are shown in Fig. 14. From the results, we can observe that the performance of proposed registration method is much better than the minutiae-based method in verification rate. We observe that matching errors are caused mainly by inaccurate minutiae detection, which is seriously effected by image quality. In addition, inaccurate registration caused by distortion also affects the matcher performance. VI. CONCLUSION AND DISCUSSION We have proposed a novel fingerprint registration algorithm. The orientation field of fingerprint images, a relatively stable feature representing global characteristics of fingerprints, is introduced into fingerprint registration. MI is used to measure the similarity between orientation fields. Then, registration between two fingerprints is achieved through maximization of NMI between features extracted from their orientation fields. The primary characteristic of our algorithm is that it uses relatively stable global characteristics to align fingerprints, which may resemble the human behavior when comparing two fingerprints. This algorithm is also robust to image quality. As a result, the errors of misalignment, which often occur in pixel

9 1108 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 15, NO. 5, MAY 2006 Fig. 10. Registration comparison of pixel correlation and proposed metho. (a) Template image. (b) Input image. (c) Result of proposed method. (d) Result of pixel correlation. Fig. 11. Block diagram of proposed matching algorithm. Fig. 12. Tolerance box around minutia. correlation algorithm, are dramatically decreased, resulting in better verification performance. Experimental results show that our algorithm can generally find the accurate registration and can achieve better verification performance than approaches using only minutiae. From the experimental results, we find out that proposed algorithm is more robust to image quality so that it may work better than pixel correlation and minutiae-based algorithms on relatively poor quality images. This is because it uses overall information of fingerprint images which is insensitive to local changes. As long as the orientation field in most areas of images can be generally correctly estimated, the correct registration can be found. While minutiae-based algorithms are very sensitive to local image changes, minutiae extraction results will be seriously affected by image quality. But when images are seriously corrupted, it is impossible to correctly estimate orientation field so that correct registration cannot be found using proposed method. In such cases, other methods, such as minutiae-based approaches, may also fail. So restoration of corrupted images is very important for all methods. We find that the main drawback of proposed algorithm is that it requires adequate samples to estimate distribution of orientation field. Thus, when overlapped area is small, correct alignment may not be found. In practice, we can resolve this problem by restricting fingers position when acquiring images. Distortion through elastic deformation is indeed the most serious and difficult problem to be solved. In order to compare different registration methods regarding distortion, a standard mutual degree of image distortion is needed to be developed in future. There is always nonlinear distortion existing in fingerprint images because of the elasticity of skin. If distortion is very large, it will seriously affect registration and matching results. Distortion is usually compensated in elastic minutiae matching, which may, however, increase the likelihood of false matching. Further study is needed to account for distortion during registration. One possible solution may be to use neural networks with nonlinear function and two trained classes (distortion and normal) of fingerprints to determine the degree of distortion.

10 LIU et al.: FINGERPRINT REGISTRATION BY MAXIMIZATION OF MI 1109 Fig. 13. Registration comparison of minutiae-based and proposed method. (a) Template imag. (b) Input image. (c) Result of proposed method. (d) Result of minutiae-based method. Fig. 14. ROC curves. ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their significant and constructive critiques and suggestions, which improved the paper very much. The would also like to thank X. Pan at University of Chicago for his careful proofreading of the manuscript, and their colleagues for useful discussion. They would also like to thank the Universit di Bologna, Italy, for access to their fingerprint database for testing our algorithm. REFERENCES [1] A. Almansa and L. Cohen, Fingerprint image matching by minimization of a thin-plate energy using a two-step algorithm with auxiliary variables, in Proc. IEEE 5th Workshop Applications Computer Vision, Dec. 2000, pp [2] R. Bahuguna, Fingerprint verification using hologram matched filterings, presented at the 8th Meeting Biometric Consortium, San Jose, CA, Jun [3] A. M. Bazen, G. T. B. Verwaaijen, S. H. Gerez, L. P. J. Veelenturf, and B. J. van der Zwaag, A correlation-based fingerprint verification system, in Proc. ProRISC Workshops Circuits, Systems, Signal Processing, Veldhoven, The Netherlands, Nov. 2000, pp [4] A. M. Bazen and S. Gerez, Fingerprint matching by thin-plate spline modeling of elastic deformations, Pattern Recognit., vol. 36, no. 8, pp , Aug [5] Y. S. Chen and W. H. Hsu, A modified fast parallel algorithm for thinning digital patterns, Pattern Recognit. Lett., vol. 7, no. 2, pp , [6] A. Farina, Z. M. Kovcs-Vajna, and A. Leone, Fingerprint minutiae extraction from skeletonized binary images, Pattern Recognit., vol. 32, no. 5, pp , [7] S. Gold and A. Rangarajan, A graduated assignment algorithm for graph matching, IEEE Trans. Pattern Anal. Mach. Intell., vol. 18, no. 4, pp , Apr [8] L. Hong, Y. F. Wan, and A. K. Jain, Fingerprint image enhancement: algorithm and performance evaluation, IEEE Trans. Pattern Anal. Mach. Intell., vol. 20, no. 8, pp , Aug [9] D. K. Isenor and S. G. Zaky, Fingerprint identification using graph matching, Pattern Recognit., vol. 19, no. 2, pp , [10] A. K. Jain, L. Hong, and R. Bolle, On-line fingerprint verification, IEEE Trans. Pattern Anal. Mach. Intell., vol. 19, no. 4, pp , Apr [11] A. K. Jain, L. Hong, S. Pankanti, and R. Bolle, An identity authentication system using fingerprints, Proc. IEEE, vol. 85, no. 9, pp , Sep [12] A. K. Jain, S. Prabhakar, L. Hong, and S. Pankanti, Filterbank-based fingerprint matching, IEEE Trans. Image Process., vol. 9, no. 5, pp , May [13] X. Jiang and W. Yau, Fingerprint minutiae matching based on the local and global structures, in Proc. 15th Int. Conf. Pattern Recognition, vol. 2, Barcelona, Spain, Sep. 2000, pp [14] H. C. Lee and R. E. Gaensslen, Eds., Advances in Fingerprint Technology. New York: Elsevier, [15] D. Maltoni, D. Maio, A. K. Jain, and S. Prabhakar, Handbook of Fingerprint Recognition. New York: Springer-Verlag, [16] A. Ranade and A. Rosenfeld, Point pattern matching by relaxation, Pattern Recognit., vol. 12, no. 2, pp , [17] A. Rao, A Taxonomy for Texture Description and Identification. New York: Springer-Verlag, 1990.

11 1110 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 15, NO. 5, MAY 2006 [18] N. Ratha, K. Karu, S. Chen, and A. K. Jain, A real-time matching system for large fingerprint databases, IEEE Trans. Pattern Anal. Mach. Intell., vol. 18, no. 8, pp , Aug [19] A. Ross, S. Dass, and A. K. Jain, Estimating fingerprint deformation, in Proc. Int. Conf. Biometric Authentication (ICBA), vol. 3072, Hong Kong, Jul. 2004, pp [20] A. Ross, A. K. Jain, and J. Reisman, A hybrid fingerprint matcher, Pattern Recognit., vol. 36, no. 7, pp , Jul [21] A. Ross, J. Reisman, and A. K. Jain, Fingerprint matching using feature space correlation, in Proc. Int. ECCV Workshop Biometric Authentication, vol. 2359, Copenhagen, Denmark, Jun. 2002, pp [22] J. P. P. Starink and E. Backer, Finding point correspondence using simulated annealing, Pattern Recognit., vol. 28, no. 2, pp , [23] C. Studholme, D. L. G. Hill, and D. J. Hawkes, An overlap invariant entropy measure of 3D medical image alignment, Pattern Recognit., vol. 32, no. 1, pp , [24] J. Ton and A. K. Jain, Registering landset images by point matching, IEEE Trans. Geosci. Remote Sens., vol. 27, no. 5, pp , May [25] O. D. Trier and A. K. Jain, Goal-directed evaluation of binarization methods, IEEE Trans. Pattern Anal. Mach. Intell., vol. 17, no. 12, pp , Dec [26] P. Viola, Alignment by maximization of mutual information, Ph.D. dissertation, Artificial Intelligence Lab., Mass. Inst. Technol., Cambridge, [27] W. M. Wells III, P. Viola, H. Atsumi, S. Nakajima, and R. Kikinis, Multi-modal volume registration by maximization of mutual information, Med. Image Anal., vol. 1, no. 1, pp , [28] J. Yang, L. Liu, and T. Jiang, An improved method for extraction of fingerprint features, in Proc. Int. Conf. Image Graph., Anhui, China, Aug. 2002, pp [29] J. Yang, L. Liu, T. Jiang, and Y. Fan, A modified Gabor filter design method for fingerprint image enhancement, Pattern Recognit. Lett., vol. 24, no. 12, pp , Aug Tianzi Jiang received the B.Sc. degree from Lanzhou University, Lanzhou, China, in 1984, and the M.Sc. and Ph.D. degrees from Zhejiang University, Hangzhou, China, in 1992 and 1994, respectively. From August 1984 to September 1989, he was an Assistant Lecturer with Suzhou Silk Engineering Institute. Since 1994, he has been with the National Laboratory of Pattern Recognition, as a Postdoctoral Research Fellow (1994 to 1996), Associate Research Professor (1996 to 1999), and Research Professor (1999 to present). He was also adjunctively with the School of Mathematics, University of New South Wales, New South Wales, Australia (1997 to 1999); Signal and Image Processing Group, Max-Planck Institute of Cognitive Neuroscience, Leipzig, Germany (1999 to 2000); School of Computer Science, Queen s University of Belfast, Belfast, U.K. (2000 to 2001); School of Computer Science, University of Houston, Houston, TX (2002 to 2003); and Zhejiang University, Beijing, China (2004 to present). In April 2001, he went back to the National Laboratory of Pattern Recognition again as a Full Professor and the Leader of Medical Imaging and Computing, supported by the Hundred Talents Programs of the Chinese Academy of Sciences, Beijing, China. His research interests include statistical analysis of fmri data, extraction of quantitative parameters useful for diagnosis (shape, texture, and motion), spatial registration of images acquired at different times, fusion of multimodal images, analysis of pathologies, imaging genomics, analysis of complex brain networks based on neuroimaging, and so on. Jianwei Yang received the B.E. degree from Tianjing University, Tianjing, China, in 2000, and the M.E. degree from the National Laboratory of Pattern Recognition, Institute of Automation, the Chinese Academy of Sciences, Beijing, in He is currently with Fangzheng Company, Beijing. Lifeng Liu received the B.E. degree in communications engineering from the Changchun Institute of Posts and Telecommunications, Beijing, China, in 2000 and the M.E. degree in pattern recognition and artificial intelligence from the Institute of Automation, Chinese Academy of Sciences, Beijing, in He is currently pursuing the M.Sc. degree at the University of Calgary, Calgary, AB, Canada. Chaozhe Zhu received the M.Sc degree from Beijing Institute of Technology, Beijing, China, in 2001, and the Ph.D. from Graduate School of Chinese Academy of Sciences (CAS), Beijing, in He is currently an Assistant Professor at CAS. His current research focuses on statistical learning based neuroimage computing.