Human iris image, as an externally visible object, is the most reliable and stable template of recognition. With the increasing demand for a trustworthy personal identification system and the increasing encouragement by the governments and private entities, iris recognition is progressing at a persuasive rate, proving to be a mainstream viable security technology [5, 7, 8]. An iris pattern has several features, such as furrows, ridges, arching ligaments, crypts, rings, corona, freckles, and the collarets, which together make a complex iris texture, as shown in Figure 1 [7, 22].
A typical iris recognition system has practically five modules, such as detecting and excluding any superimposed occlusions of eyelashes and reflections, finding the limbic (outer) and pupillary (inner) boundaries of the iris, fitting its upper and lower eyelids with irregular shape, feature extraction, and matching.
Most literature studies have focused on the improvement or introduction of a method for segmentation and extraction of the signature, but not both. This is due to the complexity of these two phases.
In our research, systems of iris recognition were investigated to be best suited to hardware implementation afterward, taking into account the system complexity and performance so as to improve the entire system (improved segmentation phase and the extraction of the signature phase).
The existing iris recognition systems represent a variety of challenges. For example, in the segmentation process, the iris is often partially occluded by eyelashes, eyelids, and corneal reflections especially when the user wears glasses. Also, in the feature extraction process, iris recognition systems rely heavily on how to accurately represent local details of the iris texture.
All of these challenges make the realization of a practical iris recognition system difficult; therefore, a fast, accurate, and robust iris recognition system is highly desirable. The remainder parts of this article are organized as follows: Section 2 is a literature review. Section 3 is a description of the proposed method. Section 4 discusses the experimental results. Finally, in Section 5, the conclusion and future works are presented.
2 Literature Review
The random iris texture is a research field that attracts many researchers who have proposed a variety of algorithms. Daugman developed an integro differential operator to frame iris regions by two circles  and the quadrature two-dimensional (2D) Gabor wavelet to extract the phase information of the iris texture. Masek  used an edge map and Hough transformation to frame the pupil and the iris region by two non-concentric circles and 1D Log-Gabor wavelets to encode iris texture. This method did not pay much attention on eyelid localization and reflections.
Other methods used active contour such as GVF (gradient vector flow), shrinking, and expanding to frame iris regions [16, 26]. These methods are not good enough especially for the smaller pupil, a bright iris image, and with deflected reflection spots inside the iris region  because the highlighted regions disturb the convergence toward the region of interest (ROI) in addition to the contour initialization difficulties. More recent methods tried to enhance circle models [1, 31] whose efficiency has actually been proved in commercial systems .
Several methods of the state of art [1, 4, 21, 34] never ceased to improve the method of Masek as one of the famous circle model techniques. Some of them tried to optimize its parameters [4, 29]. Uhl and Wild enhanced the iris matching process . Liu et al. improved the segmentation process by reversing the detection order between outer and inner iris boundaries and by bringing some changes to the Hough transform .
From the above description, two important issues are identified in iris recognition: one is to accurately localize the iris boundaries (pupil, iris, eyelids, and eyelashes), and the other is to extract the feature of the iris. Although impressive recognition accuracy has been obtained by the previous methods that tried to enhance the Masek approach as a circle model approach, many important issues have not yet been adequately addressed and remain an unsolved problem. After a detailed analysis of the flowchart of the Masek approach , a fundamental modification is proposed in this work. A new corneal reflection removal method was introduced to clean the input image, which uses morphological reconstruction and pixel connectivity. Moreover, we started by a picture size reduction then a convolution. The interpolation method was also changed at the picture redimensioning step to enhance computation time and accuracy. Four matrices were proposed to compute image gradient and orientation. In the localized iris region, the top and lower eyelids were detected using Radon transform and the least squares fitting method. The eyelashes region was localized by applying a diagonal gradient and adaptive threshold. For feature extraction, the monogenic filter was used as a feature compact representation with little information loss. Finally, the modified Hamming distance (HD) and cosine distance were chosen for template matching.
3 Description of the Proposed Method
Figure 2 shows the flowchart of the proposed method. Because CASIA iris database V3.0 images  are collected with infrared light, they include noise such as corneal reflection points as shown in Figure 1. First, a preprocessing phase is used to remove the noisy points and reduce the processing time in the circle detection phase using Hough transformation (see Figure 4 and Section 3.1). To localize the iris region within the input image, the outer (limbic) and inner (pupillary) boundaries of the iris regions are detected successively following the same steps (algorithm A in Figure 3). The localized iris region includes the occlusions caused by the eyelids and the eyelashes. The eyelids are detected by Radon transform and polynomial curve fitting, using the least squares fitting method as shown in Figures 10 and 11 (see Section 3.3). Eyelashes are detected by a diagonal-gradient-based approach followed by a thresholding method, as shown in Figures 13 and 18 (see Section 3.4). Once the iris is well detected (reflection points, eyelashes, and eyelids are eliminated), there is definitely a need for a permanent solution to address the problem of the change in pupil size, iris orientation, distance to the eye, camera angles, and position  (see Figure 14 and Section 3.5). Therefore, the projected pseudo-polar coordinate system is the solution (normalization). After the normalization, two rectangular images that represent the iris and noise regions are obtained as shown in Figure 15. They are used to generate the signature of an individual in the feature extraction step (see Section 3.6). Finally, a signature is declined or confirmed in a matching process using the modified HD (see Section 3.7).
Algorithm A in Figure 3 localizes the limbic and pupillary boundaries successively, using edge detection and Hough transform (blue algorithm). It starts with image size reduction followed by convolution (Gaussian smoothing) instead of the proposition of Masek [1, 22]. Our idea in doing this is to enhance time computation by reducing both the kernel size (see Section 3.2.1) and the image size before the convolution . In convolution 2D with M × N kernel size, each sample from the input image requires (2 × M × N) multiplications and accumulations. However, if the kernel is separable and the input image is reduced, then the computation can be reduced to [2 × (M + N) × scale] multiplications and accumulations. Then, gradient magnitude and orientation are used to compute the gradients in X and Y directions using four oriented matrices (see Section 3.2.2). The image gradient magnitude is then enhanced using the gamma correction technique (see Section 3.2.3) . Finally, the edge map is obtained, using a local maxima preserving process (see Section 3.2.4) followed by the hysteresis thersholding (see Section 3.2.5), on which a circular Hough transform  is used to obtain the shape of the iris.
In the following sections, each stage of the proposed algorithm is carefully described.
3.1 Corneal Reflection Removal
Aydi et al. , Jarjes et al. , and He  argued that the gray level of the corneal reflection points is higher than that of other regions because the reflectance of the corneal surfaces is greater than that of other regions (such as the sclera and skin), as shown in Figure 1. In view of this fact, a simple and efficient method is proposed in Figure 4. The key idea first consisted in performing an image complement and then filling the corneal reflection points using the eight-pixel connectivity . Finally, and to retrieve the original image appearance but without the noisy points, the image complement is further evaluated. If they are not removed, these specular highlights would appear later in the edge map. Therefore, they can not only create errors in the accumulator space in the circle detection step using Hough transformation but also increase computation time.
3.2 Iris Boundary Localization
3.2.1 Image Size Reduction
For image shrinking operations, a scale factor inferior to 1 and an interpolation technique are both needed. In our approach, three popular techniques are tested, using different weighted averages for the surrounding pixel operators, bicubic [10, 30, 38], bilinear , and nearest . Our choice criteria consist in time processing and accuracy effects.
A comparative survey is conducted between the three techniques listed above (bicubic, bilinear, and nearest) to choose the best one in terms of accuracy and computing time. The bicubic and bilinear methods, being two weighted average operators, alter the gray-level values in the image. Such an effect disturbs the edge map, generated by the thresholding technique. In contrast, the nearest-neighbor interpolation does not alter the gray-level value, so the content is essentially left unaffected as it can also be shown by the histograms of Figure 5. Otherwise, from a computational stand point, the nearest-neighbor interpolation is the simplest and the fastest one . By looking at the histograms (cf. Figure 5) where the horizontal axis of the graph represents the gray-level variations, while the vertical axis represents the number of pixels corresponding to this level, the viewer can judge that the nearest histogram is the most similar to the original.
Following the experimental results, the scale is chosen equal to 0.3. Therefore, the size of the output image is 96 × 84 = (320 × 0.3) × (280 × 0.3) and the four vector kernel elements, defined by the following vector, are used in the Gaussian smoothing step.
3.2.2 Gradient Magnitude and Orientation
The gradient vector was computed as the first derivative of the input image Im according to the X and Y directions. The image gradient is of great interest in boundary detection as the gray level in images often changes most quickly at the boundary between objects [15, 25]. To compute the first derivative according to the X and Y directions, four matrices were used in the horizontal H, vertical V, and in the oblique directions D1 and D2, as follows. These matrices are used to keep the maximum details of the iris boundaries and eyelids in the edge map:
where, i = [0, n – 1], j = [0, m – 1], and (n,m): image size.
To compute gradient magnitude and orientation, equations (1) and (2) were adopted:
3.2.3 Gamma Correction
The gamma correction is an image enhancement technique [12, 37]. It is used to control the overall brightness of the iris image gradient. In our method, the gamma value is set at 2 for two purposes: to highlight the shadow areas in the image gradient as shown in Figure 6 and to facilitate its hardware implementation after using Cordic .
184.108.40.206 Local Maxima Preserving Process
The principle of the local maxima preserving process is to liken each point M(XM, YM) of the input image Im to its neighbors M1 and M2 according to their gradient magnitudes, to make the edges thinner. Figure 7 shows the relative positions of each point. More details were provided in previous works .
The image resulting from the local maxima preserving stage as shown in Figure 8 still contains noisy maxima; thus, hysteresis thresholding is required to track along the remaining pixels – those that were not removed .
3.2.4 Hysteresis Thresholding
The hysteresis thresholding algorithm allows noisy maxima to breakthrough if too low . This process receives the output image from the local maxima preserving process to remove the weak edges without breaking the contour. This algorithm uses two thresholds, upper (Tup) and lower (Tlow).
Any pixel whose value lies above Tup is immediately marked as an edge one. The adjacent pixels (eight connected pixels) are then recursively searched. If their values are greater than Tlow, they are also marked as edge pixels. Otherwise, they are rejected. Figure 9 depicts the result of the thresholding process.
Once the edge map of thresholded image is obtained, the pupil and iris as two regular shapes are approximated by two non-concentric circles. An eight-way symmetry algorithm is used to construct these two circles .
3.3 Boundary Detection of the Upper and Lower Eyelids
Eyelids and eyelashes are two major challenges for effective iris segmentation [13, 14, 23]. These unwanted artifacts must be removed to get a clean iris image. In this section, a fast and accurate eyelid localization method compared with the Masek approach is suggested, as shown in Figures 10 and 11. Moreover, our approach has fewer parameters than those in the literature [17, 14, 24]. In fact, previous works assumed the top and lower eyelids by a parabolic curve using parabolic Hough transformation, making the process more computationally demanding.
Let us take the localization of the upper eyelid, as an example, as depicted in the flowchart in Figure 10. Our method works as follows:
First the region between the two upper horizontal tangents of the non-concentric circles of iris was considered, as shown in Figure 10A.
The IROI was split into two equal rectangular regions (see Figure 10B).
The line in the IROI_left was detected using Radon transform . First, an edge map was created following the same steps used to detect iris region, and only horizontal gradient information was considered. Then, we applied the Radon transform to detect the left line. The Radon transform is more suitable (time computation and stability)  to detect lines than the Hough transform (see Figure 10C).
The line in the IROI_right was detected using Radon transform (see Figure 10D).
Polynomial curve fitting was done using the least squares fitting method. It consists in a mathematical procedure used to find the best-fitting curve by minimizing the sum of the offset squares computed on each point of the curve.
Figure 12 shows an example of some segmented iris images using the proposed method.
3.4 Eyelash Detection
The detection of the eyelashes was achieved using a diagonal-gradient-based approach followed by a thresholding method. As a first step, the diagonal gradient was computed using the D1 matrix shown in Section 3.2.2 as demonstrated in Figure 13B. The diagonal gradient is a plain linear gradient where the start/stop point is in a diagonal direction.
As shown in Figure 13B, the eyelashes possess the largest values of gray level; therefore, and based on this observation, it was possible to create a new segmentation mask for the eyelashes, by applying the thresholding method on the output image of the diagonal gradient, as follows:
where Th is the threshold set empirically then confirmed in the whole CASIA V3.0 database of the eye images and I(i, j) is the output image of the diagonal gradient.
3.5 Normalization 
The normalization phase is able to rescale the iris region so that it maintains a constant rectangular form. This is a technique developed by Masek and based on Daugman’s rubber sheet model [see equation (4)].
In equation (4), x(r, θ) and y(r, θ) are expressed as a function of the number of pupillary boundary points xp(θ), yp(θ) and limbus boundary points xs(θ), ys(θ). As the pupil and iris are not necessarily concentric, a remapping formula is needed to compute the distance r, between the pupil and iris contours, at an angle θ, as shown in Figure 14 and given by equation (4).
The pupil center is considered as the reference point. From this point, a set of radial lines are drawn, which pass though the iris region. The number of radial lines is defined as the angular resolution, while the number of data points along each line is defined as the radial resolution as shown in Figure 14:
Figure 15 shows an example of some normalized iris images on the top and their noise region in the bottom. White regions denote detected eyelids and eyelashes regions.
3.5.1 Feature Extraction
In the proposed method, the feature extraction procedure was better refined by monogenic signal. In fact, monogenic signal analysis is a compact representation of features with little information loss  and is also a framework to analyze images in terms of local orientation and local magnitude . It is worth noting that monogenic filters are a 2D generalization of the 1D analytic signal [6, 36]. The following isotropic filters in frequency domain are revealed by equation (5). Details are provided in Reference :
where u and v are the horizontal and vertical frequency grids and i is the complex number. In our case, two frequency grids (u and v) were constructed with the same size as the input image as shown in Figure 16. Thereafter, H1 and H2 were computed.
The two filters H1 and H2 are oriented in frequency space but they are not selective in terms of frequency magnitudes. To maintain the independence between the energy (local amplitude) and structure (local phase) and to produce different band-pass versions of the two monogenic filters H1 and H2, they were multiplied by 2D Log-Gabor filter. The frequency response of this filter is expressed by the following transfer function [6, 11]:
where f0 indicates the center frequency of the filter and σ is the scaling factor of the bandwidth.
The 2D Log-Gabor filter possesses crucial advantages as compared with 2D Gabor filters as it
Discards the DC component of the signal compared with the Gabor filter,
Overcomes the bandwidth limitation of the Gabor filters, and
Has a Gaussian-shaped response along a logarithmic frequency.
To encode the normalized iris I, the real part of the following expressions Hx, Hy was considered:
where FFT–1 is the inverse fast Fourier transform and FFT is the fast Fourier transform. Hx and Hy are two matrices with complex numbers.
The angle ϕ [equation (9)] for the real part of each number is quantized to one of the four quadrants as shown in Figure 17, setting 2 bits of phase information. The result is a vector 9600 bits long:
where Real means the real part.
3.6 Iris Templates Matching
At this level, the generated and stored templates were matched, and similarity or dissimilarity scores were calculated.
In our experiment, the cosine distance and modified HD were selected as similarity measures to evaluate the performance of the proposed method compared with previous works.
Modified HD 
The modified HD between two templates, TA and TB, defined by equation (10), is the number of disagreement bits over the number of the uncorrupted bits.
The HD also uses noise masking (TAM and TBM), which corresponds to the corrupted regions (eyelashes, eyelids, and the reflection points) in the iris regions, so that only the significant bits are considered in the calculation.
The modified HD between two templates from the same iris has a smaller value (near zero). However, it is near 0.5 for two templates generated from different irises.
where and are the two templates, and are their corresponding noise mask bit vectors, and n is the template size. The modified HD  between two templates from the same iris has a smaller value (close to zero). However, it is near 0.5 for two templates generated from different irises.
The angular cosine distance  is one of the most popular similarity measures. This metric is often used whenever we need to determine the similarity between two documents. In our experiment, the two templates TA and TB were converted into two vectors. The cosine distance is then determined by equation (11):
4 Experimental Results and Discussion
The proposed method was tested using 2655 images from the CASIA V3.0 database . All iris images used in our experiments had an 8-bit gray scale with a resolution of 320 × 280 pixels. This database has also non-ideal iris images such as rotated eyes and blurred images. All parameters of the proposed iris recognition system were selected through a rigorous experiment.
Two different distances were tested at the matching stage: modified HD and cosine distance. The performance of our iris recognition system was assessed with two kinds of error rates: false acceptance rate (FAR) and false rejection rate (FRR), in addition to the area under ROC curve (AUC), detection error trade-off graph (DET), and speed. Those performance tests were all used to give quantitative evaluations of recognition accuracy. Figure 18 gives some typical segmentation examples of degraded images from the CASIA iris database (occluded, blurred, etc.) using the proposed method.
As shown in Table 1, the proposed method was compared with three algorithms. They were all implemented and simulated using Matlab 9.0, and a Duo CPU 2 GHz computer with 2.99Go of RAM, on all images of database V3.0 .
Tables 1 and 2 show that the proposed method using the dissimilarity modified HD improves the accuracy of iris recognition, with FAR = 3% and FRR = 3% compared with Uhl and Wild’s , Khanfir’s fractal analysis [18, 19], and Khanfir’s Meyer wavelet . Moreover, our method with the modified HD is more accurate than the cosine similarity measure, as shown in Tables 3 and 4. Second, from a computational stand point and as shown in Table 2, our method is faster in segmentation than that of Uhl and Wild , and 8 times and 11 times faster than Khanfir’s fractal analysis [18, 19] and Khanfir’s Meyer wavelet , respectively.
Several aspects of the used method contributed to this enhancement. First, the addition of a corneal reflection point removal in the Masek algorithm led to a more accurate iris localization. This step eliminated most of the noisy edge points (all reflection points in the input image) because each point had its own effect, which results in a more globally optimal circle and a reduction in time computation.
Second, the choice of the scale and the method of interpolation in the reduction phase of the image size as well as the reversal of order between convolution and resizing improved the execution time and accuracy. Third, the Radon transforms and the polynomial curve fitting, using the least squares fitting method, provided excellent approximation to the eyelid boundaries. The polynomial curve fitting was tolerant to deviations of the detected edge points. Thus, it was efficient with the shape irregularity compared with linear Hough transformation. Fourth, an adaptive diagonal gradient and simple thresholding methods excluded the annoying eyelashes. Fifth, the combination of monogenic signal and 2D Log-Gabor filter was adopted to extract robust phase information. The monogenic filters were isotropic and had a compact representation of features with little information loss. Finally, the modified HD was chosen as a metric for recognition.
According to Table 2 and the profiling analysis, 98% of the computational time was required to process the segmentation. More precisely, this time was reserved for the circular Hough transformation step. Thus, to enhance this part, it was necessary to use an iris detector such as Adaboost built to extract a rough position of the iris center. This detector allows further reducing the search area of the two circles of the iris.
Figures 19 and 20 show the evolution of the FAR and the FRR for different values of the threshold. The X-axis shows the threshold taken from 0 to 1, while the left and right Y-axis represent the FAR and FRR, respectively. These graphs give a good representation of the device performance. In high-security systems, even one falsely accepted criminal can cause substantial damage. Therefore, the FAR is a high priority in this situation. In contrast, for example, for personal home-computer log-ins, easiness and convenience are an important consideration and the FRR counts more. There is no single set of FAR and FRR useful for all systems. It depends on the system requirements. Therefore, from Figures 19 and 20, a high-security system can be chosen if the threshold is <0.4, where FAR is close to 0 and FRR is quite low. To have a looser security system, it is necessary to choose the threshold equal to 0.5. However, in this case, the FAR is a little high.
To have a trade-off between the two rates, the equal error rate (EER) is suitable. The EER is where the FAR and FRR curve meets and gives the threshold value for the best separability of the imposter and client classes (see Tables 3 and 4).
Figures 21 and 22 show the inter-class and intra-class distributions of cosine distance and modified HD. Inter-class distribution is the result obtained by matching the template of a person with a template of another one, while intra-class distribution is obtained by matching two templates provided from the same person. In our experiments, 4127 intra-class and 1,491,458 inter-class distances were obtained (from 249 individuals), on the interval [0, 1]; the appearance of the normalized distance frequencies was then calculated. Thus, an intra-class (or inter-class) distribution of distances is a representation of the normalized frequency appearance, depending on the distance.
Figures 21 and 22 show the cosine distance and modified HD distributions with a slight overlap. However, the means of the intra-class and inter-class distributions are still clearly separated, so recognition is still possible. The accuracy of recognition with these distributions can be determined by calculating their FAR and FRR with different separation points (as shown in Tables 3–5).
With the CASIA-V3.0 data set, perfect recognition is not possible owing to the overlapping distributions (inter- and intra-class) as shown in Figures 21 and 22. With a separation point of 0.445 (as shown in Table 3), a FAR and FRR of 3% are achieved, which still allows accurate recognition. For cosine distance, a FAR and FRR of 4% are achieved with the separation point 0.433.
The effectiveness of the proposed method to the studied systems can also be graphically represented by the so-called DET graph. Meanwhile, the DET curve approaches the lower left corner of the graph. The system shows the best performance.
Figure 23 shows how the FAR and FRR in the studied methods would change as we vary the threshold decision. In Figure 23, we can see that the proposed method using the modified HD dissimilarity measure outperforms the proposed method using the cosine similarity measure, Khanfir’s Meyer wavelet, Khanfir’s fractal analysis, and Uhl and Wild’s method in accuracy. The reasons are explained in Section 4. Moreover, we can see that the proposed method using cosine distance is a little better than FAR values >0.3. As for lower 0.2, the proposed method using the HD modified dissimilarity measure is better. Thus, as a perspective, the two measurement techniques might be combined to further improve the performance of the proposed system.
5 Conclusions and Future Works
In this article, a robust feature extraction method for an iris recognition system based on a monogenic filter is proposed. Tests and evaluation were carried out on the CASIA-IrisV3-Interval database.
The experimental results show that the proposed method using the modified HD with a recognition rate equal to 97.85% achieves Uhl and Wild’s method, Khanfir’s fractal analysis, Khanfir’s Meyer wavelet, and the proposed method using cosine distance in terms of accuracy and computation time. This important improvement is due to our contribution to enhancing the Masek approach. Moreover, the complexity of the proposed feature extraction method was obviously low and thus achieved a considerable computational reduction. Further investigation in this regard shall focus on the implementation of the proposed method using multicore digital signal processors.
The authors are grateful to Kamel Maaloul, translator and English professor at the Faculty of Sciences of Sfax, for having proofread our manuscript.
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