# A Synthetic Fusion Rule Based on FLDA and PCA for Iris Recognition Using 1D Log-Gabor Filter

Authors: Rachida Tobji; Wu Di; Naeem Ayoub
Journal: Mathematical Problems in Engineering
 (2019)

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## Abstract

Iris recognition is one of the most useful methods to identify or verify people in biometric recognition systems. Iris patterns contain many features that distinguish people from each other. In this paper, a novel iris recognition method is proposed based on the fusion of Fisher Linear Discriminate Analysis (FLDA) with embedding Principal Component Analysis (PCA) method. In this work, firstly we use 1D Log-Gabor to elicit the iris features from an approximation part. Secondly, we obtain an appropriate degree of clarity for the iris with fusion of FLDA/PCA to eliminate the optical reflections on the iris image. Experiments of our proposed algorithm are performed on the CASIA V1 database. The results of our proposed approach show a good performance with recognition rate up to 99.99%.


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## Body

## 1. Introduction

Recognition systems have become a role of the large and effective, especially after the progress that has occurred in the area of information technology. The biometric identification methods allow recognizing or verifying the identity of people with a higher degree of reliability [1]. The texture of the iris is remarkable for its ability to obtain systems with a very low error rate [2]. It was used for the first time in environments of high safety such as installations at high-risk nuclear power plants. However, this high level of performance can only be achieved at the cost of heavy restrictions imposed on the person in the course of acquisition [3, 4]. The prospects are to relax these constraints in order to make the systems more user-friendly, but the resulting image quality is strongly degraded due to blur and lighting variations. It has been shown that the use of particular information (shape of the eyelid, the inner corner of the eye, eyelashes…), in addition to the classic texture of the iris makes important improvements in this degraded context [5]. Figure 1 shows some examples of different contrast enhancement levels such as imadjust, clahe, and msr. For illustration, we have chosen one image from CASIA iris database V1.Figure 1
Different contrast enhancement levels: from left to right, original image, imadjust, clahe, and msr, respectively.The biometric authentication decision is based on a comparison between two irises. The texture must be transformed into a dimensionless coordinate system to handle variability such as pupil dilation. In the rubber sheet model introduced by Daugman [3], the two nonconcentric borders of iris and the texture were represented by a rectangle. The parametric contours of the iris region were used to unroll the texture of the iris to produce the normalized image. Finally, the identification of the pixels included in the iris image made it possible to generate a segmentation mask, which was used to remove artifacts from the normalized image at the mapping step.Most of the approaches for iris segmentation look for contours from a gradient active contouring technique [6, 7]. In 1936, for the first time, Frank Bruch [8] proposed the idea of using the texture information of iris. Dr. Leonard Flom et al. [9] proposed the idea of a difference between the iris patterns of two different people. For the first time, in 1987, the same authors proposed using iris identification methods to identify the people in biometric security systems. In 1991, Daugman, an ophthalmologist, proposed a mathematical model for people identification through iris patterns [10]. In 1994, Daugman introduced the complete method for iris recognition [11]. Daugman’s iris identification method is one of the most successful methods and is mostly used in iris identification systems [12]. Iris recognition systems are more successful for the people identification on border controls and highly sensitive areas. UAE is one of the top successful countries to use this biometric security system [10], as more than 3 billion comparisons are made each day with the no false acceptance being observed according to the officials of Ministry of Interior. Iris recognition methods are also adopted by other agencies to identify people like Daugman whose system was used to identify an Afghan photographed in 2002. The iris identification systems show the probability of correctness close to 100% in identifying the women [13]. Wildes et al. [14] constructed the iris texture with Laplacian pyramid with 4-level different resolutions. They used normalized correlation scheme to determine the similarity between the input images and model image. Lim et al. [15] proposed a new method for iris texture information extraction by decomposing the image into four levels with 2D Haar wavelet transformation. They quantized the high frequency to form 87-bit code. Bae et al. [16] used independent component analysis to derive iris signals and projected them onto a bank of basis vectors. They also used quantization method for the resultant coefficient as feature. Sepehr et al. [17] used the real term of 1D Gabor filter and reduced the dimensionality of the extracted features by 2D-PCA. Wen-Shiung et al. [18] presented a biometric iris recognition using 2D-LDA embedding with 2D-PCA and Euclidean distance to recognize the iris pattern by comparing the iris features with the iris features enrolled in the database. Fusion based techniques such as data-level fusion, features-level fusion, and features extraction-level fusion are also actively used in recognition and tracking algorithms [19]. Effective fusion of RGB and infrared modalities is very important for exploiting the correlation between the heterogeneous modalities [20, 21]. Lan et al. [22] proposed a joint sparse representation algorithm for feature-level fusion. In this method, feature-level fusion is performed on reliable features by ignoring the detected unreliable features.In this paper, a new PCA and Fisher LDA fusion based iris recognition by using 1D log-Gabor filter algorithm is developed.(1)
In our proposed method, to find an optimal transformation, we use FLDA method that utilizes the conventional Fisher criterion to minimize the within-class distance and maximize the between-class distance. Then feature vectors are formed by applying PCA on the approximation band.(2)
The eigenvectors of the covariance matrices computed by FLDA and PCA methods are fused into a single covariance matrix. The resultant fused matrix is then used to compute the eigenvectors for data projection.(3)
We integrate the pixels’ data multiplied by filters and coefficients over their support domain. Then the image texture information is extracted and encoded to mark the corrupted bits in the template by its associated noise mask of feature template.Remaining sections in this paper are organized as follows: related work is briefly discussed regarding iris biometric systems based on hamming distance with feature encoding schemes adopted by different researchers in Section2. Detailed description of iris recognition system components with preprocessing, that is, image acquisition, segmentation and normalization, feature extraction and encoding, and matching with proposed Iris detection method are discussed in Section 3. Experimental results and discussion are presented in Section 4. Finally, conclusion is made in Section 5.


## 2. Related Works

Many researchers have used different segmentation, analyzation, and characterization techniques in their iris detection methods. For the segmentation of the iris, two methods were commonly used: the integrodifferential operator [23] and the Hough transform [24–28]. For the characterization of the iris, the most useful methods are the Gabor wavelet transform applied by Daugman, the Gabor filter [24], the Laplacian pyramid [25], and orientable pyramid transform method [26]. We have studied various well-known algorithms for iris recognition [17, 18, 27, 29–35] and propose a new method for iris detection based on the fusion of FLDA/PCA. We also employ 1D Log-Gabor filter and used hamming distance for comparison between two iris templates. We have compared the results of our proposed iris recognition approach with state-of-the art algorithms.


### 2.1. Proposed Method

In this paper, we use a statistical method to account eyelashes [6]; we apply the feature extraction algorithm based on fusion of the FLDA and PCA on original image patches to compute the projection matrices. Based on these matrices’ information, the iris images can be analyzed to lower dimension. The recognition is done with the help of an iris matcher with 1D Log-Gabor filter features based on the hamming distance to uniquely identify iris. Figure 2 shows flow diagram of iris biometric system, which is described in detail in the following subsection. In our experiments, for the purpose of illustration, we use CASIA V1 database [36]. All images in this database are grayscale and the value of each pixel is a single sample.Figure 2
Flow diagram proposed iris biometric system.


### 2.2. Preprocessing

#### 2.2.1. Image Acquisition

The acquisition of an iris image is considered one of the most important parts in biometric systems. In the eye image, an iris is a dark object located behind the cornea, which is a highly reflective mirror. It is a very difficult object to make a photograph with all these characteristics. Once the image of the iris is acquired, an iris system can be composed of several modules comprising iris recognition: segmentation, normalization, and finally correction of light and contrast enhancement. For the illustration purpose, we use images from CASIA iris v1 database.


#### 2.2.2. Iris Segmentation

The image of the eye which is acquired does not only include the information of the iris. It is necessary to segment and isolate this information of the image from the rest. Segmentation process is based on isolating the iris from the white area of the eye and the eyelids, as well as detecting the pupil inside the disc of the iris. Generally, the iris and pupil are approximated by circles and eyelids by ellipses. We applied the Hough transform [25, 37, 38] which is a technique that can be used to isolate objects of simple geometric shapes in the image. In general, we limit ourselves to the lines, circles, or ellipses present in the image. Figure 3 shows the segmentation results of the iris image. One of the great advantages of the Hough transform is that it is tolerant to occlusions in the desired objects and remains relatively unaffected by noise. Figure 4 shows general diagram of an iris segmentation system.Figure 3
Example of segmentation of an iris image: (a) iris borders; (b) mask iris.
(a) (b)Figure 4
General diagram of an iris segmentation system.


#### 2.2.3. Iris Normalization

The iris is a disc pierced inside the pupil. The two circles that constitute the borders of the iris with the white area of the eye and the borders of the pupil with the iris are not perfectly concentric. In addition, with the contractions and dilations of the iris and the variation of the acquisition distances between people and the lens, the size of the disk of the iris is not always constant. To allow a comparison of two irises, it is therefore necessary to normalize the iris detected at a fixed size.For this, it is a question of transforming the region of the iris characterized by parametric outlines in a band of invariant size. Daugman [3] proposed using the rubber sheet transformation to make the transition from a Cartesian system to a pseudopolar system normalization of the disk of the iris whose pictorial meaning could be seen as an attempt to extend the disk of the iris like rubber sheet. The process can be explained as follows.Each pixel of the iris in the Cartesian domain is assigned by a correspondent bit in the pseudopolar domain according to the distance of the pixel from the centers of the circles and the angle. More precisely, the transformation is done as follows:(1)xr,θ=1-rxpθ+rxsθ(2)yr,θ=1-rypθ+rysθwhere xpθ represents the abscissa of the point of the detected boundary of the pupil segment that passes through and ypθ represents the ordinate of this same point and the center of the pupil that makes an angle θ with a chosen direction. Then xsθ and ysθ represent the coordinates of the points obtained by the same principle but on the contour of the iris. The normalized image is rectangular of constant with the size of 80 ×512 pixels. The width of the image represents the variation on the angular axis, while the height represents the variations on the radial axis. Figure 5 shows illustration of the iris normalization module.Figure 5
Illustration of the task of the iris normalization module: (a) standardization; (b) rubber sheet transformation [35].
(a)
Standardization (b)
Rubber sheet transformation


#### 2.2.4. Iris Enhancement

In this step, homomorphic filter is used for iris image enhancement. To apply this filter, first, we reduced the contribution of illumination using the illumination-reflectance model [39]. By using this technique, an image ix,y can be expressed as the product of the amount of illumination reflected by the objects in the scene and the illumination component as follows:(3)ix,y=rx,y∗lx,ywhere rx,y and lx,y are the reflectance component and the illumination component, respectively.Homomorphic filtering is used to enhance the reflectance and reduce the contribution (only high frequencies) of illumination retaining. However, the two components should be independent. In order to separate them, we applied the logarithm transform on (3) as follows:(4)Sx,y=log⁡ix,y=ln⁡rx,y+ln⁡lx,yThen, the Fourier transform R is applied:(5)RSx,y=Rln⁡rx,y+Rln⁡lx,yEquation (5) can be written as(6)Su,v=FRu,v+FLu,vwhere FRu,v and FLu,v represent the Fourier transforms of ln⁡rx,y and ln⁡lx,y, respectively. In the frequency domain, Su,v represents the high passed by means of a filter function Hu,v [40]. The filtered version Pu,v can be calculated as follows:(7)Pu,v=Su,v∗Hu,v(8)Pu,v=Hu,v∗FRu,v+Hu,v∗FLu,vThen we take the inverse Fourier transform of (8):(9)Sx,y=R-1Su,vBy applying the exponential operation on Sx,y, we obtained the filtered image i′x,y:(10)i′x,y=exp⁡Sx,yFinally, we calculated the high pass filter as follows:(11)Hu,v=11+D0/Du,v2nwhere D0 is the cutoff distance from the center andn defines the order of the filter. D(u,v) is given by(12)Du,v=u-M22+v-N221/2where M is the number of rows and N is the number of columns of the original image. Figure 6 shows the homomorphic filtering process.Figure 6
Flowchart of homomorphic filter.Algorithm1 and Figure 7 show the procedure of iris preprocessing.Algorithm 1:Preprocessing.
(1)  Function Pre-Processing(images) (2) Pre-Processed ←[] (3) forimage ∈ images do (4) eyes ← crop-to-eyes(image) (5) eyes ← greyscale(eyes) (6) eyes ← segmentation(eyes) (7) iris ←detectioniris(eyes) (8) iris ←normalization(iris) (9) enhancement ← Homomorphic-filter(iris) (10) Pre-Processed ←PreProcessed ∪ enhancement (11) return Pre-ProcessingFigure 7
(a) The original image. (b) Segmentation. (c) Normalization. (d) Removal of eyelashes and eyelids. (e) Enhancement.
(a) (b) (c) (d) (e)


## 2.1. Proposed Method

In this paper, we use a statistical method to account eyelashes [6]; we apply the feature extraction algorithm based on fusion of the FLDA and PCA on original image patches to compute the projection matrices. Based on these matrices’ information, the iris images can be analyzed to lower dimension. The recognition is done with the help of an iris matcher with 1D Log-Gabor filter features based on the hamming distance to uniquely identify iris. Figure 2 shows flow diagram of iris biometric system, which is described in detail in the following subsection. In our experiments, for the purpose of illustration, we use CASIA V1 database [36]. All images in this database are grayscale and the value of each pixel is a single sample.Figure 2
Flow diagram proposed iris biometric system.


## 2.2. Preprocessing

### 2.2.1. Image Acquisition

The acquisition of an iris image is considered one of the most important parts in biometric systems. In the eye image, an iris is a dark object located behind the cornea, which is a highly reflective mirror. It is a very difficult object to make a photograph with all these characteristics. Once the image of the iris is acquired, an iris system can be composed of several modules comprising iris recognition: segmentation, normalization, and finally correction of light and contrast enhancement. For the illustration purpose, we use images from CASIA iris v1 database.


### 2.2.2. Iris Segmentation

The image of the eye which is acquired does not only include the information of the iris. It is necessary to segment and isolate this information of the image from the rest. Segmentation process is based on isolating the iris from the white area of the eye and the eyelids, as well as detecting the pupil inside the disc of the iris. Generally, the iris and pupil are approximated by circles and eyelids by ellipses. We applied the Hough transform [25, 37, 38] which is a technique that can be used to isolate objects of simple geometric shapes in the image. In general, we limit ourselves to the lines, circles, or ellipses present in the image. Figure 3 shows the segmentation results of the iris image. One of the great advantages of the Hough transform is that it is tolerant to occlusions in the desired objects and remains relatively unaffected by noise. Figure 4 shows general diagram of an iris segmentation system.Figure 3
Example of segmentation of an iris image: (a) iris borders; (b) mask iris.
(a) (b)Figure 4
General diagram of an iris segmentation system.


### 2.2.3. Iris Normalization

The iris is a disc pierced inside the pupil. The two circles that constitute the borders of the iris with the white area of the eye and the borders of the pupil with the iris are not perfectly concentric. In addition, with the contractions and dilations of the iris and the variation of the acquisition distances between people and the lens, the size of the disk of the iris is not always constant. To allow a comparison of two irises, it is therefore necessary to normalize the iris detected at a fixed size.For this, it is a question of transforming the region of the iris characterized by parametric outlines in a band of invariant size. Daugman [3] proposed using the rubber sheet transformation to make the transition from a Cartesian system to a pseudopolar system normalization of the disk of the iris whose pictorial meaning could be seen as an attempt to extend the disk of the iris like rubber sheet. The process can be explained as follows.Each pixel of the iris in the Cartesian domain is assigned by a correspondent bit in the pseudopolar domain according to the distance of the pixel from the centers of the circles and the angle. More precisely, the transformation is done as follows:(1)xr,θ=1-rxpθ+rxsθ(2)yr,θ=1-rypθ+rysθwhere xpθ represents the abscissa of the point of the detected boundary of the pupil segment that passes through and ypθ represents the ordinate of this same point and the center of the pupil that makes an angle θ with a chosen direction. Then xsθ and ysθ represent the coordinates of the points obtained by the same principle but on the contour of the iris. The normalized image is rectangular of constant with the size of 80 ×512 pixels. The width of the image represents the variation on the angular axis, while the height represents the variations on the radial axis. Figure 5 shows illustration of the iris normalization module.Figure 5
Illustration of the task of the iris normalization module: (a) standardization; (b) rubber sheet transformation [35].
(a)
Standardization (b)
Rubber sheet transformation


### 2.2.4. Iris Enhancement

In this step, homomorphic filter is used for iris image enhancement. To apply this filter, first, we reduced the contribution of illumination using the illumination-reflectance model [39]. By using this technique, an image ix,y can be expressed as the product of the amount of illumination reflected by the objects in the scene and the illumination component as follows:(3)ix,y=rx,y∗lx,ywhere rx,y and lx,y are the reflectance component and the illumination component, respectively.Homomorphic filtering is used to enhance the reflectance and reduce the contribution (only high frequencies) of illumination retaining. However, the two components should be independent. In order to separate them, we applied the logarithm transform on (3) as follows:(4)Sx,y=log⁡ix,y=ln⁡rx,y+ln⁡lx,yThen, the Fourier transform R is applied:(5)RSx,y=Rln⁡rx,y+Rln⁡lx,yEquation (5) can be written as(6)Su,v=FRu,v+FLu,vwhere FRu,v and FLu,v represent the Fourier transforms of ln⁡rx,y and ln⁡lx,y, respectively. In the frequency domain, Su,v represents the high passed by means of a filter function Hu,v [40]. The filtered version Pu,v can be calculated as follows:(7)Pu,v=Su,v∗Hu,v(8)Pu,v=Hu,v∗FRu,v+Hu,v∗FLu,vThen we take the inverse Fourier transform of (8):(9)Sx,y=R-1Su,vBy applying the exponential operation on Sx,y, we obtained the filtered image i′x,y:(10)i′x,y=exp⁡Sx,yFinally, we calculated the high pass filter as follows:(11)Hu,v=11+D0/Du,v2nwhere D0 is the cutoff distance from the center andn defines the order of the filter. D(u,v) is given by(12)Du,v=u-M22+v-N221/2where M is the number of rows and N is the number of columns of the original image. Figure 6 shows the homomorphic filtering process.Figure 6
Flowchart of homomorphic filter.Algorithm1 and Figure 7 show the procedure of iris preprocessing.Algorithm 1:Preprocessing.
(1)  Function Pre-Processing(images) (2) Pre-Processed ←[] (3) forimage ∈ images do (4) eyes ← crop-to-eyes(image) (5) eyes ← greyscale(eyes) (6) eyes ← segmentation(eyes) (7) iris ←detectioniris(eyes) (8) iris ←normalization(iris) (9) enhancement ← Homomorphic-filter(iris) (10) Pre-Processed ←PreProcessed ∪ enhancement (11) return Pre-ProcessingFigure 7
(a) The original image. (b) Segmentation. (c) Normalization. (d) Removal of eyelashes and eyelids. (e) Enhancement.
(a) (b) (c) (d) (e)


## 2.2.1. Image Acquisition

The acquisition of an iris image is considered one of the most important parts in biometric systems. In the eye image, an iris is a dark object located behind the cornea, which is a highly reflective mirror. It is a very difficult object to make a photograph with all these characteristics. Once the image of the iris is acquired, an iris system can be composed of several modules comprising iris recognition: segmentation, normalization, and finally correction of light and contrast enhancement. For the illustration purpose, we use images from CASIA iris v1 database.


## 2.2.2. Iris Segmentation

The image of the eye which is acquired does not only include the information of the iris. It is necessary to segment and isolate this information of the image from the rest. Segmentation process is based on isolating the iris from the white area of the eye and the eyelids, as well as detecting the pupil inside the disc of the iris. Generally, the iris and pupil are approximated by circles and eyelids by ellipses. We applied the Hough transform [25, 37, 38] which is a technique that can be used to isolate objects of simple geometric shapes in the image. In general, we limit ourselves to the lines, circles, or ellipses present in the image. Figure 3 shows the segmentation results of the iris image. One of the great advantages of the Hough transform is that it is tolerant to occlusions in the desired objects and remains relatively unaffected by noise. Figure 4 shows general diagram of an iris segmentation system.Figure 3
Example of segmentation of an iris image: (a) iris borders; (b) mask iris.
(a) (b)Figure 4
General diagram of an iris segmentation system.


## 2.2.3. Iris Normalization

The iris is a disc pierced inside the pupil. The two circles that constitute the borders of the iris with the white area of the eye and the borders of the pupil with the iris are not perfectly concentric. In addition, with the contractions and dilations of the iris and the variation of the acquisition distances between people and the lens, the size of the disk of the iris is not always constant. To allow a comparison of two irises, it is therefore necessary to normalize the iris detected at a fixed size.For this, it is a question of transforming the region of the iris characterized by parametric outlines in a band of invariant size. Daugman [3] proposed using the rubber sheet transformation to make the transition from a Cartesian system to a pseudopolar system normalization of the disk of the iris whose pictorial meaning could be seen as an attempt to extend the disk of the iris like rubber sheet. The process can be explained as follows.Each pixel of the iris in the Cartesian domain is assigned by a correspondent bit in the pseudopolar domain according to the distance of the pixel from the centers of the circles and the angle. More precisely, the transformation is done as follows:(1)xr,θ=1-rxpθ+rxsθ(2)yr,θ=1-rypθ+rysθwhere xpθ represents the abscissa of the point of the detected boundary of the pupil segment that passes through and ypθ represents the ordinate of this same point and the center of the pupil that makes an angle θ with a chosen direction. Then xsθ and ysθ represent the coordinates of the points obtained by the same principle but on the contour of the iris. The normalized image is rectangular of constant with the size of 80 ×512 pixels. The width of the image represents the variation on the angular axis, while the height represents the variations on the radial axis. Figure 5 shows illustration of the iris normalization module.Figure 5
Illustration of the task of the iris normalization module: (a) standardization; (b) rubber sheet transformation [35].
(a)
Standardization (b)
Rubber sheet transformation


## 2.2.4. Iris Enhancement

In this step, homomorphic filter is used for iris image enhancement. To apply this filter, first, we reduced the contribution of illumination using the illumination-reflectance model [39]. By using this technique, an image ix,y can be expressed as the product of the amount of illumination reflected by the objects in the scene and the illumination component as follows:(3)ix,y=rx,y∗lx,ywhere rx,y and lx,y are the reflectance component and the illumination component, respectively.Homomorphic filtering is used to enhance the reflectance and reduce the contribution (only high frequencies) of illumination retaining. However, the two components should be independent. In order to separate them, we applied the logarithm transform on (3) as follows:(4)Sx,y=log⁡ix,y=ln⁡rx,y+ln⁡lx,yThen, the Fourier transform R is applied:(5)RSx,y=Rln⁡rx,y+Rln⁡lx,yEquation (5) can be written as(6)Su,v=FRu,v+FLu,vwhere FRu,v and FLu,v represent the Fourier transforms of ln⁡rx,y and ln⁡lx,y, respectively. In the frequency domain, Su,v represents the high passed by means of a filter function Hu,v [40]. The filtered version Pu,v can be calculated as follows:(7)Pu,v=Su,v∗Hu,v(8)Pu,v=Hu,v∗FRu,v+Hu,v∗FLu,vThen we take the inverse Fourier transform of (8):(9)Sx,y=R-1Su,vBy applying the exponential operation on Sx,y, we obtained the filtered image i′x,y:(10)i′x,y=exp⁡Sx,yFinally, we calculated the high pass filter as follows:(11)Hu,v=11+D0/Du,v2nwhere D0 is the cutoff distance from the center andn defines the order of the filter. D(u,v) is given by(12)Du,v=u-M22+v-N221/2where M is the number of rows and N is the number of columns of the original image. Figure 6 shows the homomorphic filtering process.Figure 6
Flowchart of homomorphic filter.Algorithm1 and Figure 7 show the procedure of iris preprocessing.Algorithm 1:Preprocessing.
(1)  Function Pre-Processing(images) (2) Pre-Processed ←[] (3) forimage ∈ images do (4) eyes ← crop-to-eyes(image) (5) eyes ← greyscale(eyes) (6) eyes ← segmentation(eyes) (7) iris ←detectioniris(eyes) (8) iris ←normalization(iris) (9) enhancement ← Homomorphic-filter(iris) (10) Pre-Processed ←PreProcessed ∪ enhancement (11) return Pre-ProcessingFigure 7
(a) The original image. (b) Segmentation. (c) Normalization. (d) Removal of eyelashes and eyelids. (e) Enhancement.
(a) (b) (c) (d) (e)


## 3. Feature Extraction and Encoding

### 3.1. FLDA/PCA

In previous works, many feature extraction algorithms have been proposed; in this section, we describe our FLDA/PCA fusion based iris feature extraction scheme.FLDA utilizes the conventional Fisher criterion and minimizing the within-class distance and maximizing the between-class distance to find an optimal transformation, accepting that there areC training classes;N = 64 × 256. The within-class matrix and the between-class matrix are calculated in order as(13)GW=∑i=1C∑xK∈XixK-μi∗xK-μiT(14)GB=∑i=1CNiμi-μ∗μi-μTwhere Ni describes number of samples class of Xi and μi means image of class Xi. GW is selected in the nonsingular optimal projection Mopt as the matrix that maximizes the ratio of the between-class scatter matrix of projection samples; the determinant of the within-class scatter matrix of the projection samples is defined as(15)Mopt=arg⁡maxMMTGBMMTGMM=M1,M2,…,Mm(16)GBMi=λiGWMiwhere {Mi/i=1,2,…m} is the set of generalized eigenvectors of GB and GW and {λi/i=1,2,…m} are eigenvalues for the advantage of class-specific linear projection. The trace of GW and GB can be defined in mathematical form as follows:(17)traceGW=∑i=1C∑xKϵXixK-μi22(18)traceGB=∑i=1CNiμi-μ22Hence, by trace of GWandGB, it can be calculated as(19)FW=traceWGWWT-1WGBWTFor finding the optimal transformation W, we should maximized trace (WGWWT) and minimize (WGBWT) which is represented as FW. The result can be calculated as follows:(20)∂FW∂W=0To solve this equation, we apply the PCA to the matrix GW-1GB.The recognition rates are achieved with eigenmethod for dimensionality reduction and simple classifiers are used in the reduced features space by applying specific linear methods [41]. The training of iris detector by PCA is presented as the following steps:(1)
Define the mean of the input eyes images.(2)
Obtain the mean-shifted images by subtracting the mean from the input images.(3)
Calculate and determinate the eigenvectorsMi and eigenvalues λi of the mean-shifted images of HbT∗Hb with λi≠0, Db=diagramλ1,λ2,…λm, and Hb=Ni(μi-μ)…NC(μi-μ)(4)
Order the eigenvectors in decreasing order by their corresponding eigenvalues.(5)
Retain only the largest eigenvalues with the eigenvectors.(6)
Use the retained eigenvectors for a project of the mean-shifted images into the eigenspace.(7)
AllowZ=U∗Db-1/2 to compute the eigenvectors and eigenvalues of ZTSWZ.(8)
Let A=UTZT where it gives transforming space Dw-1/2∗A.(9)
The iris image is presented by iris image code as (X) whereX=Dw-1/2∗A∗xK.(10)
Finally reduce the data dimension using 1D Log-Gabor.


### 3.2. 1D Log-Gabor

The purpose of this step is to extract a characteristic and discriminating representation of the iris and to produce a template for verification in the pattern comparison step. In general, the main existing methods in the literature use the 1D Log-Gabor filter [27, 42, 43], the 2D Gabor filter [3, 6, 44, 45], the wavelet transform [46–48], or the discretionary cosine transform [49]. A comparative study of the different extraction filters of iris characteristics reported in the literatures has been proposed to identify their impact on iris recognition. This study showed that the Log-Gabor filter provides the best recognition performance.Log-Gabor filter is used to create the templates based on information of iris pattern in feature encoding step [50]. Difference between the pixel-intensity levels represents the difference between two iris mages and error that occurred while comparing lighting. To overcome this issue, Daugman [11] used normalization method and extracted features from iris image by convolution with 1D Log-Gabor filter. 1D Log-Gabor filter can be calculated as follows:(21)GX,y=e-log⁡radius/f02/2∗log⁡sigmaOnf2In this method, pixels data multiplied by filters and coefficients are generated by integrating them over their support domain. The image texture information is extracted and encoded to mark the corrupted bits in the template by its associated noise mask of feature template.


### 3.3. Matching

Iris recognition involves mapping between two iris codes. A dissimilarity score is calculated to characterize the degree of resemblance or not between two iris code. The matching algorithm consists of score which is calculated by means of the hamming distance by (22). This distance is expressed by the XOR operator noted ⊕ and the logical operator AND noted ∩. This similarity score represents the number of unmasked bits different between the two iris codes normalized by the number of unmasked bits common to both iris codes.(22)HD=CodeA⊕CodeB∩MaskA∩MaskBMaskA∩MaskBwhere CodeA and CodeB are two codes computed from two iris images by the method previously described and MaskA and MaskB represent their associated masks. Literally, the hamming distance calculates the number of different and valid bits for both iris images between CodeA and CodeB, which contain 20∗480=9600 template bits and 20∗480=9600 mask bits, respectively. The total number of comparisons is represented by MaskA∩MaskB. The lower the hamming distance is, the more similar the two codes are. A distance0 corresponds to a perfect match between the two images, whereas two images of different people will have a hamming distance close to 0.5.


## 3.1. FLDA/PCA

In previous works, many feature extraction algorithms have been proposed; in this section, we describe our FLDA/PCA fusion based iris feature extraction scheme.FLDA utilizes the conventional Fisher criterion and minimizing the within-class distance and maximizing the between-class distance to find an optimal transformation, accepting that there areC training classes;N = 64 × 256. The within-class matrix and the between-class matrix are calculated in order as(13)GW=∑i=1C∑xK∈XixK-μi∗xK-μiT(14)GB=∑i=1CNiμi-μ∗μi-μTwhere Ni describes number of samples class of Xi and μi means image of class Xi. GW is selected in the nonsingular optimal projection Mopt as the matrix that maximizes the ratio of the between-class scatter matrix of projection samples; the determinant of the within-class scatter matrix of the projection samples is defined as(15)Mopt=arg⁡maxMMTGBMMTGMM=M1,M2,…,Mm(16)GBMi=λiGWMiwhere {Mi/i=1,2,…m} is the set of generalized eigenvectors of GB and GW and {λi/i=1,2,…m} are eigenvalues for the advantage of class-specific linear projection. The trace of GW and GB can be defined in mathematical form as follows:(17)traceGW=∑i=1C∑xKϵXixK-μi22(18)traceGB=∑i=1CNiμi-μ22Hence, by trace of GWandGB, it can be calculated as(19)FW=traceWGWWT-1WGBWTFor finding the optimal transformation W, we should maximized trace (WGWWT) and minimize (WGBWT) which is represented as FW. The result can be calculated as follows:(20)∂FW∂W=0To solve this equation, we apply the PCA to the matrix GW-1GB.The recognition rates are achieved with eigenmethod for dimensionality reduction and simple classifiers are used in the reduced features space by applying specific linear methods [41]. The training of iris detector by PCA is presented as the following steps:(1)
Define the mean of the input eyes images.(2)
Obtain the mean-shifted images by subtracting the mean from the input images.(3)
Calculate and determinate the eigenvectorsMi and eigenvalues λi of the mean-shifted images of HbT∗Hb with λi≠0, Db=diagramλ1,λ2,…λm, and Hb=Ni(μi-μ)…NC(μi-μ)(4)
Order the eigenvectors in decreasing order by their corresponding eigenvalues.(5)
Retain only the largest eigenvalues with the eigenvectors.(6)
Use the retained eigenvectors for a project of the mean-shifted images into the eigenspace.(7)
AllowZ=U∗Db-1/2 to compute the eigenvectors and eigenvalues of ZTSWZ.(8)
Let A=UTZT where it gives transforming space Dw-1/2∗A.(9)
The iris image is presented by iris image code as (X) whereX=Dw-1/2∗A∗xK.(10)
Finally reduce the data dimension using 1D Log-Gabor.


## 3.2. 1D Log-Gabor

The purpose of this step is to extract a characteristic and discriminating representation of the iris and to produce a template for verification in the pattern comparison step. In general, the main existing methods in the literature use the 1D Log-Gabor filter [27, 42, 43], the 2D Gabor filter [3, 6, 44, 45], the wavelet transform [46–48], or the discretionary cosine transform [49]. A comparative study of the different extraction filters of iris characteristics reported in the literatures has been proposed to identify their impact on iris recognition. This study showed that the Log-Gabor filter provides the best recognition performance.Log-Gabor filter is used to create the templates based on information of iris pattern in feature encoding step [50]. Difference between the pixel-intensity levels represents the difference between two iris mages and error that occurred while comparing lighting. To overcome this issue, Daugman [11] used normalization method and extracted features from iris image by convolution with 1D Log-Gabor filter. 1D Log-Gabor filter can be calculated as follows:(21)GX,y=e-log⁡radius/f02/2∗log⁡sigmaOnf2In this method, pixels data multiplied by filters and coefficients are generated by integrating them over their support domain. The image texture information is extracted and encoded to mark the corrupted bits in the template by its associated noise mask of feature template.


## 3.3. Matching

Iris recognition involves mapping between two iris codes. A dissimilarity score is calculated to characterize the degree of resemblance or not between two iris code. The matching algorithm consists of score which is calculated by means of the hamming distance by (22). This distance is expressed by the XOR operator noted ⊕ and the logical operator AND noted ∩. This similarity score represents the number of unmasked bits different between the two iris codes normalized by the number of unmasked bits common to both iris codes.(22)HD=CodeA⊕CodeB∩MaskA∩MaskBMaskA∩MaskBwhere CodeA and CodeB are two codes computed from two iris images by the method previously described and MaskA and MaskB represent their associated masks. Literally, the hamming distance calculates the number of different and valid bits for both iris images between CodeA and CodeB, which contain 20∗480=9600 template bits and 20∗480=9600 mask bits, respectively. The total number of comparisons is represented by MaskA∩MaskB. The lower the hamming distance is, the more similar the two codes are. A distance0 corresponds to a perfect match between the two images, whereas two images of different people will have a hamming distance close to 0.5.


## 4. Experimental Results and Discussion

### 4.1. Dataset

To evaluate the performance, we tested the proposed schemes on the CASIA iris image database (version 1.0) including 756 images of 108 people. For each person, 7 images were acquired in two separate sessions. Totally,756∗755/2=285390 pairs of comparisons for each algorithm, 2268 for intraclass comparisons, and 283122 for interclass comparisons, which contain 9600 template bits and also for mask bits, respectively. The resolution of CASIAv1 images is 320∗280.The experimental results are evaluated based on parameters such as False Acceptance Rate (FAR), False Rejection Rate (FRR), Equal Error Rate (EER), Receiver Operating Curve (ROC), and different downsampling factors and different patches (FLDA/PCA).The error rate can be minimized by selecting the threshold value on the intersection of FAR and FRR. The system obtains the recognition performance of about EER =0.01.Figure8 shows comparisons of Receiver Operating Curve (ROC) and recognition rate for the experiment.Figure 8
ROC curve for the system based on different recognition rate.


### 4.2. Intraclass Comparisons

In our work, 2268 intraclass comparisons of iris templates were successfully performed and their hamming distance distribution is shown in Figure9.Figure 9
Intraclass hamming distance distribution.


### 4.3. Interclass Comparisons

In our work, 283122 interclass comparisons of iris templates were executed successfully and the histogram of distribution is shown in Figure10.Figure 10
Interclass hamming distance distribution.


### 4.4. Intraclass and Interclass Comparisons

Among all the results of intraclass comparisons and interclass comparisons, very few values were seen to overlap. Their combined hamming distance distribution for756∗755/2=285390 pairs of comparisons for each algorithm is shown in Figure 11.Figure 11
Intraclass and interclass hamming distance distribution.Table1 and Figure 12 show the result of the original image with different downsampling factors and different patches.Table 1
Result with different downsampling factors and different patches.
Original(%) Imadjust(%) Clahe(%) msr(%) bilinear bicubic PCA/FLDA bilinear bicubic PCA/FLDA bilinear bicubic PCA/FLDA bilinear bicubic PCA/FLDA PSNR 38.40 39.52 41.73 37.68 38.67 40.06 34.24 36.73 38.24 38.97 40.20 41.94 1/2 MSE 10.27 7.31 4.39 11.18 8.90 6.45 24.67 13.90 9.81 8.30 6.25 4.19 SSIM 0.67 0.8 0.9 0.8 0.77 0.86 0.66 0.66 0.79 0.79 0.84 0.91  PSNR 40.68 40.94 41.12 40.11 39.43 40.21 38.19 37.27 38.78 41.31 41.60 41.66 1/4 MSE 5.60 5.27 5.06 6.39 7.46 6.24 9.93 12.28 8.66 4.85 4.53 4.47 SSIM 0.85 0.86 0.88 0.85 0.82 0.86 0.78 0.73 0.82 0.89 0.9 0.89  PSNR 40.96 41.01 41.99 39.93 40.12 41.01 38.77 38.30 39.08 41.57 41.41 42.01 1/6 MSE 5.25 5.19 4.14 6.65 6.37 5.19 8.68 9.68 8.09 4.56 4.73 4.12 SSIM 0.88 0.88 0.9 0.85 0.85 0.88 0.81 0.79 0.83 0.9 0.89 0.9  PSNR 41.58 41.70 42.29 40.79 40.36 40.93 38.94 38.38 39.27 41.48 41.41 42.16 1/8 MSE 4.55 4.43 3.86 5.46 6.02 5.29 8.35 9.50 7.75 4.66 4.73 3.98 SSIM 0.89 0.89 0.91 0.87 0.86 0.88 0.83 0.8 0.83 0.89 0.89 0.91Figure 12
Result of original images with different downsampling factors.Here, we use 756 iris images of the set as high-resolution reference images. Then we sampled the images of the iris using a bicubic interpolation by a factor of 2n (e.g., the images are resized to 1/(2n) of the original size), and we use all the sampled iris images. Then we follow the downsampled approach of the techniques and sampled the images due to the lack of the database with low-resolution images and corresponding high-resolution reference images. Then we compare our results with bilinear and bicubic interpolation and also for three different contrast enhancement algorithms (imadjust, clahe, and msr) with the images of the iris.We measure the performance of the algorithm by calculating the PSNR (in dB), MSE, and SSIM values ​​between the original images and the images of different contrast. We also compare the result for different patch sizes corresponding to 1/2, 1/4, 1/6, and 1/8 of the low-resolution image size. Then we declare the size of the patch proportional to the size of the low-resolution images. Here, the size of the patches is the precious parameter. After calculating the PSNR, MSE, and SSIM values, we obtain that the FLDA/PCA method performs better than bilinear or bicubic interpolation even at very low resolution [51]. We can therefore conclude that it is more resilient than reducing the resolution of the image. We also obtain that bilinear and bicubic interpolation have similar performances for the small downsampling factors, but a better performance is obtained at very low resolution. We observe that as the resolution decreases, more artifacts appear in the images.Table2 shows the comparisons performance of the proposed method in terms of recognition rate, False Acceptance Rate (FAR), and False Rejection Rate (FRR). The recognition rate of 99.99%, where FAR= 0.16 and FRR = 0.00, shows the success of method.Table 2
Comparison of results.
Methods Database Matching process Feature extraction FAR(%) FRR(%) EER(%) Recognition rate (%) Attarchi et al. [17] CASIA Database - 1-D Log-Gabor and 2D-PCA - - 0.68 99.32 Wen-Shiung et al. [18] UBIRIS Euclidean distance 2D-LDA and 2D-PCA 0.00 0.216 0.74 99.20 Masek [27] Dataset Hamming distance with XOR 2D Gabor 0.005 0.238 0.35 99.65 Avila [29] Database Hamming distance Zero-Crossing 0.03 2.08 0.21 99.79 Li Ma et al. [30] Database Expanded binary feature vector and exclusive OR operations Class of 1D Wavelets, i.e.,1-D Intensity Signals 0.02 1.98 0.29 99.71 Tisse [31] Database Hamming distance 2D Gabor 1.84 8.78 0.41 99.59 Rai et al. [32] CASIA Database SVM and hamming distance with XOR 1-D Log-Gabor wavelets 0.07 0.33 - - Soliman et al. [33] CASIA-V3 CASIA-V1 Hamming distance with XOR 1-D Log-Gabor wavelets - - - 98.80 Dehkordi et al. [34] CASIA-V3 Adaptive hamming distance with XOR 2-D Log-Gabor wavelets - 0.06 - 99.96 YONG et al. [35] IITD Database Hamming distance 2D Gabor Filter/1D Log-Gabor and LDA - - - 98.92 Proposed CASIA-V1 Hamming distance with XOR FLDA/PCA and 1D Log-Gabor filter 0.16 0.00 0.01 99.99


## 4.1. Dataset

To evaluate the performance, we tested the proposed schemes on the CASIA iris image database (version 1.0) including 756 images of 108 people. For each person, 7 images were acquired in two separate sessions. Totally,756∗755/2=285390 pairs of comparisons for each algorithm, 2268 for intraclass comparisons, and 283122 for interclass comparisons, which contain 9600 template bits and also for mask bits, respectively. The resolution of CASIAv1 images is 320∗280.The experimental results are evaluated based on parameters such as False Acceptance Rate (FAR), False Rejection Rate (FRR), Equal Error Rate (EER), Receiver Operating Curve (ROC), and different downsampling factors and different patches (FLDA/PCA).The error rate can be minimized by selecting the threshold value on the intersection of FAR and FRR. The system obtains the recognition performance of about EER =0.01.Figure8 shows comparisons of Receiver Operating Curve (ROC) and recognition rate for the experiment.Figure 8
ROC curve for the system based on different recognition rate.


## 4.2. Intraclass Comparisons

In our work, 2268 intraclass comparisons of iris templates were successfully performed and their hamming distance distribution is shown in Figure9.Figure 9
Intraclass hamming distance distribution.


## 4.3. Interclass Comparisons

In our work, 283122 interclass comparisons of iris templates were executed successfully and the histogram of distribution is shown in Figure10.Figure 10
Interclass hamming distance distribution.


## 4.4. Intraclass and Interclass Comparisons

Among all the results of intraclass comparisons and interclass comparisons, very few values were seen to overlap. Their combined hamming distance distribution for756∗755/2=285390 pairs of comparisons for each algorithm is shown in Figure 11.Figure 11
Intraclass and interclass hamming distance distribution.Table1 and Figure 12 show the result of the original image with different downsampling factors and different patches.Table 1
Result with different downsampling factors and different patches.
Original(%) Imadjust(%) Clahe(%) msr(%) bilinear bicubic PCA/FLDA bilinear bicubic PCA/FLDA bilinear bicubic PCA/FLDA bilinear bicubic PCA/FLDA PSNR 38.40 39.52 41.73 37.68 38.67 40.06 34.24 36.73 38.24 38.97 40.20 41.94 1/2 MSE 10.27 7.31 4.39 11.18 8.90 6.45 24.67 13.90 9.81 8.30 6.25 4.19 SSIM 0.67 0.8 0.9 0.8 0.77 0.86 0.66 0.66 0.79 0.79 0.84 0.91  PSNR 40.68 40.94 41.12 40.11 39.43 40.21 38.19 37.27 38.78 41.31 41.60 41.66 1/4 MSE 5.60 5.27 5.06 6.39 7.46 6.24 9.93 12.28 8.66 4.85 4.53 4.47 SSIM 0.85 0.86 0.88 0.85 0.82 0.86 0.78 0.73 0.82 0.89 0.9 0.89  PSNR 40.96 41.01 41.99 39.93 40.12 41.01 38.77 38.30 39.08 41.57 41.41 42.01 1/6 MSE 5.25 5.19 4.14 6.65 6.37 5.19 8.68 9.68 8.09 4.56 4.73 4.12 SSIM 0.88 0.88 0.9 0.85 0.85 0.88 0.81 0.79 0.83 0.9 0.89 0.9  PSNR 41.58 41.70 42.29 40.79 40.36 40.93 38.94 38.38 39.27 41.48 41.41 42.16 1/8 MSE 4.55 4.43 3.86 5.46 6.02 5.29 8.35 9.50 7.75 4.66 4.73 3.98 SSIM 0.89 0.89 0.91 0.87 0.86 0.88 0.83 0.8 0.83 0.89 0.89 0.91Figure 12
Result of original images with different downsampling factors.Here, we use 756 iris images of the set as high-resolution reference images. Then we sampled the images of the iris using a bicubic interpolation by a factor of 2n (e.g., the images are resized to 1/(2n) of the original size), and we use all the sampled iris images. Then we follow the downsampled approach of the techniques and sampled the images due to the lack of the database with low-resolution images and corresponding high-resolution reference images. Then we compare our results with bilinear and bicubic interpolation and also for three different contrast enhancement algorithms (imadjust, clahe, and msr) with the images of the iris.We measure the performance of the algorithm by calculating the PSNR (in dB), MSE, and SSIM values ​​between the original images and the images of different contrast. We also compare the result for different patch sizes corresponding to 1/2, 1/4, 1/6, and 1/8 of the low-resolution image size. Then we declare the size of the patch proportional to the size of the low-resolution images. Here, the size of the patches is the precious parameter. After calculating the PSNR, MSE, and SSIM values, we obtain that the FLDA/PCA method performs better than bilinear or bicubic interpolation even at very low resolution [51]. We can therefore conclude that it is more resilient than reducing the resolution of the image. We also obtain that bilinear and bicubic interpolation have similar performances for the small downsampling factors, but a better performance is obtained at very low resolution. We observe that as the resolution decreases, more artifacts appear in the images.Table2 shows the comparisons performance of the proposed method in terms of recognition rate, False Acceptance Rate (FAR), and False Rejection Rate (FRR). The recognition rate of 99.99%, where FAR= 0.16 and FRR = 0.00, shows the success of method.Table 2
Comparison of results.
Methods Database Matching process Feature extraction FAR(%) FRR(%) EER(%) Recognition rate (%) Attarchi et al. [17] CASIA Database - 1-D Log-Gabor and 2D-PCA - - 0.68 99.32 Wen-Shiung et al. [18] UBIRIS Euclidean distance 2D-LDA and 2D-PCA 0.00 0.216 0.74 99.20 Masek [27] Dataset Hamming distance with XOR 2D Gabor 0.005 0.238 0.35 99.65 Avila [29] Database Hamming distance Zero-Crossing 0.03 2.08 0.21 99.79 Li Ma et al. [30] Database Expanded binary feature vector and exclusive OR operations Class of 1D Wavelets, i.e.,1-D Intensity Signals 0.02 1.98 0.29 99.71 Tisse [31] Database Hamming distance 2D Gabor 1.84 8.78 0.41 99.59 Rai et al. [32] CASIA Database SVM and hamming distance with XOR 1-D Log-Gabor wavelets 0.07 0.33 - - Soliman et al. [33] CASIA-V3 CASIA-V1 Hamming distance with XOR 1-D Log-Gabor wavelets - - - 98.80 Dehkordi et al. [34] CASIA-V3 Adaptive hamming distance with XOR 2-D Log-Gabor wavelets - 0.06 - 99.96 YONG et al. [35] IITD Database Hamming distance 2D Gabor Filter/1D Log-Gabor and LDA - - - 98.92 Proposed CASIA-V1 Hamming distance with XOR FLDA/PCA and 1D Log-Gabor filter 0.16 0.00 0.01 99.99


## 5. Conclusions

In this paper, we propose a novel iris recognition method by using 1D Log-Gabor filter and a fusion of FLDA/PCA. Our algorithm is duly tested on a CASIA V1 database of grayscale eye images for the verification of its efficiency. This research offers a robust and fast iris recognition technology through implementing FLDA/PCA method in a new optimized manner with time-saving in performing. Our proposed algorithm is superior to bilinear and bicubic interpolation with a recognition rate of 99.99%.



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*Source: 7951320-2019-08-21.xml*