SINGULAR VALUE DECOMPOSITION AND 2D PRINCIPAL COMPONENT ANALYSIS OF IRIS-BIOMETRICS FOR AUTOMATIC HUMAN IDENTIFICATION. A thesis presented to

Transcription

1 SINGULAR VALUE DECOMPOSITION AND 2D PRINCIPAL COMPONENT ANALYSIS OF IRIS-BIOMETRICS FOR AUTOMATIC HUMAN IDENTIFICATION A thesis presented to the faculty of the Russ College of Engineering and Technology at Ohio University In partial fulfillment of the requirements for the degree Master of Science Michael J. Brown June 2006

2 This thesis entitled SINGULAR VALUE DECOMPOSITION AND 2D PRINCIPAL COMPONENT ANALYSIS OF IRIS-BIOMETRICS FOR AUTOMATIC HUMAN IDENTIFICATION by MICHAEL J. BROWN has been approved for the School of Electrical Engineering and Computer Science and the Russ College of Engineering and Technology by Mehmet Celenk Associate Professor of Electrical Engineering and Computer Science Dennis Irwin Dean, Russ College of Engineering and Technology

3 Abstract BROWN, MICHAEL J., M.S., June 2006, Electrical Engineering SINGULAR VALUE DECOMPOSITION AND 2D PRINCIPAL COMPONENT ANALYSIS OF IRIS-BIOMETRICS FOR AUTOMATIC HUMAN IDENTIFICATION (95 pp.) Director of Thesis: Mehmet Celenk With the recent emphasis given to security, automatic human identification has received significant attention. In particular, iris based subject recognition has become especially important because of its high level of complexity which lends itself to high confidence recognition. In addition, the eye is well protected and generally does not change very much over extended periods of time. This thesis gives a review of some currently available methods that have already been investigated. A wide sense stationary approximation for gray scale values is explored as a possible means of feature extraction. The singular value decomposition (SVD) is discussed as a low bit rate tool for iris discrimination. The 2D principal component analysis (2DPCA) is explored as a method for feature extraction. It is determined experimentally that the SVD for iris recognition is a novel way to significantly reduce the storage requirements (133 bits) for iris recognition as compared to other methods (2048 bits). However, recognition accuracy has not reached a desirable level. The 2DPCA, on the other hand, significantly improves recognition accuracy on the same dataset, but at the cost of greater storage requirements.

4 Acknowledgements Thanks to Mehmet Celenk, Yi Luo, and Jason Kaufman.

5 v Table of Contents Page Abstract...iii List of Tables... vii List of Figures...viii Chapter 1. Introduction Biometric Identification and Iris Recognition Iris Physiology Literature Review Image Acquisition and Selection Chapter 2. Fixed and Variable Size Window Sampling and Stochastic Analysis Wide Sense Stationary Approximation Feature Generation with Correlation Matrices Chapter 3. Image Preprocessing Histogram Analysis Iris Extraction Image Unwrapping Image Enhancement Chapter 4. Singular Value Decomposition of Iris Biometrics The Singular Value Decomposition Feature Extraction with the SVD Classification Performance with the SVD... 39

6 vi 4.4 Future Improvements Chapter 5. 2D Principal Component Analysis (2DPCA) of Iris Biometrics The 2DPCA Feature Extraction with the 2DPCA Classification Performance with the 2DPCA Chapter 6. Conclusions and Discussion Bibliography Appendix A. Additional Images for four subjects Appendix B. Software Flow Appendix C. Source code Section C.1 - Recognize.m Section C.2 - Reader.m Section C.3 - Preproc.m Section C.4 - Recognizetwodpca.m Section C.5 - Twod_pca.m Section C.6 - My_eig.m... 86

7 vii List of Tables Page Table 4.1. SVD Integer Storage Requirements

8 viii List of Figures Page Figure 1.1 Anatomy of the human eye (from [8])... 4 Figure 1.2. Iris boundaries and corresponding iris code (from [1])... 6 Figure 1.3. Calculated Hamming distances (from [1])... 7 Figure 1.4. Stages of iris unwrapping (from [3])... 8 Figure 1.5. Sample zero crossing iris representation (from [6]) Figure 1.6. Image with excessive occlusion (from [7]) Figure 1.7. Image with minimal occlusion (from [7]) Figure 2.1. Cropped iris image (from [10]) Figure 2.2. Fixed size windows (from [10]) Figure 2.3. Difference matrix feature space (from [10]) Figure 2.4. Three dimensional feature space for fixed window size (from [10]) Figure 2.5. Three dimensional feature space for variable window size (from [10]) Figure 3.1. Sample iris image (from [7]) Figure 3.2. Typical grayscale distribution for iris image Figure 3.3. Iris image with excessive eyelid glare (from [7]) Figure 3.4. Grayscale distribution of Figure Figure 3.5. Grayscale distribution of Figure 3.3 compensated for glare Figure 3.6. Typical iris extraction progression Figure 3.7. Cropped localized iris image Figure 3.8. Localized iris image with corresponding pupil boundary and centroid... 28

9 ix Figure 3.9. Local iris image with inner and outer boundaries indicated Figure Unwrapped iris image Figure Sample illumination pattern of a normalized unwrapped image Figure Enhanced unwrapped image after illumination subtraction Figure 4.1. Classification performance (η) with different radius multipliers Figure 4.2. Between class distances with different radius multipliers Figure 4.3. Within class distances using different radius multipliers Figure 4.4. Classification performance (η) using different numbers of iris images Figure 4.5. Average intraclass distance using different numbers of images Figure 4.6. Average between class distance using different numbers of images Figure 4.7. Performance with varying numbers of singular values Figure 4.8. Average intraclass distance with varying numbers of singular values Figure 4.9. Average interclass separation with different numbers of singular values Figure Incorrectly located pupil Figure Unwrapped image including too much conjunctiva Figure 5.1. Classification performance with different radius multipliers Figure 5.2. Average intraclass distance with different radius multipliers Figure 5.3. Average interclass distances with different radius multipliers Figure 5.4. Classification performance with different numbers of Eigenvectors Figure 5.5. Average intraclass distance with different numbers of Eigenvectors Figure 5.6. Average interclass distance with different numbers of Eigenvectors... 60

10 1 Chapter 1. Introduction 1.1 Biometric Identification and Iris Recognition As a greater need for secure identification methods is addressed, biometrics are at the forefront of modern research. Conventional systems are generally either token (key) or knowledge (password) [24] based, which makes them susceptible to numerous problems. Obvious examples are losing a key or forgetting one s password. In addition, unauthorized individuals may still be able to use a key, and passwords that are easy for someone to remember are often easy to guess [25]. Clearly, a more robust and flexible system for identification would alleviate many of these and other associated problems. For these reasons, considerable effort has been devoted to biometrics as an alternative to conventional methods. Biometric traits are inherent to a person s physical appearance, making them based on who you are [25]. In addition, they are not susceptible to being lost or easily duplicated in most cases. Some common biometric identifiers that have been researched include facial characteristics, hand geometry, retinal blood vessel patterns, fingerprints, speech and voice patterns, gait, and iris features [24]. When using handprints or fingerprints, a high degree of accuracy is achieved due to the complexity of the feature. However, more interaction is required since the subject must touch a sensing device [27]. Facial features and gait recognition do not require as much cooperation from the subject, but they are generally less accurate when making

11 2 identifications [27]. In addition, different facial expressions and styles of walking make these systems more susceptible to variations that could hinder identification [1]. One feature that is not limited by these factors is the iris. In general, the eye is well protected from danger by the eyelid. In addition, since vision is a sense that most individuals rely heavily on, care is usually taken to avoid damage to the eye. This makes the iris especially desirable since it does not change appreciably over time in most cases. [1]. In the following pages, different aspects of this challenging technology are discussed. A variety of algorithms were explored both for image segmentation and feature extraction. Discussions on different approaches for both included. In Chapter 1, a brief discussion of the physiology of the iris is presented, along with a review of the currently available literature and methods. Image acquisition and selection is also briefly discussed. Chapter 2 covers the initial research conducted using a wide sense stationary approximation of the iris. Chapter 3 discusses image preprocessing for use with the singular value decomposition as detailed in Chapter 4. Chapter 5 details a novel use of the 2D principal component analysis for feature extraction.

12 3 1.2 Iris Physiology The iris is the concentric area located in the eye between the cornea and the lens (see Figure 1.1) which gives the eye its color. It is made up of tiny muscles that dilate and contract the pupil for varying lighting conditions [8]. Beginning in the third month of gestation [1], a process known as chaotic morphogenesis causes the iris to develop in a mostly random manner. Since this process is unrelated to an individual s genetics, even identical twins will have irises that are very different from one another [1]. The main function of the iris is to vary the size of the pupil in response to different lighting conditions. This is done involuntarily with the aid of muscles which are within the iris. As a result, this can be used to verify that several sequential images are from an actual eye by looking for variations in pupil size [1].

13 Figure 1.1 Anatomy of the human eye (from [8]) 4

14 5 1.3 Literature Review The most prevalent method for iris identification currently in use was developed by Daugman [1,2]. A digital video camera is employed to capture several sequential images of an iris in the near infrared (NIR) frequency range, usually with the subject s cooperation to center the eye in the view of the camera via a feedback video loop. NIR is used because it provides more richly detailed images of the iris, so more useful features can be extracted [1]. It also is less intrusive to human subjects [1]. While the images are being acquired, the image quality is assessed by measuring the spectral power in the mid to high frequency portion of the two dimensional Fourier transform. This quantity is then maximized by either adjusting the camera or indicating to the subject a need for adjustment [1]. During the processing stage, the boundaries of the iris are located using a coarse to fine strategy with an integrodifferential edge detection operator which searches for the maximum of the blurred partial derivative [1,2]. A similar operation is also applied to locate the upper and lower eyelid boundaries. Once the boundaries have been located, quadrature 2-D Gabor wavelets [2] are used to extract the phase information present in the picture. It is important to note that only phase information is used, as amplitude information was deemed to be too susceptible to illumination and other environmental factors by the author. The extracted phase information is converted and stored as a 2048 bit iris code, along with a 2048 bit masking code to determine what information will actually be used in the identification process. An example of the calculated boundaries and an iris code are shown in Figure 1.2.

15 6 Figure 1.2. Iris boundaries and corresponding iris code (from [1]) In order to classify an iris code, a test for statistical independence was implemented using the fractional Hamming distance (HD), where an HD of zero would indicate a match that is perfect [1]. Figure 1.3 shows a comparison of the HD for the same iris versus two different irises with 2.3 million comparisons under non-ideal circumstances.

16 7 Figure 1.3. Calculated Hamming distances (from [1]) An examination of the histogram inerror! Reference source not found. Figure 1.3 suggests that a suitable classifier could be implemented by placing the decision boundary at an HD of about 0.33 when using 1 million different iris patterns. This value could be raised or lowered depending on the desired security. In order to achieve this performance, the image I(x,y) was remapped to dimensionless polar coordinates, which allows the algorithm to correct for changes in the pupil s size. In addition, multiple iterations were computed over several different angles in order to achieve invariance to the image s orientation. Finally, a decision confidence level was calculated with a decidability index (denoted by d ) [1] based on the separation of the distributions such as in Figure 1.3. The results obtained by this method would give a false match probability of about one in four million and would require 2048 iris code bits and 2048 masking bits.

17 8 In the method presented in [3], the authors propose a different approach. Initially, the iris and pupil are assumed to be circular, and simple filtering and edge detection methods are used to find the iris in the picture. The image is then normalized and unwrapped [3]. These steps are shown in Figure 1.4. Figure 1.4(a) shows an initial iris image, and Figure 1.4(b) illustrates the iris after the boundaries are located. The unwrapped iris is presented in Figure 1.4(c), and the unwrapped iris with additional enhancement is depicted in Figure 1.4(d). Figure 1.4. Stages of iris unwrapping (from [3]) After unwrapping, the iris was characterized using frequency and orientation information. This was done by using a bank of circular symmetric filters [3] to capture frequency information, which the authors contend is the most useful for iris identification. The filters used were circular Gabor filters, which were modified for each frequency to be captured. These filters do not capture orientation information. The iris is divided into several different regions of interest, and each is characterized using the

18 9 circular symmetric filter at a different frequency. Once the features are extracted from the iris, a nearest feature line (NFL) classifier [3] was used to identify the iris. The results obtained by the author are less accurate than those obtained in the method presented by Daugman [1,2]. In [4] and [5], the authors use the same localization and unwrapping approaches outlined in [3]. However, classifiers are generated in different manners. With the method presented in [4], features are generated by looking for key local variations in the unwrapped image. Dyadic wavelet transforms are used for this purpose. In [5], Gabor filters are chosen in the spatial domain in order to extract features. In [6], yet another method for iris identification is presented. In this approach, the iris edges are detected using simple filtering and edge detection techniques. Then, the image is cropped to create a new picture. The center of the pupil is found by assuming a circular shape for both the iris and the pupil, and a scaling factor is chosen for the dyadic wavelet transform to make sure features are extracted from the same portions of the iris [6]. Concentric circles are followed around the iris to create gray level representations, and this process is repeated until a suitable number of 1-D signals are obtained. The dyadic wavelet transform is applied, and zero crossings from different wavelet resolution levels are captured to create an iris signature [6] as shown in Figure 1.5. In addition, since higher resolution levels are discarded, the authors contend that high frequency noise will have little effect on the identification accuracy. Once these features are found, comparisons are made using the zero crossing iris signatures [6]. Identification was implemented by finding the iris in the database with the least amount of dissimilarity.

19 One problem with the presentation of this method is that the author has selected a significantly smaller database than the other approaches detailed here. 10 Figure 1.5. Sample zero crossing iris representation (from [6]) In comparison to the algorithms that are currently available, the approach presented in this thesis only requires 133 bits for the iris identification code to provide a maximum recognition rate of 83% using the singular value decomposition. This was achieved with 18 different subjects taken from the CASIA iris image database [7]. This method was also limited by the number of subjects that were tested, but it produces promising results with a comparatively small feature space. The recognition accuracy was then improved to 89% using the 2D principal component analysis (2DPCA), but the storage requirements for this method are greater.

20 Image Acquisition and Selection Initially, images were selected from the CASIA iris image database [7]. This database is maintained by the National Laboratory of Pattern Recognition (NLPR), the Institute of Automation(IA), and the Chinese Academy of Sciences (CAS). The database consists of 108 classes (subjects). For each subject, there are a total of seven images; three from one session, and four from another [7]. Each uses 8 bits per pixel for gray scale values, and is stored as a 320x280 (width x height) bitmap. Pictures with too much eyelash or eyelid occlusion were less ideal, as shown in Figures 1.6 and 1.7. Initially they were rejected, but later the algorithm was tested with both types of images. Figure 1.6. Image with excessive occlusion (from [7])

21 Figure 1.7. Image with minimal occlusion (from [7]) 12

22 13 Chapter 2. Fixed and Variable Size Window Sampling and Stochastic Analysis 2.1 Wide Sense Stationary Approximation In the initial phase of research that was conducted and outlined in [10], a wide sense stationary approximation was used for texture characterization, and second order statistics were explored as a method for classification of iris images [10]. Initially, the iris was cropped from the image using a rectangular mask [11], and the pupil was detected by analyzing a histogram of gray scale values. The pupil and the area surrounding the iris were then assigned a gray scale value of zero (black) to make subsequent processing easier as shown in Figure 2.1. Figure 2.1. Cropped iris image (from [10])

23 14 Figure 2.2. Fixed size windows (from [10]) Two small fixed size windows were then extracted from the image; one at the left and one at the right boundary of the pupil as illustrated in Figure 2.2. Next, the two dimensional (2-D) discrete auto- (R XX (m,n;k,l)) and cross- (R XY (m,n;k,l)) correlations [14] for the rectangular sub-images of Figure 2.2 were calculated. Since the image data is twodimensional, by definition the ensuing correlation functions would be four dimensional. (4-D) [10]. In order to reduce the complexity of the system, a wide sense stationary approximation was used when calculating the autocorrelation (R xx ) and cross-correlation (R xy ) using [26] R XX R XY [ X ( k, l) X ( k m, l )] ( m, n) = E n (2.1) [ X ( k, l) Y( k m, l )] ( m, n) = E n (2.2) where E indicates the expected value, and X(k,l) is a pixel value of the subimage X at location (k,l). The autocorrelation matrix was determined for each sub-image in the first iris image window and used as a reference. Next, the cross correlation was computed

24 between corresponding windows of different iris images to create a new difference matrix D defined as [10]: 15 D XX XY ( m, n) = RXX ( m, n) RXY ( m, n) (2.3) It is prudent to note that, for a sub-image of size NxN, the correlation and difference matrices are size (2N-1)x(2N-1) [10], which can be quite large. In testing, one of the images was used as a reference or training value, and another as a comparison or test value. The 2-D autocorrelation was found as described earlier for each rectangular sub-image on either side of the pupil (see Figure 2.2). The difference matrix was calculated, along with its mean and summation. It was found through experimentation that the magnitude of the difference matrix was generally quite large when comparing two different irises. However, it was significantly smaller when comparing two different images of the same iris. Figure 2.3 shows a sample classification using two different irises. A decision boundary could be easily defined in this case to separate the two irises. This serves to show that a low dimensional feature space might have been possible using a wide sense stationary assumption [26].

25 Figure 2.3. Difference matrix feature space (from [10]) 16

26 Feature Generation with Correlation Matrices Based on the initial results, the correlation matrices were then used to attempt to create feature vectors instead of directly comparing two pictures [10]. Again, the image was first cropped as shown in Figure 2.1. Next, moving windows of fixed size were used, and starting at the inside edge of the iris, the windows were moved outwards a single pixel at a time. For each shift, the autocorrelation was calculated for both windows, as well as the cross correlation between the two [10]. Then, the features were extracted from the matrices by finding the maximum, minimum, sum, mean, and diagonal summation (trace). In a similar attempt, the windows were also increased in size by a single pixel for each iteration while the inside edge remained stationary [10]. Features were generated in the same manner once the auto- and cross-correlation matrices were created. After the feature vectors had been created, the difference was computed to check for classification performance. Using eight images from four subjects (two images per person), finding the minimum distance classifier correctly identified each iris. This method was also tested using the Euclidean distance with the same results [10]. By examining a three dimensional feature space, the performance using fixed and variable sized windows can be seen in Figures 2.4 and 2.5, respectively. It is noticeable that there is not a large amount of interclass separation, but the grouping for each class is reasonably well defined.

27 Figure 2.4. Three dimensional feature space for fixed window size (from [10]) 18

28 19 Figure 2.5. Three dimensional feature space for variable window size (from [10]) Following these initial findings, further attempts were made to explore this window sampling technique on a larger number of samples. However, the results indicated that the use of these second order statistics were not enough for useful iris feature classification purposes. It was also discovered that the preprocessing steps that were implemented to find the iris may not have been sufficiently robust for use on a larger number of images.

29 20 Because the orientation and slope of the vectors that were generated seemed to be a promising feature as well, additional experiments were performed using the first and second order derivatives of the curves shown in Figures 2.4 and 2.5. However, this did not significantly improve correct identifications, and it was determined that a different approach was required. In following iterations based on this windowing approach, attempts were made to generate useful features using the Fourier transform, as well as the Hadamard transform and the singular value decomposition (SVD). None of these produced significantly better results, most likely because the image preprocessing steps used were unable to accurately locate the iris in all cases. Additionally, there was no image size normalization, so differences in the size of the iris had a profound effect on generated feature vectors. With this in mind, more powerful preprocessing steps along with the singular value decomposition were implemented to provide a far more accurate identification technique as described in Chapters 3 and 4, respectively.

30 21 Chapter 3. Image Preprocessing 3.1 Histogram Analysis Once a suitable number of training samples were selected, preprocessing was required to isolate the iris for identification. First, a grayscale distribution is generated from an image such as the one shown in Figure 3.1 by counting the number of pixels with each gray scale value from 0 to 255. A sample histogram showing such a distribution is given in Figure 3.2. By examining the histogram, we can see that the largest number of pixels have a gray scale value of around 48, which corresponds to the pupil in the image. In some cases, however, an image will have two peaks if there is significant glare from the eyelid as is evident in Figure 3.3. This is detected by testing to make sure the maximum value in the distribution is not larger than the mean grayscale value of the image. If the test fails, as would happen in Figure 3.4, a new distribution is created by discarding all grayscale values greater than the mean as shown in Figure 3.5. The size of the pupil is then estimated by using the maximum value in the gray level distribution as the area of a circle A and calculating the radius r using r = A/π (3.1)

31 22 Figure 3.1. Sample iris image (from [7]) Figure 3.2. Typical grayscale distribution for iris image

32 23 Figure 3.3. Iris image with excessive eyelid glare (from [7]) Figure 3.4. Grayscale distribution of Figure 3.3

33 Figure 3.5. Grayscale distribution of Figure 3.3 compensated for glare 24

34 Iris Extraction In order to define the iris boundaries for feature extraction, the pupil s center is first estimated and a cropped image is created. This is followed by edge detection of the iris and definition of the outer iris boundary. Next, a ring defined by the inner and outer boundaries is unwrapped [3,4,5] to a rectangular coordinate system and enhanced. A typical progression of these steps is shown in Figure 3.6. A more detailed discussion of each is presented below. Figure 3.6. Typical iris extraction progression

35 26 The center of the pupil is estimated in the image by searching row and column wise for the minimum summation value along each direction. As outlined in [3,4,5], the pupil center at (X p,y p ) is located in the original image I(x,y) with X p = arg min ( I ( x, y)) x y Y p = arg min ( I( x, y)) (3.2) y x Once an estimate is found for the pupil s center, the original image is cropped with a rectangular mask [11] to further isolate the iris using the pupil s estimated radius in (3.1) as a reference for sizing. The actual cropped image must be larger than the pupil, and a suitable scaling factor was found for the estimated radius with experimentation. This method is applied once again to the subimage to further refine the location of the pupil s center. A sample cropped image is shown in Figure 3.7.

36 27 Figure 3.7. Cropped localized iris image Following the pupil and iris location, the image is binarized [3] using the gray scale distribution s maximum value, so that all pixels located in the pupil have a grayscale value of zero. Simple edge detection is then applied to find the actual boundary between the iris and the pupil. During detection, each pixel on the edge is counted, and the center of mass, or centroid, (x c,y c ) of the iris is calculated using a discrete version of the method outlined in [19] as x c = 1 N b N b i= 1 x i y c N 1 b = yi (3.3) N b i= 1

37 28 where N b is the total number of pixels on the detected boundary, and (x i,y i ) is a pixel location on the boundary. Figure 3.8 demonstrates a cropped iris image with its corresponding detected inner boundary and center of mass. Figure 3.8. Localized iris image with corresponding pupil boundary and centroid After finding an inner boundary for the iris, an outer boundary must also be determined. In this case, the radius of the outer boundary was calculated by simply multiplying the inner boundary s radius by an experimentally determined value of The outer points (x b,y b ) of the boundary are then created with x b ( θ ) = r cos( θ ) yb ( θ ) = r sin( θ ) (3.4)

38 29 with θ varying from zero to 2π, and r being the calculated radius of the outer boundary. Sample inner and outer calculated boundaries are presented in Figure 3.9. Additional sample images are included in Appendix A. Figure 3.9. Local iris image with inner and outer boundaries indicated

39 Image Unwrapping Following the boundary generation, the iris is unwrapped to a rectangular block of a fixed size as discussed in [3,4,5]. This is similar to the method employed by [1] and [2], which projected the iris image from a rectangular coordinate system to a doubly dimensionless pseudopolar coordinate system [3,4,5]. By doing so, the system can compensate for iris changes due to different lighting conditions and imaging distances, which will make the processing that follows easier to accomplish [3,4,5]. The unwrapping is performed by using [3,4,5] I ( X, Y) I ( x, y) n = o x = x p ( θ ) + (( xi ( θ ) x p ( θ )) Y M Y y = y p ( θ ) + (( yi ( θ ) y p ( θ )) (3.5) M θ = 2πX / N where I n represents an MxN normalized and unwrapped image. In this case, M and N are 48 and 256, respectively. The coordinates of the inner and outer boundaries of the iris at angle θ in the original image I o are represented by (x p (θ), y p (θ)) and (x i (θ), y i (θ)), respectively. A sample unwrapped image is included in Figure 3.10.

40 Figure Unwrapped iris image 31

41 Image Enhancement After unwrapping the image, the gray scale values are adjusted to account for differences in illumination and other factors. In [11], several methods are presented that help to balance the image in addition to improving contrast. After examining the available images, however, it was determined that the contrast was suitable. In order to compensate for illumination differences, the image is first scanned to find the average grayscale value of each 16x16 block in the picture as described in [3,4,5]. This gives a rough estimate of the illumination present in each portion of the image, and makes later processing somewhat easier. Figure 3.11 is representative of a typical calculated illumination pattern. Once it has been determined, it is applied to the original image by simple subtraction to produce an enhanced image as presented in Figure It is interesting to note that, although there are detectable rectangular artifacts in the enhanced image after using this method, it still improves feature extraction and recognition performance significantly when compared to no image enhancement. After preprocessing, the enhanced and unwrapped image is used to extract texture characterization features by employing the singular value decomposition (SVD).

42 33 Figure Sample illumination pattern of a normalized unwrapped image Figure Enhanced unwrapped image after illumination subtraction

43 34 Chapter 4. Singular Value Decomposition of Iris Biometrics 4.1 The Singular Value Decomposition The singular value decomposition (SVD) is a linear transform used often in pattern recognition because it possesses good information packing characteristics [9]. In addition, the SVD is considered to be more resistant to small changes in a matrix, as opposed to using only the eigenvalues, which can change significantly when the matrix is altered [16]. This characteristic also contributes to it being less susceptible to noise as described in [12]. This is ideal for pattern characterization since there almost certainly will be small variations among the images that are used. Care should be used when dealing with the SVD, for as mentioned in [17], some of its applications rely on inconsistent assumptions about dimensionality. In the case of this thesis, however, the SVD is performed on a dimensionless matrix (consisting of only numbers), so its application is valid as described in [17]. The SVD has been used for texture characterization and image restoration in [18], in addition to its use for facial recognition in [23]. For a matrix with elements that are spatially unrelated [18], the singular values will be of similar magnitudes. However, if they are related, the singular values will decrease in size along the SVD from lower order to higher order singular values [18]. In the case of feature extraction for iris images as presented in this chapter, it was found that lower order singular values are much larger than those of higher order. Since the approximation error for an image is simply the sum

44 35 of all unused singular values [9], removing the higher order values will not significantly reduce the approximation accuracy. The SVD has also proven useful for purposes of image compression as outlined in [20] and [21]. In both methods presented, a large amount of image data could be reduced significantly without losing much appreciable image quality. This seems to indicate that the SVD is of particular interest in extracting spatially important data from an image matrix, making it ideal for feature generation. To define the SVD, it is useful to first define eigenvalues and eigenvectors. A nonzero vector x can be defined as an eigenvector of a square matrix A if there exists a scalar value λ (known as an eigenvalue) such that [13] Ax = λx (4.1) Beginning with an M x N matrix X, it can be shown that there is an M x M unitary matrix U and an N x N unitary matrix V such that [9] X 1/ Λ = U O 2 O V 0 H or Y 1/ Λ O 2 O = U 0 H XV (4.2)

45 where 1/ 2 Λ is an r x r diagonal matrix with elements λi 1/2, and λ i is the i th nonzero 36 eigenvalue of the matrix X H X. H refers to the Hermitian operation of complex conjugation and transposition of a matrix [9], and O represents a zero element matrix. In the case of this work, the Hermitian operation can be replaced by transposition since only real vales are being used. By further working with (4.2), we can reconstruct X with [9] r 1 = 1/ 2 H X λ i uivi (4.3) = 0 i where u i and v i are the first r columns of U and V, respectively, as shown in [9]. This means that u i is an eigenvector for XX H and v i is an eigenvector for X H X. The subsequent eigenvalues λ i are thus known as singular values, and the matrix X can be reconstructed to varying levels of accuracy with different values for r [9] by using the algorithm presented in (4.3).

46 Feature Extraction with the SVD After performing image preprocessing and iris localization, features are extracted from the iris for the purpose of identification. For each unwrapped and enhanced image, the singular value decomposition is performed on a range of horizontal lines in the unwrapped imaged, and the singular values are stored as a vector. The optimal horizontal sampling range was determined in experiments. Initially, only one image was selected to generate the feature vectors used for classification. This method is flawed, however, because there still tend to be some variations in the calculated SVD that produced spurious results and hindered classification. When this was attempted, a recognition rate of only about 55% was achieved. In an attempt to improve classification accuracy, an approach was implemented using averaging. Because the CASIA database [7] is divided into images from two different sessions, it was deemed appropriate to generate a feature vector from each session. The SVD was again calculated separately for each image, while the feature vector was created by finding the average of the singular values along each dimension from several images. Each value was converted to an integer using rounding in order to reduce the total amount of space required for storing each iris signature. Based on the nature of the SVD, higher order singular values are smaller in magnitude than those of lower order [18], and an optimal approximation can be achieved with a mean square error equal only to the sum of all singular values not included. During this phase of testing, it was determined

47 38 that only the first 15 singular values were necessary. Table 1 summarizes the iris signature s size and storage requirements. The first row indicates the index of the singular value, with the second row showing the maximum integer value encountered during testing. The third row then shows the number of bits that would be required to represent each of these maximum values. Summing these indicates that 133 bits would be required for the iris representation using this method. Table 4.1. SVD integer storage requirements SVD Index Max Value Bits Required

48 Classification Performance with the SVD After features were generated using the SVD, classification was implemented by calculating the Euclidean distances between a test set and each training feature vector. This distance was minimized, and the image was included in the class it was nearest to in the feature space. In the case of this experiment, the images from the first session in the CASIA database [7] were used to create the feature vectors for the training section, and the pictures from the second session were used for testing purposes. This seemed to be the best use of the available images to effectively simulate a real-world situation. The ability of the system to correctly identify an iris was impacted by several factors that will be outlined here. Testing was conducted using 18 different subjects comprising a total of 125 available iris images. In each case, the average intraclass and interclass distances were calculated, as well as the classification performance, η, given by Number of correct classifications η = (4.4) Total number of comparisons The selection of the outer radius of the iris was the first major factor in determining how well the system would work. It was desired that the value would allow for a large amount of information to be extracted, but it was also important to not include too much of the surrounding eyelid or eyelashes. Figure 4.1 shows the system performance with different multiplying values for the outer radius. Figures 4.2 and 4.3

49 40 show the average between class and within class distances for different radius multipliers, respectively. By examining Figure 4.1, it can be determined that, once the multiplier is around 1.25, the performance reaches an 83% correct recognition rate. As was expected, a multiplier very close to 1 yielded poor results because very little information was contained in the region used. Additionally, Figures 4.2 and 4.3 indicate that a radius near 1.25 yields higher confidence recognition since the classes are better clustered and separated. Increasing the radius multiplier any further tended to include too much of the surrounding eyelid and other areas. Figure 4.1. Classification performance (η) with different radius multipliers

50 Figure 4.2. Between class distances with different radius multipliers 41

51 42 Figure 4.3. Within class distances using different radius multipliers The number of images used for feature generation was also explored to determine its effect on the system s performance. Figure 4.4 shows the classification performance of the system with various numbers of images used for both the training and testing sections of the experiment. Figures 4.5 and 4.6 show the within class and between class distances, respectively. From Figure 4.4, it is clear that using more images will yield better performance that eventually reaches a maximum of 83%. If only one image is used for the test and control signatures, we find that the correct identification rate drops to around This data indicates that even more images would likely produce better results. By inspecting

52 43 Figure 4.5, it can be seen that the clustering of classes also improves with a larger number of images being used. However, the average between class distance as shown in Figure 4.6 changes very little. This is possibly because of the mostly random nature of the textures being characterized. Figure 4.4. Classification performance (η) using different numbers of iris images

53 Figure 4.5. Average intraclass distance using different numbers of images 44

54 45 Figure 4.6. Average between class distance using different numbers of images The use of image enhancement also had a significant positive effect on the ability of the system to correctly identify an iris. Without correcting for illumination differences, the system was only able to correctly identify an iris with 61.11% accuracy. In addition, the average between class distance became 1,895 and the within class distance increased to approximately 240. This seems to be a clear indicator that the use of image enhancement to correct for illumination differences is vital for accurate identification. Finally, the number of singular values used for the feature vector was explored to determine how many were needed to provide optimal recognition results. Because the singular values decrease in magnitude along the SVD (see Table 1), many with smaller

55 46 magnitudes can be omitted without appreciably decreasing the system s overall performance. Figure 4.7 depicts the system s recognition performance with different numbers of singular values. Figures 4.8 and 4.9 illustrate the intraclass and interclass separation, respectively, with different numbers of singular values. By examining Figure 4.7, it can be noted that the recognition rate does not improve when using any more than 15 singular values. This is also the limit where the average inter- and intraclass separations cease to change considerably. Figure 4.7. Performance with varying numbers of singular values

56 47 Figure 4.8. Average intraclass distance with varying numbers of singular values Figure 4.9. Average interclass separation with different numbers of singular values

57 Future Improvements The iris identification system that has been presented certainly allows room for improvement in several areas such as preprocessing, iris localization, and feature generation. In the preprocessing stage, the system still had some difficulty identifying the true center of the pupil if there were a large number of very dark eyelashes. A sample cropped image that was created with an incorrectly located pupil is shown in Figure An improved method for pupil location could help to remedy this issue. In addition, some type of filtering to reduce the appearance of the eyelashes may also be useful. It should be noted that its effect on classification performance must be considered since it would affect the spatial gray level properties of the iris as well. Figure Incorrectly located pupil

58 49 Another consideration for improvement is the location and unwrapping of the iris. In some instances, the unwrapped image will include too many pixels from the pupil or the surrounding parts of the eye. This falls in line with an incorrect determination of the pupil s location. Performance is affected by the introduction of spurious pixels to the calculation of the SVD and reducing the ability of the system to make a correct identification. An image with too much of the area surrounding the iris (the conjunctiva) [8] is shown in Figure In the current work, this was corrected for by simply selecting a range of the unwrapped image instead of using it in its entirety for feature generation. An improvement of this method could be very beneficial to improving recognition accuracy. Figure Unwrapped image including too much conjunctiva.

59 50 Image quality assessment is also a useful addition that could be made to this approach. In the work of [5], a discussion is presented that outlines an approach for ensuring that an iris is properly in focus and suitable for feature extraction. This method involves searching for three main categories of unsuitable images: those that are out of focus, those that are blurred because of movement, and those that have too much occlusion from the eyelid or eyelashes [5]. By examining the image with a quality descriptor that uses the 2-D Fourier transform, it is possible to look for key frequency ranges that indicate the presence of these types of images. In the work presented by [1], a 2-D Fourier transform is also used, and frequencies in the upper and middle bands are assessed in real time to determine if the image is in focus [1]. Both of these approaches produce desirable results in determining image quality. Finally, another performance enhancement to be considered involves feature generation. The singular value decomposition has shown itself to be a useful tool for texture characterization. However, the recognition rates achieved with this system would have to be improved to make it an effective tool for identification. One way to improve this would be the use of more iris images for each feature vector, thus helping to remove the effects of a large variation in a single image. In addition, it may be helpful to compare each SVD to others from the same eye, discarding signatures that are found to be beyond a previously determined tolerance. In this manner, it would be possible to further improve recognition performance while still allowing for a very small iris signature. Additionally, the use of multiple biometrics could be included as outlined in [24] to improve recognition rates.

60 51 While discussing the use of multiple images, it is also interesting to examine the use of principal component analysis (PCA) for feature extraction since it works for characterizing statistics based on a set of vectors. In the work presented in [15], the two dimensional PCA (2DPCA) is applied successfully for facial recognition purposes, making its use for iris recognition attractive. The use of the 2DPCA as a tool for improved feature extraction is discussed in Chapter 5.

61 52 Chapter 5. 2D Principal Component Analysis (2DPCA) of Iris Biometrics 5.1 The 2DPCA The two dimensional principal component analysis (2DPCA) has been used successfully to characterize facial characteristics in [15]. It can also be used for reconstruction of images to varying degrees of accuracy, much like the SVD. However, the 2DPCA analyzes groups of input samples as opposed to individual images. By applying a transformation matrix X to an input A, a new matrix Y results from [15] Y=AX (5.1) The matrix X is determined by using all available training samples from each class. First, the covariance matrix for the entire training set is determined by [15] G t M 1 = ( A M j= 1 j A) T ( A j A) (5.2) where G t is the square covariance matrix determined from M available images. A j is the jth image, and A is the mean image of the ensemble computed with [15]

62 53 A = 1 M M A j j= 1. (5.3) Upon determination of G t, its first N eigenvectors corresponding to the N largest eigenvalues are used to make up the transformation matrix X. This gives the optimal directions upon which to project the input A. Similar to the SVD, the number of eigenvectors used to create X directly influences reconstruction accuracy when performing the inverse transform. Since X is unitary,  can be reconstructed with  =YX T (5.4) If N is equal to the total number of available eigenvectors, then  =A, and a perfect reconstruction is achieved.

63 Feature Extraction with the 2DPCA As described in Chapter 4, the CASIA iris image database [7] contains seven iris images for each individual. The images are divided into two sessions, with three images corresponding to the first session and four belonging to the second. The first session was again used for training, and the second session was used for testing purposes. Testing was performed with the same 18 classes that were tested with the SVD implementation in Chapter 4. First, a transformation matrix X is computed by finding the mean image and covariance matrix from all training samples as outlined in (5.2) and (5.3). The eigenvectors for the N largest eigenvalues of X were then used to create the transformation matrix. This matrix was then applied to each training image to yield Y k,l where k is the class, and l is the corresponding image number ranging from one to three. For each test sample, four images are available. The transformation matrix X is applied to each test image to yield W m, where m is the image number from one to four. Classification is performed by finding the Euclidean distance (DE) from W m to each Y k,l, and placing the test sample in the class where the distance is minimized.

64 Classification Performance with the 2DPCA Like the SVD implementation discussed in Chapter 4, experiments were conducted by altering parameters to optimize the system s performance. Maximizing classification performance as defined in (4.4) is the main consideration, but grouping and separation of classes is also discussed here. A factor that had a huge impact on performance was the use of illumination compensation in the unwrapped image as discussed in Chapter 3. When illumination correction was included, the classification performance dropped to below 20%. It is likely that, since the 2DPCA relies on the covariance matrix, any steps that significantly alter the mean gray scale value will have a catastrophic effect on performance. Without correcting for illumination, the maximum classification accuracy was found to be 89%. The radius multiplier for determining the outer iris boundary was explored. Once again it was desired that the region contained by the boundaries would contain as much useful information as possible. Figure 5.1 shows classification performance with different radius multipliers. Figures 5.2 and 5.3 show average intraclass and interclass separation, respectively. It is clear from Figure 5.1 that a radius multiplier of 1.4 yields the best performance of about 89%. This is also the point that seems to minimize the within class distances as demonstrated in Figure 5.2.

65 Figure 5.1. Classification performance with different radius multipliers 56

66 57 Figure 5.2. Average intraclass distance with different radius multipliers Figure 5.3. Average interclass distances with different radius multipliers Another factor to consider was the number of eigenvectors to include in the transformation matrix X. It is useful to optimize this value not only to decrease storage requirements, but also to reduce the computational complexity associated with finding the matrix transforms. Figure 5.4 shows classification performance as a function of the number of eigenvectors used to form X. Figures 5.5 and 5.5 show average class grouping and separation versus different numbers of eigenvectors, respectively. It is clear from Figure 5.4 that using any more than 64 eigenvectors in X will not yield any improvement in performance.

67 Figure 5.4. Classification performance with different numbers of Eigenvectors 58

68 Figure 5.5. Average intraclass distance with different numbers of Eigenvectors 59

69 Figure 5.6. Average interclass distance with different numbers of Eigenvectors 60

70 61 Chapter 6. Conclusions and Discussion Biometrics are powerful tools for human identification that have a wide range of applications. In comparison to more conventional security systems that use a password or keycard, biometrics are difficult to lose, forget, or forge. Research has been conducted on the use of biometrics that include facial characteristics, hand geometry, retinal blood vessel patterns, fingerprints, speech and voice patterns, gait, and iris features [24]. Several novel approaches to iris classification have been investigated and reported in this thesis. A wide sense stationary approximation was first attempted by using the auto- and cross-correlation. Following that, more robust preprocessing steps were implemented to more accurately locate the iris and its boundaries. The steps outlined in [3,4,5] for iris unwrapping and image enhancement were also repeated successfully to aid in image normalization and enhancement. In comparison to the other methods that have been reported, one approach outlined in this thesis has the advantage of requiring very few bits to achieve the results reported. By using only 133 bits, the SVD based system described in Chapter 4 is able to correctly identify an iris 83% of the time. This employs far fewer bits than the system presented by Daugman [1,2], which uses a total of 2048 identification bits and 2048 masking bits. However, that method is able to achieve a nearly 100% recognition rate. This leaves considerable room to investigate increasing the dimensionality of the feature space to improve system performance. In the method presented in [5], 200 features are used, but the storage requirements of these features were not discussed. The recognition accuracy of this approach was 99.43%. When using the 2DPCA based approach

71 62 presented in Chapter 5, a significant performance increase was observed as the recognition accuracy jumped to 89%. It is expected that more image samples would further improve these results. However, the storage requirements associated with the 2DPCA are greater than those of the SVD. One possibility may be to use the SVD in conjunction with the 2DPCA to further reduce the storage requirements of the system while still providing a high classification accuracy. Both the SVD and 2DPCA also have the distinction of being very different from the wavelet transform methods employed in [1,2,3,4,5,6]. The iris as a biometric is attractive because it is well protected, has a very complex structure, and changes very little over time. Several new methods have been investigated that use the iris as a biometric identifier. The use of the SVD allows for very small storage requirements but is somewhat lacking in classification accuracy. The 2DPCA, however, has been shown to have a higher recognition accuracy, but with greater storage requirements. Both are novel approaches that have produced desirable results for iris recognition.

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75 66 Appendix A. Additional Images for four subjects Figure A.1 Original, boundary, and unwrapped images for subject 1

76 Figure A.2 Original, boundary, and unwrapped images for subject 2 67

77 Figure A.3 Original, boundary, and unwrapped images for subject 3 68