Robust Direction Estimation of Gradient Vector Field for Iris Recognition
Robust Direction Estimation of Gradient Vector Field for Iris Recognition Zhenan Sun, Yunhong Wang, Tieniu Tan, Jiali Cui Center for Biometrics Authentication and Testing National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, P.O. Box 2728, Beijing, 100080, P.R. China {znsun, wangyh, tnt, jlcui}@nlpr.ia.ac.cn Abstract As a reliable personal identification method, iris recognition has been receiving increasing attention. Based on the theory of robust statistics, a novel geometry-driven method for iris recognition is presented in this paper. An iris image is considered as a 3D surface of piecewise smooth patches. The direction of the 2D vector, which is the planar projection of the normal vector of image surface, is illumination insensitive and opposite to the direction of gradient vector. So the directional information of iris image’s gradient vector field (GVF) is used to represent iris pattern. Robust direction estimation, direction diffusion followed by vector directional filtering, is performed on the GVF to extract stable iris feature. Extensive experimental results demonstrate that the recognition performance of the proposed algorithm is comparable with the best method in the open literature.
representation of one dimensional wavelet transform was used by Boles et al. [6] for iris recognition. Iris images naturally provide rich texture information, so statistical texture analysis methods are also helpful for iris pattern representation [7,8,9]. Based on the wavelet frame decomposition, Noh et al. [10] derived two types of features for iris matching. In [11], Tan et al. described an algorithm for iris recognition by characterizing key local variations. Using Gaussian-Hermite moments, Tan et al. [12] represented the shape of one-dimensional intensity signals as iris features.
(a)
(b)
1. Introduction (c)
The increasing demands of reliable personal identification for applications such as assess control have resulted in an unprecedented interest in biometrics. Biometrics makes use of the physiological or behavioral characteristics of people such as fingerprint, iris, face, palmprint, gait, voice, etc. to identify a person [1]. The biometrics’ advantages over traditional human verification methods are straightforward: universality, uniqueness and convenience. After testing seven popular biometric systems, it was reported in [2] that iris recognition is the most reliable for human authentication. A typical iris recognition system includes localization, normalization, feature extraction and matching (Fig. 1 illustrates the preprocessing step). Regarding the iris image as the modulation result based on multi-scale Gabor wavelets, Daugman encoded the phase information as iris features and the matching is based on a test of statistical independence [3,4]. After area-based image registration, Wildes et al. [5] employed the normalized correlation results at four different resolutions as the matching metric. The zero-crossings
Figure 1. Preprocessing of iris image; (a)Original image; (b)Result of iris localization; (c)Normalized iris image. For iris recognition algorithms, it is crucial to design an efficient scheme to extract each class’ inherent features, which should be robust to all sources of noises and discover meaningful information about the image data. In order to achieve this goal, a geometry-driven iris recognition algorithm is proposed in this paper. Based on the theory of robust statistics, local dominant direction of gradient vector field is encoded as iris feature. Details of this approach are described in Section 2. In Section 3, the experimental results are reported prior to conclusions in Section 4.
2. Robust orientation estimation of local image surface 2.1. Motivation The central issue in iris recognition is iris pattern
0-7695-2128-2/04 $20.00 (C) 2004 IEEE
representation. No matter the phase value [3,4], representation of zero-crossings [6] or texture signature [7,8,9], iris features must indicate meaningful information of iris image structure. In order to precisely capture the fine spatial changes of the iris, the distinguishing characteristics of iris used for recognition are usually local and minute. But the measurements from minutiae are easily affected by noises, such as occlusions by eyelids and eyelashes, localization error and deformation during normalization, etc., which greatly limits the system’s accuracy. So a robust statistical procedure [13] is helpful to strengthen the robustness of the feature extraction algorithm. Then the idea of iris pattern representation can be formulated in a model to guide the robust estimation process. Furthermore, the estimated local feature is coarsely encoded to iris code not only facilitating matching and storage but also strengthening the robustness of iris feature. In conclusion, the idea of local robust encoding strategy, a general solution for iris recognition, is illustrated in Figure 2.
Robust estimation
JJK
N p , whose direction is independent of illumination and contrast and indicates the inherent characteristics of the
JJK
iris. Another benefit of N p is that it is opposite to the
JJK
direction of gradient vector G p (Fig.3) as shown in the following: Suppose point P ( x 0, y 0, I 0 ) is on the planar surface
F ( x, y, I ) . The unit normal vector of the surface is JJK
denoted by N ( n x , n y , n I ) (suppose n I ≠ 0 ). Its projection
JJK
T
onto the x − y plane is N p = ( n x ,n y ) , then the plane F ( x, y, I ) can be represented as
nx ( x − x0 ) + n y ( y − y0 ) + nI ( I − I 0 ) = 0
Model Original data in local window
where gradient vector field G can be defined. The vertical JK component of the surface’s normal vector N reflects the absolute measure of local intensity contrast and determines the modulus of the gradient vector. The JJK projection of N onto the x − y plane is denoted by
Local feature
Coarse quantization
Iris code
Figure 2. Block diagram of local robust encoding
2.2. Geometry of iris image structure Local image structure plays an important role in iris recognition, so an intuitive idea of iris pattern representation is based on the geometric structure of image data in a small region. By considering the gray-level normalized iris image in a 3D Cartesian coordinate system (Fig.3), each image pixel can be denoted by a point (x,y,I), where x and y are the coordinates in the image plane, and I denotes grey level intensity. So the objective of iris analysis is to infer stable signatures reflecting the inherent structure of the image surface. If the image surface is piecewise smooth, then the orientation of local image surface should be a good choice of iris feature because it indicates the spatial details of iris image and is stable. In fact, representing the image data by piecewise planar surface is not new in the literature. Besl et al. [14] provided a general architecture for local surface fitting using robust window operators that preserves gray level and gradient discontinuities in digital images. In his framework, a robust regression procedure was implemented via the M-estimator [14]. You et al. [15] exploited a class of fourth-order PDEs to evolve the original image to piecewise planar image. But the computational costs of these methods are too high to satisfy the real time requirement of iris recognition. Thus a more efficient technique must be studied. Figure 3 illustrates a patch of the image surface. The image can also be modeled as a quantitative field I(x,y)
i.e. the image intensity I on this plane is ny n I ( x, y ) = − x ( x − x0 ) − ( y − y0 ) + I 0 nI nI JJ K ∂I ∂I 1 JJJK ∂I n x ∂I n y =− , So =− , G p = ( , ) = − N p . ∂x ∂y nI ∂x n I ∂y n I
JJK
(1)
(2) (3)
JJK
Therefore G p is opposite to N p . I I0
I'
JJK N
F ( x, y, I )
y'
JJJK Np
x'
x
x0
y0
JJJK Gp
y
JJJK Np
Figure 3. A patch of iris image surface approximated by planar surface At last the problem of iris feature extraction is turned to direction estimation of image gradient vector, i.e. the model in local robust encoding diagram (Fig.2) is constructed. Because original directional data is noise prone, it is necessary to implement direction diffusion to obtain a coarse representation of GVF. And the piecewise smooth image surface results in the similar direction of GVF in local region, so the assumption of piecewise planar image is more reasonable after direction diffusion.
2.3. Robust direction estimation As another module of local robust encoding scheme, a novel method for robust estimation of the dominant
0-7695-2128-2/04 $20.00 (C) 2004 IEEE
direction of gradient vector in local region is proposed, named as Robust Direction Estimation (RDE). RDE includes two parts: direction diffusion followed by direction filtering. The aim of direction diffusion is to enhance the main direction in a patch and to suppress noises. Many published algorithms about direction or orientation diffusion can serve for this idea [16,17]. But the numerical implementation of these methods all involves many iterations, and what we care is not the process of diffusion or detail preserving, but the result of diffusion. So a simplification of their ideas is described as follows: 1) Gradient vector field computation. Sobel operator is utilized to generate the two components of image gradient vector, G x and G y . 2) Isotropic derivatives diffusion. Gaussian filter is the only kernel qualified for linear scale space generation. So the coarse representation of G x or G y is the result of convolution with a Gaussian window: G 'x =G x∗g δ , G 'y =G y∗g δ
(4)
where g δ is a Gaussian filter with scale δ .
3) The phase angle A of the complex G 'x +i G 'y is the diffusion result. After direction diffusion, the enhanced gradient vector angle A across image plane can be regarded as a vector valued image. In the next step the iris feature—local dominant direction, should be robustly estimated from each region of A . Vector directional filters, a class of multi-channel image processing filters, are employed to select a typical one from the input angles in each window [18]. Following ideas from basic vector directional filter [18], directional filter (DF) is defined as follows: Definition: The output of the DF, for input { Ai , i = 1, 2, " , n }, is ADF = DF { Ai , i = 1, 2, " , n} , such that ADF ∈ { Ai , i = 1, 2, " , n} and
where
n
n
i =1
i =1
∑ Dis ( ADF , Ai )≤ ∑ Dis ( A j , Ai ), ∀ j =1,2,",n Dis ( Ai , A j )
(5)
(6)
denotes the minimum angular
difference between the angles Ai and A j . It had been proved that the angle ADF is the least error estimate of the angle location [18]. After coarse quantization, a more compact representation is obtained and the robustness of the whole statistical procedure is further strengthened. It should be pointed out the selection of quantization level is a tradeoff between the robustness, discriminability and other factors such as storage cost, computational costs. In this case, the angle scale of ADF , from −π to π , is quantized into six discrete values. The effect of robust direction encoding is illustrated in Fig. 4 which shows the
output of the method when regarding Fig. 1c as the input.
(a)
(b)
Figure 4. Example of robust direction encoding; (a)Direction encoding result of GVF from Figure 1(c) without RDE; each color represents a direction quantization level; (b) Direction encoding result of GVF using RDE; its scale is obviously much coarser than that of (a). After downsampling, the output of RDE is ordered to constitute a fixed length iris feature vector (C 1,C 2,",C N ) , where Ci ∈ {1, 2,3, 4,5, 6}(i = 1, 2," , N ) and N is the dimension of the vector. To balance recognition accuracy and the complexity, N is chosen as 2560. Similar to Daugman’s idea, the Hamming distance is adopted for measuring the dissimilarity between the acquired iris and the template iris. In order to complement the possible rotation difference between the two irises, template iris feature is converted to eleven versions corresponding to rotation angles −10D,−8D,−6D,−4D,−2D,0D,2D,4D,6D,8D,10D respectively. And the minimum Hamming distance between the input and the eleven rotated versions of the template is the final matching result.
3. Experiments In order to evaluate the proposed algorithm, CASIA Iris Image Database is used as the test dataset, which has been worldwide shared for research purposes [19]. The proposed algorithm is tested in two modes: identification and verification. In identification mode, the proposed algorithm achieves 100% correct recognition rate. In verification mode, all possible comparisons are made between the iris images collected at two different times. There are totally 3,711 intra-class comparisons and 1,131,855 inter-class comparisons. The ROC (Receiver Operating Characteristic) curve, a plot of FRR against FAR under different threshold values of Hamming distance, is illustrated in Figure 5. Daugman’s algorithm [3,4] has been widely used in commercial systems and Noh’s scheme [10] is the most recent one (only local feature used here for comparison). The algorithm in [11] is our early best method achieving high performance in both speed and accuracy. For the purpose of comparison, the verification performance of these three methods in the same dataset is also shown in Fig. 5. It should be pointed out that both Daugman’s and Noh’s algorithms are coded following their publications [3,10] and the length of their iris code is 256 Bytes and 144 Bytes respectively.
0-7695-2128-2/04 $20.00 (C) 2004 IEEE
Without strict image quality control or further filtering of poor quality images, the performance of their algorithms in our dataset is worse than that reported in their publications. 0.06
EER Robust Direction Estimation Daugman's method [3] Tan et al.'s method [11] Noh et al.'s local feature [10]
0.05
FRR
0.04
0.03
0.02
0.01
0 -6 10
-5
10
-4
-3
10
10
-2
10
-1
10
FAR
Figure 5. Comparison of ROCs From the Figure 5, we can see the recognition performance of the proposed algorithm is comparable with the best method in the field of iris recognition. The reason is that the presented method extracts robust features with explicit physical meanings from the geometric image structure directly. The basic idea of Noh’s local feature [10] is a sort of 1D zero-crossing description because the wavelet frame coefficients were encoded to 0s or 255s based on their signs (positive or negative). In terms of accuracy, this method [10] is worse than the other algorithms derived from 2D image information. Compared with other methods, the robust direction encoder pays more attention to strengthen the robustness of the feature extraction procedure. So it achieves the lowest EER (Equal Error Rate) in the challenging benchmark. In terms of computer resources, the proposed method costs a little more than other algorithms, but it still could be implemented in real time.
4. Conclusions In this paper, a simple but effective iris recognition algorithm is formulated. The effectiveness of the iris feature depends on its meanings and the robustness of the process to derive it. Bearing this in mind, robust direction encoder is designed to estimate the local dominant direction of GVF which indicates the iris texture’s inherent characteristics. The test on large-scale iris image database including some poor quality images has confirmed this idea. As another contribution, a general framework for iris recognition named local robust encoding is formulated in this paper. With the guidance of this architecture, new and improved iris recognition algorithms may be further developed.
Acknowledgments This work is sponsored by the Natural Sciences Foundation of China under grant No. 60335010,
60121302, 60275003, 60332010, 69825105 and the CAS.
References [1] A. Jain, R. Bolle, and S. Pankanti, Biometrics: Personal Identification in a Networked Society, Kluwer, Norwell, 1999. [2] T. Mansfield, G. Kelly, D. Chandler, and J. Kane, Biometric Product Testing Final Report, issue 1.0, National Physical Laboratory of UK, 2001. [3] J. Daugman, “High Confidence Visual Recognition of Persons by a Test of Statistical Independence”, IEEE Trans. PAMI, Vol.15, No.11, 1993, pp.1148-1161. [4] J. Daugman, “Statistical Richness of Visual Phase Information: Update on Recognizing Persons by Iris Patterns”, IJCV, Vol. 45(1), 2001, pp.25-38. [5] R.P. Wildes, J.C. Asmuth, et al., “A Machine-vision System for Iris Recognition”, Machine Vision and Applications, Vol.9, 1996, pp.1-8. [6] W.W. Boles and B. Boashash, “A Human Identification Technique Using Images of the Iris and Wavelet Transform”, IEEE Trans. Signal Processing, Vol.46, No.4, 1998, pp.1185-1188. [7] Y. Zhu, T. Tan, and Y. Wang, “Biometric Personal Identification Based on Iris Patterns”, ICPR’2000, Vol.II, pp.805-808. [8] L. Ma, Y. Wang, and T. Tan, “Iris Recognition Using Circular Symmetric Filters”, ICPR’2002, Vol.II, pp.414-417. [9] L. Ma, T. Tan, Y. Wang, and D. Zhang, “Personal identification based on iris texture analysis”, IEEE Trans. PAMI, Vol. 25, No.12, 2003, pp.1519- 1533. [10] S. Noh, K. Bae, and J. Kim, "A Novel Method to Extract Features for Iris Recognition System", AVBPA’2003, pp.838-844. [11] L. Ma, T. Tan, Y. Wang, and D. Zhang, “Efficient Iris Recognition by Characterizing Key Local Variations”, IEEE Trans. Image Processing. (Accepted) [12] L. Ma, T. Tan, D. Zhang, and Y. Wang, “Local Intensity Variation Analysis for Iris Recognition”, Pattern Recognition. (Accepted) [13] F. R. Hampel, E. M. Ronchetti, P. J. Rousseeuw, and W. A. Stahel, Robust Statistics: The Approach Based on Influence Functions, Wiley, New York, 1986. [14] P.J. Besl, J. B. Birch, and L. T. Watson, "Robust Window Operators", ICCV’1989, pp.591-600. [15] Y. L. You and M. Kaveh, "Fourth order partial differential equations for noise removal", IEEE Trans. Image Processing, Vol.9, No.10, 2000, pp.1723-1730. [16] P. Perona, “Orientation diffusion”, IEEE Trans. Image Processing, 7 (1998), pp. 457-467. [17] B. Tang, G. Sapiro, and V. Caselles, “Diffusion of general data on non-flat manifolds via harmonic maps theory : The direction diffusion case”, IJCV, 36(2), February 2000, pp.149-161. [18] P. E. Trahanias and A.N. Venetsanopoueos, “Vector Directional Filters—A New Class of Multichannel Image Processing Filters”, IEEE Trans. Image Processing, 2 (1993), pp. 528-534. [19] CASIA Iris Image Database, Chinese Academy of sciences, http://www.sinobiometrics.com/casiairis.htm.
0-7695-2128-2/04 $20.00 (C) 2004 IEEE
representation of one dimensional wavelet transform was used by Boles et al. [6] for iris recognition. Iris images naturally provide rich texture information, so statistical texture analysis methods are also helpful for iris pattern representation [7,8,9]. Based on the wavelet frame decomposition, Noh et al. [10] derived two types of features for iris matching. In [11], Tan et al. described an algorithm for iris recognition by characterizing key local variations. Using Gaussian-Hermite moments, Tan et al. [12] represented the shape of one-dimensional intensity signals as iris features.
(a)
(b)
1. Introduction (c)
The increasing demands of reliable personal identification for applications such as assess control have resulted in an unprecedented interest in biometrics. Biometrics makes use of the physiological or behavioral characteristics of people such as fingerprint, iris, face, palmprint, gait, voice, etc. to identify a person [1]. The biometrics’ advantages over traditional human verification methods are straightforward: universality, uniqueness and convenience. After testing seven popular biometric systems, it was reported in [2] that iris recognition is the most reliable for human authentication. A typical iris recognition system includes localization, normalization, feature extraction and matching (Fig. 1 illustrates the preprocessing step). Regarding the iris image as the modulation result based on multi-scale Gabor wavelets, Daugman encoded the phase information as iris features and the matching is based on a test of statistical independence [3,4]. After area-based image registration, Wildes et al. [5] employed the normalized correlation results at four different resolutions as the matching metric. The zero-crossings
Figure 1. Preprocessing of iris image; (a)Original image; (b)Result of iris localization; (c)Normalized iris image. For iris recognition algorithms, it is crucial to design an efficient scheme to extract each class’ inherent features, which should be robust to all sources of noises and discover meaningful information about the image data. In order to achieve this goal, a geometry-driven iris recognition algorithm is proposed in this paper. Based on the theory of robust statistics, local dominant direction of gradient vector field is encoded as iris feature. Details of this approach are described in Section 2. In Section 3, the experimental results are reported prior to conclusions in Section 4.
2. Robust orientation estimation of local image surface 2.1. Motivation The central issue in iris recognition is iris pattern
0-7695-2128-2/04 $20.00 (C) 2004 IEEE
representation. No matter the phase value [3,4], representation of zero-crossings [6] or texture signature [7,8,9], iris features must indicate meaningful information of iris image structure. In order to precisely capture the fine spatial changes of the iris, the distinguishing characteristics of iris used for recognition are usually local and minute. But the measurements from minutiae are easily affected by noises, such as occlusions by eyelids and eyelashes, localization error and deformation during normalization, etc., which greatly limits the system’s accuracy. So a robust statistical procedure [13] is helpful to strengthen the robustness of the feature extraction algorithm. Then the idea of iris pattern representation can be formulated in a model to guide the robust estimation process. Furthermore, the estimated local feature is coarsely encoded to iris code not only facilitating matching and storage but also strengthening the robustness of iris feature. In conclusion, the idea of local robust encoding strategy, a general solution for iris recognition, is illustrated in Figure 2.
Robust estimation
JJK
N p , whose direction is independent of illumination and contrast and indicates the inherent characteristics of the
JJK
iris. Another benefit of N p is that it is opposite to the
JJK
direction of gradient vector G p (Fig.3) as shown in the following: Suppose point P ( x 0, y 0, I 0 ) is on the planar surface
F ( x, y, I ) . The unit normal vector of the surface is JJK
denoted by N ( n x , n y , n I ) (suppose n I ≠ 0 ). Its projection
JJK
T
onto the x − y plane is N p = ( n x ,n y ) , then the plane F ( x, y, I ) can be represented as
nx ( x − x0 ) + n y ( y − y0 ) + nI ( I − I 0 ) = 0
Model Original data in local window
where gradient vector field G can be defined. The vertical JK component of the surface’s normal vector N reflects the absolute measure of local intensity contrast and determines the modulus of the gradient vector. The JJK projection of N onto the x − y plane is denoted by
Local feature
Coarse quantization
Iris code
Figure 2. Block diagram of local robust encoding
2.2. Geometry of iris image structure Local image structure plays an important role in iris recognition, so an intuitive idea of iris pattern representation is based on the geometric structure of image data in a small region. By considering the gray-level normalized iris image in a 3D Cartesian coordinate system (Fig.3), each image pixel can be denoted by a point (x,y,I), where x and y are the coordinates in the image plane, and I denotes grey level intensity. So the objective of iris analysis is to infer stable signatures reflecting the inherent structure of the image surface. If the image surface is piecewise smooth, then the orientation of local image surface should be a good choice of iris feature because it indicates the spatial details of iris image and is stable. In fact, representing the image data by piecewise planar surface is not new in the literature. Besl et al. [14] provided a general architecture for local surface fitting using robust window operators that preserves gray level and gradient discontinuities in digital images. In his framework, a robust regression procedure was implemented via the M-estimator [14]. You et al. [15] exploited a class of fourth-order PDEs to evolve the original image to piecewise planar image. But the computational costs of these methods are too high to satisfy the real time requirement of iris recognition. Thus a more efficient technique must be studied. Figure 3 illustrates a patch of the image surface. The image can also be modeled as a quantitative field I(x,y)
i.e. the image intensity I on this plane is ny n I ( x, y ) = − x ( x − x0 ) − ( y − y0 ) + I 0 nI nI JJ K ∂I ∂I 1 JJJK ∂I n x ∂I n y =− , So =− , G p = ( , ) = − N p . ∂x ∂y nI ∂x n I ∂y n I
JJK
(1)
(2) (3)
JJK
Therefore G p is opposite to N p . I I0
I'
JJK N
F ( x, y, I )
y'
JJJK Np
x'
x
x0
y0
JJJK Gp
y
JJJK Np
Figure 3. A patch of iris image surface approximated by planar surface At last the problem of iris feature extraction is turned to direction estimation of image gradient vector, i.e. the model in local robust encoding diagram (Fig.2) is constructed. Because original directional data is noise prone, it is necessary to implement direction diffusion to obtain a coarse representation of GVF. And the piecewise smooth image surface results in the similar direction of GVF in local region, so the assumption of piecewise planar image is more reasonable after direction diffusion.
2.3. Robust direction estimation As another module of local robust encoding scheme, a novel method for robust estimation of the dominant
0-7695-2128-2/04 $20.00 (C) 2004 IEEE
direction of gradient vector in local region is proposed, named as Robust Direction Estimation (RDE). RDE includes two parts: direction diffusion followed by direction filtering. The aim of direction diffusion is to enhance the main direction in a patch and to suppress noises. Many published algorithms about direction or orientation diffusion can serve for this idea [16,17]. But the numerical implementation of these methods all involves many iterations, and what we care is not the process of diffusion or detail preserving, but the result of diffusion. So a simplification of their ideas is described as follows: 1) Gradient vector field computation. Sobel operator is utilized to generate the two components of image gradient vector, G x and G y . 2) Isotropic derivatives diffusion. Gaussian filter is the only kernel qualified for linear scale space generation. So the coarse representation of G x or G y is the result of convolution with a Gaussian window: G 'x =G x∗g δ , G 'y =G y∗g δ
(4)
where g δ is a Gaussian filter with scale δ .
3) The phase angle A of the complex G 'x +i G 'y is the diffusion result. After direction diffusion, the enhanced gradient vector angle A across image plane can be regarded as a vector valued image. In the next step the iris feature—local dominant direction, should be robustly estimated from each region of A . Vector directional filters, a class of multi-channel image processing filters, are employed to select a typical one from the input angles in each window [18]. Following ideas from basic vector directional filter [18], directional filter (DF) is defined as follows: Definition: The output of the DF, for input { Ai , i = 1, 2, " , n }, is ADF = DF { Ai , i = 1, 2, " , n} , such that ADF ∈ { Ai , i = 1, 2, " , n} and
where
n
n
i =1
i =1
∑ Dis ( ADF , Ai )≤ ∑ Dis ( A j , Ai ), ∀ j =1,2,",n Dis ( Ai , A j )
(5)
(6)
denotes the minimum angular
difference between the angles Ai and A j . It had been proved that the angle ADF is the least error estimate of the angle location [18]. After coarse quantization, a more compact representation is obtained and the robustness of the whole statistical procedure is further strengthened. It should be pointed out the selection of quantization level is a tradeoff between the robustness, discriminability and other factors such as storage cost, computational costs. In this case, the angle scale of ADF , from −π to π , is quantized into six discrete values. The effect of robust direction encoding is illustrated in Fig. 4 which shows the
output of the method when regarding Fig. 1c as the input.
(a)
(b)
Figure 4. Example of robust direction encoding; (a)Direction encoding result of GVF from Figure 1(c) without RDE; each color represents a direction quantization level; (b) Direction encoding result of GVF using RDE; its scale is obviously much coarser than that of (a). After downsampling, the output of RDE is ordered to constitute a fixed length iris feature vector (C 1,C 2,",C N ) , where Ci ∈ {1, 2,3, 4,5, 6}(i = 1, 2," , N ) and N is the dimension of the vector. To balance recognition accuracy and the complexity, N is chosen as 2560. Similar to Daugman’s idea, the Hamming distance is adopted for measuring the dissimilarity between the acquired iris and the template iris. In order to complement the possible rotation difference between the two irises, template iris feature is converted to eleven versions corresponding to rotation angles −10D,−8D,−6D,−4D,−2D,0D,2D,4D,6D,8D,10D respectively. And the minimum Hamming distance between the input and the eleven rotated versions of the template is the final matching result.
3. Experiments In order to evaluate the proposed algorithm, CASIA Iris Image Database is used as the test dataset, which has been worldwide shared for research purposes [19]. The proposed algorithm is tested in two modes: identification and verification. In identification mode, the proposed algorithm achieves 100% correct recognition rate. In verification mode, all possible comparisons are made between the iris images collected at two different times. There are totally 3,711 intra-class comparisons and 1,131,855 inter-class comparisons. The ROC (Receiver Operating Characteristic) curve, a plot of FRR against FAR under different threshold values of Hamming distance, is illustrated in Figure 5. Daugman’s algorithm [3,4] has been widely used in commercial systems and Noh’s scheme [10] is the most recent one (only local feature used here for comparison). The algorithm in [11] is our early best method achieving high performance in both speed and accuracy. For the purpose of comparison, the verification performance of these three methods in the same dataset is also shown in Fig. 5. It should be pointed out that both Daugman’s and Noh’s algorithms are coded following their publications [3,10] and the length of their iris code is 256 Bytes and 144 Bytes respectively.
0-7695-2128-2/04 $20.00 (C) 2004 IEEE
Without strict image quality control or further filtering of poor quality images, the performance of their algorithms in our dataset is worse than that reported in their publications. 0.06
EER Robust Direction Estimation Daugman's method [3] Tan et al.'s method [11] Noh et al.'s local feature [10]
0.05
FRR
0.04
0.03
0.02
0.01
0 -6 10
-5
10
-4
-3
10
10
-2
10
-1
10
FAR
Figure 5. Comparison of ROCs From the Figure 5, we can see the recognition performance of the proposed algorithm is comparable with the best method in the field of iris recognition. The reason is that the presented method extracts robust features with explicit physical meanings from the geometric image structure directly. The basic idea of Noh’s local feature [10] is a sort of 1D zero-crossing description because the wavelet frame coefficients were encoded to 0s or 255s based on their signs (positive or negative). In terms of accuracy, this method [10] is worse than the other algorithms derived from 2D image information. Compared with other methods, the robust direction encoder pays more attention to strengthen the robustness of the feature extraction procedure. So it achieves the lowest EER (Equal Error Rate) in the challenging benchmark. In terms of computer resources, the proposed method costs a little more than other algorithms, but it still could be implemented in real time.
4. Conclusions In this paper, a simple but effective iris recognition algorithm is formulated. The effectiveness of the iris feature depends on its meanings and the robustness of the process to derive it. Bearing this in mind, robust direction encoder is designed to estimate the local dominant direction of GVF which indicates the iris texture’s inherent characteristics. The test on large-scale iris image database including some poor quality images has confirmed this idea. As another contribution, a general framework for iris recognition named local robust encoding is formulated in this paper. With the guidance of this architecture, new and improved iris recognition algorithms may be further developed.
Acknowledgments This work is sponsored by the Natural Sciences Foundation of China under grant No. 60335010,
60121302, 60275003, 60332010, 69825105 and the CAS.
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