Tessellation-Fingercode (STF) of the query fingerprint is repeatedly extracted when it is compared with different template fingerprints. In addition, the nonlinear ...
Fingerprint Matching Using Minutiae and Interpolation-based Square Tessellation Fingercode Lifeng Sha, Feng Zhao, and Xiaoou Tang Department of Information Engineering The Chinese University of Hong Kong Shatin, N.T., Hong Kong {lfsha1, fzhao0, xtang}@ie.cuhk.edu.hk Abstract—To improve the overall accuracy, a hybrid fingerprintmatching scheme using both minutiae and Square-TessellationFingercode has been proposed in the literature. However, for identification applications, the matching process is timeconsuming since the Fingercode of the query fingerprint is repeatedly extracted when it is compared with different template fingerprints in a large database. In addition, the matching accuracy is influenced by nonlinear distortions in fingerprint images. In this paper, we propose a new approach to solve the problem. We extract the Fignercode of the query fingerprint only once. When compared with the template fingerprints, the corresponding Fingercodes are generated by interpolation and resampling on the extracted Fingercode according to the optimally estimated mapping functions with respect to the minutiae matching results. Experimental results on NIST-4 and FVC2002 demonstrate that our algorithm outperforms the original approach in terms of both accuracy and running time.
I.
INTRODUCTION
Minutiae-based and filterbank-based matching are two popular techniques for fingerprint recognition. The minutiaebased matching algorithms first extract the local minutiae from the thinning image [8] or the grayscale image [6], and then match their relative placement in the query fingerprint with the stored template. The filterbank-based matching algorithm [4] uses a bank of Gabor filters to capture both local and global information in a fingerprint as a compact fixed-length FingerCode. The fingerprint matching is based on the Euclidean distance between two corresponding FingerCodes. The minutiae-based algorithms may not perform well if no sufficient number of common minutiae points exist in two fingerprint images. The performance of filterbank-based technique is influenced by the reference point detection. If the reference point is close to the boundary, the circular tessellation will only cover a small portion of the image. Furthermore, the reference point may not even present in small-sized fingerprints obtained using solid-state sensors. To improve the overall matching accuracy, Jain [5] proposed a hybrid fingerprint matcher that combines the minutiae-based approach with the filterbank-based approach. After minutiae alignment and matching, the registered query fingerprint is filtered with a set of eight Gabor filters and a square tessellation is then applied to the filtered images to compute the Fingercode for further matching. The square
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tessellation is performed on the entire image and hence captures more texture information than circular tessellation. Moreover, the tessellation is not based on detecting reference point but the alignment using the overall minutiae information, thus is more robust. The minutiae matching score and the Fingercode matching distance are combined to represent the final matching score. The hybrid technique performs better than a single minutiae-based matching or filterbank-based matching. It suites for fingerprint verification of images acquired using compact solid-state sensors. However, for identification applications with a large database, the matching process is computationally expensive since the SquareTessellation-Fingercode (STF) of the query fingerprint is repeatedly extracted when it is compared with different template fingerprints. In addition, the nonlinear fingerprint distortions are not taken into account in [5]. In this paper, we propose a new algorithm to deal with these difficulties. We compute the Fingercode only once and then use interpolation and resampling to compute the corresponding Fingercodes according to the minutiae matching results between the query fingerprint and the template fingerprints. Experimental results obtained on NIST-4 [9] and FVC2002 [7] confirm the efficiency and superiority of the proposed method. II. SQUARE TESSELLATION FINGERCODE To capture more reliable and rich texture information in fingerprint images, Jain [5] proposed a Square-TessellationFingerCode matching scheme. The STF Fingercode is generated using the following steps. 1.
Align the query fingerprint image with the template fingerprint using the overall minutiae information to get the optimal translation and rotation parameters (∆x, ∆y, ∆θ) that result in maximum matched minutiae pairs.
2.
Rotate the query fingerprint by ∆θ and translate it by (∆x, ∆y).
3.
Tessellate the aligned query fingerprint into a set of non-overlapping square cells, with the same size of 16x16.
4.
Normalize the pixels in each cell to a constant mean M 0 and constant variance V0 .
5.
Filter the normalized query fingerprint in eight directions (0°, 22.5°, 45°, 67.5°, 90°, 112.5°, 135°, 157.5°) using a bank of Gabor filters.
6.
Compute the average absolute deviation from the mean (AAD) of the gray values of each cell in the filtered images to form the STF Fingercode.
This alignment-based STF matching approach is suitable for fingerprint verification. However, for identification applications with a large database, the matching process is very time-consuming because the STF Fingercode needs to be repeatedly extracted after aligning the query fingerprint with different template fingerprints. The aim of alignment using the overall minutiae information is to obtain an overlapping region between the query and template fingerprints. We notice that the above alignment method assumes that only linear transformations present in fingerprints. In fact, a fingerprint is a scanned 2D image by pressing the 3D elastic finger surface on a flat sensor, which often introduces nonlinear distortions due to the elastic nature of human skin and the non-uniform pressure to the sensor surface. Therefore, the minutiae of two fingerprints cannot be exactly aligned. Generally two minutiae points within an 8x8 tolerance box are considered as matched minutiae. Fig. 1a shows an example to illustrate that the ridge skeletons of two impressions from the same finger cannot be accurately registered using traditional minutiae alignment method. III. INTERPOLATION-BASED STF MATCHING To reduce the computation time and increase the accuracy, we propose an interpolation-based STF (ISTF) matching algorithm. The STF FingerCode of the query fingerprint needs to be extracted only once, and it will be interpolated and resampled to produce the corresponding Fingercode when compared with a template fingerprint in the database.
(a)
(b)
Fig. 1. Ridge skeletons of nonlinearly distorted fingerprints that are registered by (a) traditional technique; (b) TPS model [2].
position and angle (i.e., where and in which direction) in the query fingerprint. Let ViT, j ,θ denotes the AAD feature value of the (i, j ) th tessellation cell in the θ-direction filtered template fingerprint, and ( x T , y T ) is its center point; ( x * , y * ) is the corresponding center point in the query fingerprint, ∆θ T is the relative rotation angle; VipP, jp ,θ , VipP, jp +1,θ , VipP+1, jp +1,θ , and VipP+1, jp ,θ are the AAD feature values of the four tessellation cells in the θdirection filtered query fingerprint around the center point ( x * , y * ) , and ( x p , y p ) , ( x p , y p + 16) , ( x p + 16, y p + 16) , and ( x p + 16, y p ) are their center points, respectively. The AAD
feature value in the query fingerprint ( ViTp , j ,θ ) corresponding to ViT, j ,θ can be calculated by using bilinear interpolation for the corresponding position and spline interpolation for the corresponding angle, Tp ViTp , j ,θ = fs (Vi , j ,θ − ∆θ ,θ ) ,
(1)
T
Given the extracted STF FingerCode of the query fingerprint and that of a template fingerprint, the ISTF Fingercode is computed as follows. 1.
Perform a minutiae-based matching to obtain the minutiae correspondence.
x −x y −y ) × (1 − ) 16 16 x* − x p y* − y p )×( ) + VipP, jp +1,θ × (1 − 16 16 x* − x p y* − y p + VipP+1, jp +1,θ × ( )×( ) 16 16 x* − x p y* − y p ) × (1 − ), + VipP+1, jp ,θ × ( 16 16
ViTP = VipP, jp ,θ × (1 − , j ,θ − ∆θ T
*
p
*
p
(2)
2.
Estimate the optimal mapping functions between the template and query fingerprints using the minutiae correspondence according to the TPS model [1][2].
3.
For each tessellation cell in template fingerprint, compute the corresponding center point and rotation angle in the query fingerprint with respect to the estimated mapping functions.
where fs (⋅) is a spline mapping function that circularly fits the
Compute the AAD features to form the ISTF FingerCode corresponding to the template fingerprint.
and 157.5°) to a spline curve for the estimation of the response ViTp , j ,θ at point θ , with a period of 180°.
4.
To reconstruct the elastic deformation between two fingerprints due to nonlinear distortions, we adopt the thinplate spline (TPS) model [1][2] that interpolates the control points while maintaining maximal smoothness. After registration of the two fingerprints using the estimated model, the query fingerprint can align with the template fingerprint more accurately (see Fig. 1b). Thus, for each tessellation cell in the template fingerprint, we can exactly get its corresponding
points ViTp , j ,θ − ∆θ
T
( θ =0°, 22.5°, 45°, 67.5°, 90°, 112.5°, 135°,
The ISTF Fingercode matching is based on the Euclidean distance between the query and template fingerprints,
EDInterpolation =
∑θ
i, j,
2
T Vi TP ki , j , j ,θ − Vi , j ,θ
∑θ
i, j,
ki , j
,
(3)
where ViT, j ,θ , ViTp , j ,θ are the STF Fingercode of the template fingerprint and the corresponding ISTF Fingercode of the query fingerprint; k (i, j ) denotes the confidence level of the (i, j ) th tessellation cell with value 1 for overlapping foreground cell and a value of 0 for background cell or non-overlapping cell. IV. FUSION STRATEGY In order to produce the final matching result, we combine the minutiae matching score with the ISTF matching distance using a score-level fusion rule and two decision-level fusion rules. To perform a score-level fusion, the ISTF matching distance is first converted to a matching score similar to the minutiae matching score, S FC = 1 − ED / EDmax ,
(4)
where ED denotes the matching distance between two fingerprints and EDmax is an empirically determined value. Then the two matching scores are combined using a sum rule to produce the final matching score, S = αS M + (1 − α ) S FC ,
(5)
where S M is the minutiae matching score and α ∈ [0,1] is the weight of S M . In this work, α is set to 0.5. For the decision-level fusion, we adopt the product rule and non-parameter estimation method. The product rule computes the two-dimensional probability densities as the product of the probabilities of the minutiae matching score and the ISTF matching distance, assuming that the minutiae-based matcher and the ISTF-based matcher are independent. The nonparameter method estimates the two-dimensional probability densities by computing a normalized histogram. A 2DGaussian mask is used to smooth the genuine and imposter distribution.
TABLE I. AVERAGE MATCHING TIME ON THE NIST-4 DATABASE. Methods ASTF (original) ISTF (proposed)
Time (seconds) 2 0.1
characteristic (ROC) curve, which plots the genuine acceptance rate (GAR) against the false acceptance rate (FAR) at different operating points (matching score thresholds). Fig. 2 illustrates the ROC curves of the ISTF and ASTF approaches on the NIST-4 database. As shown by the results, the minutiae-based matching performs better than both ISTF and ASTF matching for fingerprint images with relatively high quality and large size. By integrating the minutiae and STF matching approaches, we can obtain a higher overall accuracy. In addition, the proposed ISTF outperforms the ASTF over a wide range of FAR values. The results indicate that the STF matching performance can be significantly improved by taking into account the nonlinear distortions present in fingerprints. Table I shows the average matching time of the two methods. From the results, we can see that the ISTF method is much more efficient than ASTF and saves 95% of the computational time. Therefore, the ISTF method outperforms the ASTF approach in terms of both accuracy and running time. Fig. 3 shows the experimental results on the FVC2002 database. Better performance is achieved on all the four databases by combining the minutiae and ISTF matching techniques. We have higher matching accuracy on DB1 and DB2 since the fingerprint images are relatively large and of good quality. Due to the smaller image size of the fingerprints in DB3, the ISTF method even outperforms the minutiae matching at some FAR values. It implies that the minutiaebased matching approach may not work well for small-size fingerprints due to the insufficient number of extracted minutiae. Moreover, a low accuracy is obtained from DB4 consisting of synthetic fingerprints with small image size and bad quality. VI. CONCLUSION
V. EXPERIMENTS Experiments are conducted on NIST-4 and FVC2002. NIST-4 is a standard fingerprint database, which contains a set of 2000 fingerprint image pairs (512x512, 500 dpi). Each fingerprint pair has two different rolled impressions of the same finger. FVC2002 is a database for fingerprint verification competition 2002, which consists of four databases: DB1 (388x374, 500dpi), DB2 (296x560, 569dpi), DB3 (300x300, 500dpi), and DB4 (288x384, 500dpi). Each database has a total number of 880 fingerprints. The first three databases are collected by two optical and one solid-state fingerprint sensors, while the fourth database was synthetically generated by using SfinGE software [3]. To evaluate the performance of the interpolation-based Square-Tessellation-Fingercode (ISTF), we first implement the alignment-based Square-Tessellation-Fingercode (ASTF) matching algorithm using the original approach [5]. The overall matching performance is measured by the receiver operating
In this paper, we develop an efficient hybrid fingerprint matching scheme using minutiae and Square-TessellationFingercode. The Fingercode of the query fingerprint is calculated only once. When compared with a template fingerprint, we compute the corresponding Fingercode using interpolation and resampling according to the estimated optimal mapping functions with respect to the minutiae matching results. Experimental results on two large fingerprint databases show that the proposed ISTF approach achieves a better performance by alleviating the nonlinear distortion problem in fingerprints. It also saves approximately 95% matching time. ACKNOWLEDGMENT The work described in this paper was fully supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region. The work was done while all the authors are with the Chinese University of Hong Kong.
(a)
(b)
(c)
(d)
Fig. 2. The ROC curves of (a) Single matching algorithm; Combined matching algorithm using (b) score sum, (c) product rule, and (d) non-parameter estimation, on the NIST-4 database.
(a)
(b)
(c)
(d)
Fig. 3. The ROC curves of hybrid matching algorithm using product rule on (a) DB1, (b) DB2, (c) DB3, and (d) DB4 of the FVC2002 database.
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