Fingerprint Matching With Rotation-Descriptor Texture Features1 Zhengyu Ouyang, Jianjiang Feng, Fei Su, Anni Cai Beijing University of Posts and Telecommunications [email protected] Abstract A novel texture correlation matching method for fingerprint verification using Fourier-Mellin Descriptor and Phase-Only Correlation function is proposed in this paper. Fourier-Mellin Descriptor Correlation is used to align the template and query fingerprint images and a matching score is obtained. Matching takes about 1 second in Celeron 2.0 GHz processor, and the experimental results show that EER is 3.8%; fusion with minutia matching gets a better result.

1. Introduction Fingerprint is a pattern of flow-like ridges and valleys on the surface of a finger. The proven uniqueness and stability of the fingerprint make it widely used in recognition of a person’s identity. Although automatic fingerprint recognition is the first application of the biometric recognition, problems still exist in practice. Current fingerprint recognition techniques can be mainly classified as minutiae-based, ridge feature-based and correlation-based [1]. Most automatic fingerprint identification systems employ techniques based on minutiae points which are the local discontinuities and represent endings and bifurcations in the flow pattern. The minutiae-based methods require accurate detection of the minutiae from a fingerprint image [2]. Actually in practice, because of poor quality of images such as images of dry, cut, bruise and dirty fingers, improper minutiae may be obtained which would lead to false alignment and matching. Furthermore, if the overlapped region between the template and the query fingerprints is small, a high rate of false rejection may result. Ridge feature-based methods use more information of fingerprint, such as local texture information[3,4,5], than minutiae-based ones. Researchers, Anil K. Jain [3,5] and Chih-Jen Lee [4], utilize Gabor filterbanks to extract local texture features from fingerprints for

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matching. One of the critical problems in this approach is the alignment. Jain [3] first proposes to use core point to align two fingerprints. Then he [5] proposes a rectangular tessellation on two fingerprint images which are aligned by minutiae first. These methods depend heavily on the reliable minutiae and core points detecting and matching. Consequently, it will meet all the difficulties in minutiae-based approaches described above. The correlation-based techniques make two fingerprint images superimposed, and do correlation (at the intensity level) between the corresponding pixels for different alignments [6,7]. These techniques are highly sensitive to non-linear distortion, skin condition, different finger pressure and alignment. And most of these techniques use minutiae for alignment first. In order to obviate the need to use minutiae or core information to align image pair, Ross [8] supports a new scheme which utilized the extracted feature sets themselves to align and match fingerprint images. However, it just deals with the displacement without consideration of the rotation. In this paper, a novel scheme is proposed, local Fourier-Mellin Descriptor (FMD) and Phase-Only Correlation (POC)[9,10] are employed together for partial fingerprint verification. After the local FMDs and FMD Maps are calculated for template and query fingerprints, the aim is to find the most likely FMD pair from two fingerprints. According to the pair, the two fingerprints can be aligned, and the other corresponding FMD pairs are then checked if they are matched or not. POC is used during the calculations of the similarity of two FMDs and the alignment parameters. Our method obviates the use of minutiae and core information, and takes the rotation alignment into account. The rest of the paper is organized by introducing POC in section 2, FMD feature map in section 3, fingerprint matching based on FMD in section 4, and experiment and conclusion in section 5 and section 6, respectively.

This work is supported by National Natural Science Foundation of China under grant 60472069

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2. Phase-Only Correlation Consider two images s(x, y) and r(x’, y’), with the same size. The two-dimensional Discrete Fourier Transforms (2D DFT) for two images are defined by: S(u, v)= F {s(x, y)} and R(u, v)= F {r(x, y)}. Different from the traditional correlation which based on energy, the POC function is defined as follow [9,10]: ∗ h( x, y ) = F -1 { S (u, v) ⋅ R (u, v) } (1) S (u, v) ⋅ R* (u, v)

where R ∗ (u , v) denotes the complex conjugate of R(u , v) , and F -1 the two-dimensional Inverse Discrete Fourier Transform (2D IDFT). The above equation implies that the POC function will return a delta function if the two images are really the same except for a translational offset. The remarkable properties of the POC function which are shown in Fig.1, are shift and brightness invariant, highly robust against noise and with a normalized similarity degree [11]. Fig.1, (a) is a part of (b), (c) and (d) are the POC and energy-based correlation, respectively.

(a)

(b)

(c)

(d)

Figure 1. Comparison between POC and traditional correlation (a) is a part of (b), (c) is the result of POC between (a) and (b), (d) is the result of traditional correlation

3. FMD Feature Maps

(a)

(b)

(c)

Figure 2. Reconstructed image

To overcome the drawbacks of correlation-based approaches, we suggest solutions as follows: --One is for non-linear warping. Local correlations do better than the global one [7]. --Another is for variations in widths of the ridges. To circumvent this problem, in this paper, instead of original fingerprint image, the fingerprint image for future processing is reconstructed from binary skeleton of the original one [2], which will be called the reconstructed image for sententiousness. An example is given in Fig. 2. -- The third problem is the rotation when do correlation. To dodge this difficulty, we propose to perform POC on local FMD which does well for rotation alignment, and will be introduced latter.

3.1. Local FMD Local Polar Sample (LPS) is first extracted from a reconstructed fingerprint block (RFB) with a size of W hW, e.g. Fig.3.(a): (2) LPS ( ρ , θ ) = RFB ( x ρ ,θ , y ρ ,θ )

(a) Original image (b) Skeleton image (c) Reconstructed image

Considering not over-sampling the Cartesian image in the fovea and not under-sampling in the periphery, just the periphery of the RFB is sampled with equal number of samples on each ring to keep the LPS as a rectangle matrix. The LPS (Fig.3(b)) is in polar coordinates with the size of N ρ × N θ . The Local FMD of the block is then defined (Fig.3. (c)):

FMD(wρ , wθ ) =

F (wρ , wθ )

where F ( wρ , wθ ) is the 2D DFT of LPS. It should be point out that just one-dimensional window is applied on LPS along the polar axis before Fourier Transform, because the Circular Correlation of the LPSs will be performed, which will be described in Section 4.

(b)

(a)

(c)

where x ρ ,θ = (ρ0 + ρ ) ⋅ cos(2θπ / Nθ ) , yρ,θ = (ρ0 + ρ) ⋅

Figure 3. The Process of Local FMD

sin( 2θπ / Nθ ), ρ ∈ [0, N ρ − 1] , θ ∈ [0, N θ − 1] . ρ 0 is the radius of the round which is not for sample.

(a)The polar-sample on fingerprint image block (b) LPS of (a) (c) FMD of (a)

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(3)

F (wρ , wθ )

3.2. FMD Map for Template Fingerprint Because the center of relative rotation between two compared fingerprint is unknown. We assume that it is located at somewhere on a grid with intervals of N pixels. Therefore, the template reconstructed fingerprint image is tessellated as overlapped square blocks with a size of W×W pixels, centered at locations with interval of N pixels in both the horizontal and vertical directions. Within each square block elastic distortions are assumed negligible. The LPSs and local FMDs are extracted from blocks which belong to the foreground region by Equation (2) and (3) respectively. Let FMDx,y indicates the local FMD of an block whose center locates at (x,y) on the reconstructed image. The FMD Map, FMDT = {FMDx,y}, is formed. And the length of each FMDx,y is fixed to ( N ρ × N θ ).

4. Fingerprint Matching Using FMD Map Before matching process, FMDT is extracted from the template reconstructed fingerprint image, T. When a query reconstructed fingerprint image, Q, is input to the system, the matching process begins with Q and FMDT.

4.1. Local FMD Matching For FMDxQ, y of one block, local FMD matching is performed with one FMDxT, y in FMDT by using Equation (1): (4) POC ( ρ ,θ ) = F -1 ( FMDxT, y g FMDxQ,∗y ) For two image blocks from the same position of a finger, the above operation will return a peak value Vp and the peak position in θ coordinate θ p , which denote the similarity and rotation angle between Q and T, respectively.

4.2. Fingerprint Matching using FMD Map The main matching steps are as follows: 1) The Q is cropped into non-overlapped blocks with size of W×W. Then FMDxQ, y of each block is calculated, and the FMDQ is constructed. 2) One FMDxQ, y is chosen from FMDQ and is PhaseOnly Correlated with all elements from FMDT by using Equation (4). If the highest Vp is larger than a threshold, the local matching score (i.e. Vp) and one set of alignment parameters are recorded, and go to step 3; otherwise go back to the beginning of this

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step. If every FMDxQ, y has been chosen out, go to step 4. 3) According to the obtained alignment parameters, the corresponding position (x0’,y0’) of each Q T FMDxQ, y from FMD can be found in FMD . The FMDxQ, y , whose corresponding position in FMDT is on its background, will not be taken into account. Then each FMDxQ, y is phase-only correlated with FMD Tx ', y ' s in the neighborhood (x0’,y0’) in FMDT. Consequently, some local matching scores of FMDx,Q y s and sets of alignment parameters can be obtained. A global matching score which is the average of the local ones can be recorded. The global set of alignment parameters is obtained from the local ones by the minimal mean squared error estimation. Then go to step 2. 4) The largest global matching score is output, and also the corresponding alignment parameters. Based on this score and a pre-specified threshold, the matching is declared successfully or unsuccessfully. In the correlation matching stage, not only the matching score, but also the optimal alignment parameters (including the rotation) are obtained. The obtained alignment parameter can be used in other types of matching methods, such as minutiae-based one, to further improve the matching performance through fusion with the correlation method.

5. Experiment Results The dataset used is FVC2002 DB1. All matching performance indicators shown in this section have been estimated using the experimental protocol proposed in [12]. In order to make a balance among accurate rate, speed and memory, we also explore the performance of proposed method under different resolution. We resize the reconstructive image (388 h 374) to (291 h 280), (232 h 224) and (194 h 187), respectively. Here the Window size for polar-samples is 33 h 33, ρ0 = 8, N ρ = 5 , N θ = 36 . The sampling interval of the image blocks in Cartesian coordinates for template fingerprint is 4 pixels, but for query fingerprint is 33 pixels (non-overlap), in both the horizontal and vertical directions. The results are shown in Table 1. The extraction time means the average time cost for template FMD map construction for one image. And matching time denotes the average time cost for matching between template FMD map and query FMD

Table 1. Performances for different resolution Image Size Original 291h280 232h224 194h187

Time for Extraction (ms) 445 208 143 91

Memory(KB) 2 782 1 472 899 575

Time for Matching (ms) 4 147 1 099 393 181

EER 3.2% 3.8% 6.4% 11.6%

map. Three experiment results are shown in Fig.4. The first one is the result of (291 h 280) reconstructive images based on FMD only. The second one is performed with minutiae matching after alignment according to the result of FMD matching. The third one is to fuse these two results, using the average scores. From the ROC curves, it can be seen that the fusion of the two matchers results in an improved performance.

Fig. 4. Example for FMI matching result pairs

[7]

6. Conclusion A novel technique to align and match two fingerprint images is proposed in this paper. It utilizes FMD to construct a feature map which is used to represent, align and match fingerprints with POC function. Proposed approach doesn’t use any minutiae information for alignment, and it takes rotation into account. Currently we are investigating the methods to select effective and low dimensional features from obtained FMD feature vector to improve the whole performance.

7. References [1] David Maltoni, Dario Maio, Anil K. Jain, Salil Prabhakar. Handbook of Fingerprint Recognition. Springer, New York, 2003 [2] A. K. Jain, L. Hong, R. Bolle. “On-line Fingerprint Verification”. IEEE Transactions On Pattern Analysis and Machine Intelligence, Vol. 19, No. 4, pp. 302-314, 1997 [3] A. K. Jain, S. Prabhakar, L. Hong, S. Pankanti. “Filterbank-Based Fingerprint Matching”. IEEE Transactions On Image Processing, Vol. 9, No. 5, pp. 846-859, 2000 [4] C. J. Lee, S. D. Wang, K. P. Wu. “Fingerprint Recognition Using Principal Gabor Basis Function”. Proc. Of 2001 International Symposium on Intelligent Multimedia, Video and Speech Processing, pp. 393-396, Hong Kong, 2001 [5] Anil Jain, Arm Ross, Salil Prabhakar. “Fingerprint matching using minutiae and texture features”. Image Processing, 2001 International Conference on, Volume 3, Page(s):282 - 285 vol.3, 2001 [6] Ravichandran G., Casasent D., “Advanced in-plane rotation-invariant correlation filters”, Pattern Analysis

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