A Performance Evaluation of Filter Design and Coding Schemes for Palmprint Recognition Feng Yue, Wangmeng Zuo, Kuanquan Wang Biocomputing Research Center, School of Computer Science and Technology, Harbin Institute of Technology, Harbin, China
[email protected],
[email protected],
[email protected] David Zhang Biocomputing Research Center, The Hong Kong Polytechnic University, Kowloon, Hong Kong
[email protected] Abstract Palmprint recognition, as one of the most promising biometrics, has received considerable recent biometric research interest. Among various palmprint recognition techniques, coding based methods have been very successful since of its simplicity, high precision, small size of feature and rapidness for both feature extraction and matching. Several filters, such as Gabor and Gaussian, and coding schemes, such as competitive and ordinal measure, have been proposed for palmprint verification and identification. In this paper, we evaluate three filters, Gabor, Gaussian, and the second derivative of Gaussian filter, and two coding schemes, competitive code and ordinal measure on PolyU palmprint database. Results of verification experiment show that Gabor filter and competitive coding scheme is superior to other methods.
1. Introduction Automatic biometric authentication systems, which make use of distinctive anatomical and behavioral characteristics, are becoming ever more widely used for access control, surveillance, computer security, and law enforcement. Compared to classical non-biometric methods, it has a number of advantages, such as reliable, efficient, convenient and secure. So far, many biometric features, such as fingerprint, iris, face, and signature have been used for biometric recognition. Recently, a new biometric feature, palmprint, is adopted for biometric recognition and has received considerable recent biometric research interest [1]. Palmprint is the inner surface of palm, which has many
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unique features for recognition, such as principal lines, wrinkles, ridges, minutiae point and texture [2]. Various palmprint recognition techniques based on these features have been introduced [3~6]. Motivated by Daugman's iris code, a number of coding based approaches have also been proposed, including palmcode [2], fusion code [7], competitive code [8] and ordinal measure [9]. The coding-based methods are reported to have high recognition precision, small size of feature and fast speed of feature extraction and matching. The framework of these methods is first using some mask to filter palmprint image and then code the outputs according to some rule. In [8], Kong et al. proposed a competitive scheme to code the outputs of the elliptical Gabor filters with different orientations. In [9], Sun et al presented an ordinal measure to code the outputs of the elliptical Gaussian filters. So far, comprehensive evaluation of the coding based methods, however, has not been carried out to draw a solid comparison between different filters and coding schemes. In this paper, we intend to give a solid comparison between these filters and coding schemes, which can be regarded as a guidance of filter and coding scheme selection for real palmprint recognition system. The following of this paper is organized as follows. In section 2 and section 3, we introduce three filters: Gabor, Gaussian, and second derivative of Gaussian filter, and two coding schemes: the competitive and ordinal measure, which will be compared later. Experimental results are presented in section 4. We conclude this paper in section 5.
2. Filters
(a)
(b)
(c)
Figure 1. Appearance of different filters.(a) Gabor filter, (b) Gaussian filter, (c) Second derivative of Gaussian filter. lines are negative type, only the negative real part of the Gabor, which is defined as
Filter-based techniques are widely used in image processing tasks, such as texture analysis, edge detection and image enhancement. Generally speaking, filter-based methods can be grouped into two major categories, spatial domain filtering and frequency domain filtering. Actually, these two categories of methods are essentially equivalent. In this section, we focus on the spatial domain filtering method, where the most important issue is the design of suitable filter for palmprint representation. So far, a number of filters have been used for palmprint feature extraction, such as Gabor filter and Gaussian filter. We also briefly introduce the second derivative of Gaussian filter since of its wide applications to line detection.
ψ ( x, y , x 0 , y 0 , ω ,θ , κ ) =
ψ ( x, y , x0 , y0 , ω , θ , κ ) =
ω 2π κ
e
⎜ ⎝
−e
−
κ2 2
(1) , y ' = −( x − x0 ) sin θ + ( y − y 0 ) cos θ , ( x0 , y 0 ) is the center of the function; ω is the radial frequency in radians per unit length and θ is the orientation of the Gabor functions in radians. The κ is defined by x' = ( x − x0 ) cos θ + ( y − y 0 ) sin θ
where
⎛ 2 +1⎞ ⎟ δ ⎟ ⎝ 2 −1 ⎠
κ = 2 ln 2 ⎜⎜
δ
, where δ is the half-amplitude
bandwidth of the frequency response. When σ and δ are fixed, ω can be derived from ω = κ / σ . These neurophysiology-based Gabor functions are the same as the general Gabor functions but the choices of parameters are limited by neurophysiological findings and the DC of the functions are removed. Since palm
−
ω2 8κ 2
( 4 x '2 + y '2 )
κ2 ⎛ ⎜ cos(ωx ' ) − e − 2 ⎜ ⎝
⎞ ⎟ ⎟ ⎠
2.2. Gaussian filter 2-D circular Gaussian filter is mostly adopted as an image preprocessing step for image smoothing and denoising, while the 2-D elliptical Gaussian filter can be used for enhancement of lines. The elliptical Gaussian filter is formulated as follows: ⎛ ⎛ x' ⎜ f ( x , y , x 0 , y 0 , δ x , δ y , θ ) = exp ⎜ − ⎜⎜ ⎜ ⎝δx ⎝
Due to its properties of the 2-D spectral specificity of texture as well as its variation with 2-D spatial position, Gabor filter is particularly suitable for texture analysis. Based on the neurophysiological evidence and wavelet theory, Lee reformed the Gabor functions as the following form [10]: ω2 ( 4 x '2 + y '2 ) ⎛ ⎜ e ωx ' 8κ 2
2π κ
e
(2) is needed [8]. The appearance of Gabor filter is shown in Fig. 1(a).
2.1. Gabor filter
−
−ω
2
⎛ y' ⎞ ⎞ ⎟ ⎟ −⎜ ⎟ ⎜δy ⎟ ⎠ ⎝ ⎠
2
⎞ ⎟ ⎟ ⎟ ⎠
(3)
where x ', y ', x0 , y0 , θ are the same as defined in Equ. (1), δ x and δ y are the filter’s horizontal and vertical ⎞ ⎟ ⎟ ⎠
scale, respectively. The shape of the real part of a typical Gaussian filter is given in Fig. 1(b).
2.3. Second derivative of Gaussian filter The second derivative of the Gaussian filter is defined as ⎛ x '2 + y '2 ⎞ ( x '2 −δ 2 )( y ' 2 −δ 2 ) ⎟ (4) f ( x , y , x0 , y 0 , δ , θ ) = exp⎜⎜ − 10 2πδ δ 2 ⎟⎠ ⎝ where x ', y ', x0 , y0 , θ are the same as defined in Equ. (1). Fig. 1(c) is the appearance of second derivative of Gaussian filter. Note its similar appearance to that of Gabor filter.
3. Coding Schemes The coding method was first adopted by Daugman for iris recognition [11]. Kong et al. extended the
(a)
(b)
(c)
Figure 3. Illustration of ordinal coding scheme. (a) bit1, (b)
Figure 2. Illustration of competitive coding scheme.
bit2, (c) bit3.
coding method to palmprint identification and developed palm code and fusion code. Recently, new coding schemes, known as competitive code and ordinal code, were proposed for palmprint identification. Since they were reported to have better performance than others, we compare only these two coding schemes in this paper.
3.1. Competitive Coding Competitive coding scheme aims to encode the dominant orientations of palmprint lines. More concretely, let I ( x, y ) denote the preprocessed image, F ( x, y,θ ) is the filter with orientation θ , the competitive rule is defined as: j = arg max ∫∫ I ( x, y ) F ( x, y,θ ) dxdy (5) θ
where j is the winning index. According to the neurophysiological findings, the simple cells are sensitive to specific orientations with approximate bandwidths of π / 6 , thus, six filters with orientations θ p = pπ / 6 , p = {0,1,...,5} are selected for the competition. The competitive rule is applied to each sample pixel and produces a 3-bit code, as illustrated in Fig. 2.
3.2. Ordinal coding
the same: for each sample pixel, the code length is three bits. However, the ordinal code scheme can perform filter level combination. As a result, the filtering process can be performed on only three orientations, which makes it save half the time for feature extraction compared to competitive coding scheme. Further more, three bits can encode 2 3 = 8 different patterns, as ordinal coding scheme does, but the competitive coding scheme doesn’t fully utilize this capability, using only six patterns for coding.
4. Experimental Results and Discussion We use the performance of palmprint verification to evaluate the three filters and two coding schemes. The metrics we adopted are EER and ROC curve, which are widely used for evaluating the performance of biometric methods. Three filters and two coding schemes can produce six different combinations in total. Each method is performed on preprocessed images to get 384 bytes code. Then the code is matched by bitwise Hamming distance. For the sake of fair comparison, we tested a wide range of parameters and chose the best result as the final result for each method.
4.1. Dataset
Ordinal coding scheme is so called because it only cares the relative magnitude of two orthogonal linelike palmprint image regions. The ordinal coding rule is designed as follows: π
OF (θ ) = ∫∫ I ( x, y ) F ( x, y, θ )dxdy − ∫∫ I ( x, y ) F ( x, y, θ + )dxdy 2
π
= ∫∫ I ( x, y )( F ( x, y,θ ) − F ( x, y,θ + ))dxdy 2
(6) For each sample pixel in preprocessed palmprint image, three ordinal filters, OF (0) , OF (π / 6) , and OF (π / 3) are performed on it to obtain three bits code based on the sign of filtering results. The coding scheme is illustrated in Fig. 3. Note that the code size of both coding schemes is
All the methods are tested on the PolyU Palmprint Database [12] due to its wide use as a benchmark database. It contains 7752 palmprint images of 386 different palms. The images were collected on two separate occasions, roughly 10 images for each palm on each occasion.
4.2. Results and Discussion In verification experiment, each of the palmprint images is matched with all of the other images in the database. A matching is counted as a genuine matching if two palmprint images are from the same palm; otherwise it is an imposter matching. Thus there are totally 74,068 genuine and 29,968,808 imposter
Table 1. Minimum EER of all methods (%). Gabor 0.2138 0.2226
Gaussian 0.224 0.2277
SdGaussian 0.2169 0.2254
matchings. For all the parameters tested, the minimum EER of all methods are listed in table 1. It is obvious that the performance of Gaussian filter is the worst of all three filters. The EER values obtained by Gabor filter and second derivative of Gaussian filter are comparable and the former is slightly better. Competitive coding scheme can get a smaller EER for all the three filters, which means it is superior to ordinal coding scheme. To sum up, the best result is produced by the combination of Gabor filter with competitive coding scheme. Fig. 4 depicts the ROC curves of all the methods. Obviously the Gaussian filter with ordinal coding scheme is the worst of all. Gaussian filter with competitive coding scheme is a little better, but still worse than other methods. Gabor filter with both coding schemes and second derivative of Gaussian filter with competitive coding scheme are comparable and among the best methods of all. Note that these results are in accordance with those of EER. The probable reason for the superiority of competitive coding scheme is that it cares only the dominant orientation of palm lines. Since most palm lines have only one dominant orientation, the response of rest less dominant orientations and their relationship are not stable and prone to be disordered by noise. Thus competitive coding scheme is more robust than ordinal coding scheme when performing genuine matching, and achieves better performance accordingly.
5. Conclusion We have conducted the verification experiment on PolyU Database to evaluate three filters and two coding schemes used in palmprint recognition. The results indicate that: (1) competitive coding scheme is better than ordinal coding scheme. (2) Gabor filter is the most robust which can achieve best performance with both coding schemes. (3) Gabor filter with competitive coding schemes can achieve best performance among all the combinations.
Acknowledgement The work is partially supported by the CERG fund from the HKSAR Government, the central fund from Hong Kong Polytechnic University, and the NSFC/863 funds under Contract No. 60620160097 and 2006AA01Z193 in China.
0.998 Genuine acceptance rate(%)
Competitive Ordinal
1 0.999
0.997 0.996 0.995 0.994
Gabor+Competitive Gaussian+Competitive SdGaussian+Competitive Gabor+Ordinal Gaussian+Ordinal SdGaussian+Ordinal
0.993 0.992 0.991 0.99 -4 10
-3
10
-2
-1
0
10 10 10 False acceptance rate(%)
1
10
2
10
Figure 4. The ROC curves of all combinations.
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