Multiscale Competitive Code for Efficient Palmprint Recognition Wangmeng Zuo1, Feng Yue1, Kuanquan Wang1, David Zhang2 1 School of Computer Science, Harbin Institute of Technology 2 Department of Computing, Hong Kong Polytechnic University
[email protected] Abstract Coding-based method, which encodes the responses of a bank of filters into bitwise features, has been very successful in palmprint representation and matching. Palmprints, however, are typically multiscale features, where the palm lines can be represented at a higher scale while the wrinkles at a lower scale. In this work, we present a mutliscale competitive code method for efficient palmprint representation and matching. In filterbank design, we adopt the log-Gabor wavelets since of its less overlapping in the frequency domain. In palmprint representation, competitive code is used to encoding the dominant orientation of the filter responses in each scale. In palmprint matching, a fusion rule is proposed to combine the distances obtained using different scales. Experimental results indicate that the proposed method achieves better recognition accuracy and faster matching speed while compared with several state-of-the-art methods.
1. Introduction With the increasing demand of biometric solutions to security systems, palmprint recognition, a relatively novel but efficient biometric technology, has received considerable recent interest [1]. Palmprint, the inner surface of the palm, carries several kinds of distinctive features, principal lines, wrinkles, and patterns of ridges and valleys, for personal recognition. By far, a number of holistic, local feature-based, and hybrid approaches have been proposed for palmprint feature extraction and matching [2, 3, 4]. Coding-based method, which encodes the response of a bank of filters, has been very successful in palmprint representation and matching. Using 2D Gabor filter to convolve with the palmprint image, the PalmCode method encodes the phase of the filter responses as bitwise features [1]. Subsequently Kong et al. introduce a FusionCode method to encode the phase of the filter responses from a bank of Gabor filters with
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different orientations [5]. Recent research on palmprint recognition indicates that the orientation information of palm lines is one of the most promising features. Kong et al. proposed a competitive code method, where a bank of Gabor filters are utilized to extracted the orientation information, and competitive coding is used to generate a bitwise feature representation [2]. Most recently, other filters, such as elliptical Gaussian and Radon, and other coding scheme, such as ordinal measure and integer coding, have also been investigated [6, 7]. Palm lines generally are considered as typical multiscale features, where the principal lines could be analyzed at a lower resolution, and the wrinkles should be extracted at a higher resolution. Current codingbased methods, however, encode the responses of filters at only one specific scale, and neglect the multiscale characteristic of palm lines. At a specific scale, although we can get a compact and effective code, the performance of coding-based method would deteriorate when applied to matching poor quality palmprint images. Because of the influence of lighting and aging, some wrinkles in the palmprint image would appear or disappear, while principal lines are robust. To alleviate this problem, it would be better to encode the palmprint features using two or more scales. This is the first reason for us to investigate the multiscale orientation representation of palmprint images. Another potential advantage of multiscale orientation representation is the lower computational complexity in the matching stage. Most coding-based methods, however, would require much time to search a palmprint image from a large database. With the mutiscale representation, a hierarchical matching scheme can be used to facilitate the matching speed for efficient and effective palmprint identification. In this paper, we presented a multiscale competitive code method for matching of palmprint images. The remainder of this paper is organized as follows: In Section 2, we introduce the multiscale comptitive coding scheme to encode the responses of multiscale Log Gabor filters. In Section 3, we first present a
hierarchical matching scheme to facilitate the matching speed, and then propose a probabilistic score-level fusion rule to combine the matching results obtained at different scales. Section 4 presents the experimental results and Section 5 gives our conclusions.
2. Multiscale Coding
Palmprint
Orientation
⎧1, j ≤ W ( x, y ) < j + nθ / 2 C ( x, y, j ) = ⎨ , j = 1,", nθ / 2 ⎩ 0, elsewise
(3)
to compactly encode each winning index into nθ/2 bits for efficient matching of palmprint features. To further facilitate the matching speed, a downsampling procedure is used to sample a much smaller number of (e.g., 32×32) points for competitive coding. log2ωy
2.1. 2D Log-Gabor Filtering 2D log-Gabor filters are used for multiscale representation of palmprint image. When implemented in multiresolution, classical Gabor filters, however, yield a non-uniform coverage of the frequency domain [8]. Thus in this section we propose to use log-Gabor filter to obtain a multiscale palmprint representation. Log Gabor filters are defined in the log-polar coordinates of the Fourier transform domain as Gaussians shifted from the origin, G ( ρ ,θ , ρ 0 ,θ0 )
⎧ 1⎛ρ −ρ ⎞ ⎪ 0 = exp ⎨ − ⎜ ⎜ ⎟⎟ ⎪⎩ 2 ⎝ σ ρ ⎠
2
⎫ ⎪ ⎪⎧ 1 ⎛ θ − θ 0 ⎞ ⎬ exp ⎨ − ⎜ ⎟ ⎪⎭ ⎪⎩ 2 ⎝ σ θ ⎠
2
⎪⎫ ⎬ ⎪⎭
(1)
where (ρ, θ) are the log-polar coordinates, (ρ0, θ0) are the coordinates of the centre of the filter, and (σρ, σθ) denote the std. of the Gaussian along ρ and θ axes. After defining the log-Gabor filter in the frequency domain, Fourier transform can be used to transform the filter to the spatial domain. Like classical Gabor filter, log Gabor filters also have a real part and an imaginary part. Because palm lines are the most promising feature for low resolution palmprint images, we only use the real part of the log Gabor filters.
2.2. Competitive Code The competitive coding scheme is used to derive a compact and effective representation of the orientation field of palmprint. Competitive code, proposed by Kong, first estimates the orientation field of a pixel as the orientation with the maximum (sometimes, minimum) filtering responses [2]. Given a bank of log Gabor filters with different orientations, G ( ρ ,θ , ρ 0 ,θi ) , θ i = iπ / nθ , i = {0, 1, ..., nθ − 1} , let I(x, y) denote the original image and Hi(x, y) denote the convolved image using filter G ( ρ ,θ , ρ 0 ,θi ) , the competitive rule is defined as W ( x, y ) = arg min H i ( x, y ) , (2) i
where W(x, y) is the winning index of the pixel (x, y). If the number of the orientations nθ is even, a coding rule is defined as
log2ωy
Fig. 1 Schematic contours of the log-Gabor filters in the Fourier domain
2.3. Multiscale Orientation Representation In this subsection, we present a multiscale orientation representation scheme. Let I(x, y) be an original palmprint image, and Gs,θ(u, v) be the log Gabor filter with orientation θ and scale s in the frequency domain, the convolved results of image I(x, y) with orientation θ and scale s is H s ,θ ( x, y ) = real{F −1 (Gs ,θ ⋅ F ( I ( x, y )))} , (4) where F and F −1 are the Fourier and inverse Fourier transform, respectively, and the number of orientations is six, if s is even ⎧ iπ / nθ , , + i / n / 2 n , if s is odd π π ⎩ θ θ
θi = ⎨
(5)
where θi is the value of the orientation with i = {0, 1, ..., nθ − 1} , and s is the number of the scales with s=1, 2, …, ns. For each scale, we encode the winning index into its bitwise representation using the rule defined in Eq. (3). In this way, we obtain a multiscale orientation code of the original image. Compared with classical multisolution Gabor representation, the proposed method has a number of advantages. First, we use log Gabor filters rather than Gabor filters, which could cover the mid frequencies with sufficiently uniformity when implemented in multiresolution. Second, we consider the relation between the orientations and scales. Fig. 1 shows the schematic contours of the proposed multiscale filters in the frequency domain. By laying the centers of the logGabor filters on a uniform hexagonal lattice, the scheme used in this section could achieve a more uniform coverage of the mid-frequency domain. Finally,
we use the principal orientation information rather than the magnitude information, and thus the proposed multiscale representation method is robust to variation in illumination. A simple downsampling method is applied to save computational and memory requirements. At the first scale, the filtering responses are downsampled by a factor of 4. Subsequently, the filtering responses at the second, third and more larger scales are downsampled by a factor of 8, 16, etc.
3. Hierarchical Matching Scheme of Palmprint Images 3.1. Matching of Competitive Codes We use the angular distance proposed in [3] to measure the dissimilarity between competitive codes. To reduce the adverse effect of image translation, in palmprint matching, we translate the query competitive code in the horizontal and vertical directions within a specific range, and the minimum distance is adopted as the final matching score.
Similarly, if the combined angular distance Dn −1 is not s
larger than a specific threshold Tn −1 , we will further s
calculate the combined distance at the lower scale Ds = f (d n , d n −1 ,", d s ) , s
(8)
s
until ds < Ts or s = 1. In [10], You et al. proposed a hierarchical matching scheme. Compared with You’s method, the proposed scheme has two distinct characteristics. First, all the features hierarchical matching scheme used in the proposed scheme are orientation features, which is robust to variations in illumination. Second, at one scale, we use the combined angular distance to combine the distance at this scale and the higher scales. Since classifier combination has been shown to be an effective method to improve recognition performance [10], it is expected the proposed scheme could simultaneously improve the matching speed and recognition accuracy of competitive code.
3.3. Fusion of Multiscale Matching Results To combine the angular distances at different scales, we first use using Gaussians to estimate the probabilistic densities of the genuine and imposter matching scores at each scale. The reason to use Gaussian distribution is its simplicity and that the imposter distribution can be approximated using Gaussian distribution [6]. At each scale, given a set of genuine matching results M g = {d ig, s | i = 1,2,", N g } , it is simple to estimate the mean msg and standard deviation σ sg of Gaussians. Similarly, we estimate the mean msi
and standard deviation σ si of the imposter distribution. Given a set of matching distances {d j , d j +1 ,", d n } ,
Fig. 2 The hierarchical matching scheme
s
the joint imposter distribution is approximated by
3.2. Hierarchical Matching
ns
p i ( d j , d j +1 ,", d ns ) = ∏
To facilitate the fast indexing from a large scale palmprint database, we propose a hierarchical matching scheme, as shown in Fig. 2. Using the hierarchical matching scheme, we first match two palmprint images at the largest scale ns (which is faster). If the angular distance d n is larger than a specific distance Tn , we s
s
treat this matching as an imposter matching, and will not match them at any other scales. If the angular distance d n is equal or smaller than Tn , we will s
s
calculate the angular distance at the (ns-1)th scale d n′ −1 , s
and use a fusion rule to combine d n and d n −1 to s
s
produce the combined distance at the (ns-1)th scale Dn −1 = f (d n , d n −1 ) . s
s
s
(7)
j
1 2π σ ij
exp{
( x − mij ) 2 2σ ij 2
},
(9)
and the joint genuine distribution is approximated by ns
p g (d j , d j +1 ,", d ns ) = ∏ j
1 2π σ
g j
exp{
( x − m gj ) 2 2σ gj 2
}.
(10)
According to p i ( d j , d j +1 ,", d n ) and p g (d j , d j +1 ,", d n ) , s
s
the combined angular distance is defined as Dj =
ns ⎛ ⎛ ( x − mij ) 2 ( x − m gj ) 2 1 ⎜ w Sj ⎜ − wg ∑ i2 ⎜ ⎜ ns − s + 1 j = s σj σ gj 2 ⎝ ⎝
⎞⎞ ⎟⎟ , ⎟⎟ ⎠⎠
(11)
where weight wSj is associated with the scale. Compared with the imposter distribution, the genuine distribution usually is not stable and more deflective from Gaussian. Thus we introduce the weight 0 ≤ wg < 1 to alleviate the influence of the inaccurate estimation.
4. Experimental Results and Discussions In this section, we use the PolyU palmprint database (version 2) to evaluate the performance of MCC method. PolyU palmprint database consists of 7,752 images captured from 193 individuals, 386 palms. The samples of each individual were collected in two sessions, where the average interval between the first and the second sessions is around two months. In our experiments, sub-image of each original palmprint image was cropped to the size of 128 × 128. In our experiments, we let the number of scales be two. We first evaluate the verification performance of MCC. Fig. 3 shows the ROC curves of MCC, and competitive code at the first and the second scales. The verification performance of MCC is consistently superior to that of competitive code at each scale.
multiscale features, multiscale competitive code is more effective for palmprint representation and matching. Using a score level fusing method, a hierarchical matching scheme is proposed to facilitate the matching speed for efficient and effective palmprint recognition. Experimental results show that, while compared with several state-of-the-art methods, the proposed method achieves better recognition accuracy and faster matching speed.
Acknowledgements The work is partially supported by the CERG fund from the HKSAR Government, the central fund from Hong Kong Polytechnic University, the NSFC fund under Contract No. 60620160097, and the 863 fund under Contract No. 2006AA01Z193, 2006AA01Z308, and 2007AA01Z195.
References
Fig. 3 the ROC curves of MCC Table 1 Execution time and EER of multiscale competitive code, ordinal measure, and RLOC Method Feature Extraction Matching MCC 146ms 0.03ms Ordinal Measure [7,14] 63ms 0.05ms RLOC [8] 70ms 3.9ms
EER (%) 0.024% 0.05% 0.16%
We further compare the verification performance of MCC with the results reported using ordinal measure [6, 11] and RLOC [7], as shown in Table 1. The EER of multiscale competitive code is 0.024%, which is much lower than those obtained using ordinal measure (0.05%) and RLOC (0.16%). Table 1 also compares the feature extraction and matching speed of different methods. Compared with the other two methods, MCC has a faster matching speed. When applied to large scale palmprint indexing, matching speed would be the dominant step to determine the retrieval time, and thus MCC would be more promising in these cases.
5. Conclusion In this paper, we propose a multiscale competitive code method and a hierarchical matching scheme for palmprint recognition. Since palm lines are typically
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