Iris Segmentation Using the Generalized Structure Tensor Fernando Alonso-Fernandez and Josef Bigun Halmstad University. Box 823. SE 301-18 Halmstad, Sweden fferalo, [email protected] Abstract—We present a new iris segmentation algorithm of the outer (sclera) boundary. Since the pupil is generally based on the Generalized Structure Tensor (GST). We com- darker than the iris, there will be a sharper transition pare this approach with traditional iris segmentation systems which in principle will be easier to detect than the softer based on Hough transform and integro-differential oper- ators. Results are given using the CASIA-IrisV3-Interval transition between the iris and the sclera. We compare our database with respect to a segmentation made manually by algorithm with traditional iris segmentation systems based a human expert. The proposed algorithm outperforms the on Hough transform and integro-differential operators. We baseline approaches, pointing out the validity of the GST as also implement an eyelid detection step. We have used an alternative to classic iris segmentation systems. We also for our experiments the CASIA-IrisV3 Interval database, detect the cross positions between the eyelids and the outer iris boundary. Verification results using a publicly available with 2,639 iris images from 249 contributors acquired in iris recognition system based on 1D Log-Gabor wavelets are two sessions [7]. Reported results show the effectiveness also given, showing the benefits of the eyelids removal step. of the proposed algorithm, outperforming the baseline systems. In addition, verification results of the proposed system using 1D Log-Gabor wavelets are given, showing I. INTRODUCTION the benefits of incorporating the eyelids detection step. Biometrics has been receiving considerable attention over the last years due to the increasing demand for II. THE 2D STRUCTURE TENSOR automatic person recognition. It refers to automatic recog- The Ordinary Structure Tensor (OST) nition of an individual based on behavioral and/or physi- Given a gaussian smoothed image I[p], the 2D Ordi- ological characteristics (e.g., fingerprints, face, iris, voice, nary Structure Tensor [8]P at a given pixel p = [x; y] is etc.), which cannot be stolen, lost, or copied [1]. Among the 2£2 matrix Sw [p] = w [r] So[p ¡ r], where So is r all biometric techniques, iris has been traditionally re- · 2 ¸ garded as one of the most reliable and accurate biometric (fx [p]) fx [p] fy [p] the matrix So [p] = 2 . Index identification systems available [2], [3]. fx [p] fy [p](fy [p]) The iris is a ring around the pupil, surrounded by r ranges over coordinate pairs f¡m:::mg £ f¡m:::mg a white region called sclera (Figure 1). The pupil is and w[r] is a weighting window centered at p (typically generally darker than the iris and may have specular gaussian). The values fx[p], fy[p] are the estimated partial reflections due to light sources used in commercial ac- derivatives of I[p] at pixel p, commonly implemented quisition systems. Iris analysis begins with the detec- via convolutions with sampled gaussian-derivative filters. tion of the inner and outer iris boundaries. Early works It can be shown that the following (complex) linear make use of integro-differential operators, proposed by combinations of the real moments mp;q of the local power Daugman [4], and edge detection plus circular Hough spectrum, which are the matrix elements of Sw, directly transform, proposed by Wyldes [5]. They assume that relate to the eigenvalues ¸1; ¸2 (and their corresponding iris boundaries can be modeled as circles. Much of the eigenvectors e1; e2) of matrix Sw[p] [9]: subsequent research has tried to improve the Wildes idea, i2'e I20 = (m11 ¡ m22) + i2m12 = (¸1 ¡ ¸2) e 1 such as the inherent computational burden of the Hough I11 = (m11 + m22) = ¸1 + ¸2 transform or the lack of enough edge points to define a circle [2]. Some works also deal with the problem of detecting eyelids occlusion or specular reflections. Eyelashes Current issues include the development of acquisition Specular systems that allow larger distances between the subject reflecons and the sensor (typically meters), in which the apparent Sclera size of the iris and pupil will show much more variability, Iris with an important presence of motion blur, inconsistent Pupil illumination or variation in subject gaze angles [6]. Eyelid In this paper, we present a iris segmentation algorithm based on the Generalized Structure Tensor. By using circular filters sequentially, we first detect the inner (pupil) boundary and then, its center is used to refine the search Fig. 1. Iris image with typical elements labeled. PUPIL DETECTION SCLERA DETECTION EYELIDS OCCLUSION DETECTION Apply circular filter c(p) of variable radius Apply circular filter c(p) of variable radius Extract low standard deviaon regions in I₂₀/I₁₁ (across the whole image) and find radius for (around detected pupil centre only) and find across the detected sclera circle to find posion which maximum of I20 occurs radius for which maximum of I₂₀ occurs of cross-points between eyelids and sclera MaximumMaximum magnitu magnitude of I20de of I₂₀ p−p, p − p MaximumMaximum m magnitudeagnitu of I20de of I₂₀ i i Output 0.50.5 0.260.26 33 90 0.450.45 0.240.24 Circular Circular 2.52.5 0.220.22 0.40.4 filter filter 180 0 0.20.2 2 0.350.35 2 0.180.18 270 ue 0.30.3 Pupil ue 0.16 1.5 Val 0.16 Val 1.5 Value 0.14 0.250.25 radius 0.14 11 0.120.12 0.20.2 0.10.1 Sclera 0.50.5 0.150.15 0.080.08 radius 0.060.1 0.060.06 0 10 20 30 40 50 60 70 80 75 80 85 90 95 100 105 110 115 120 125 130 0 0 50 100 150 200 250 300 350 10 20 30 40 Filter radius 50 60 70 80 75 80 85 90 95 100Filter radius105 110 115 120 125 130 0 50 100 150 Angle 200 250 300 350 Filter radius Filter radius Angle Fig. 2. System model for iris segmentation using the Generalized Structure Tensor. p DIFFERENCE IN RADIUS Here i is the complex ¡1. Hence, I20 (complex) and 1 I11 (real) are the second order complex-moments of the power spectrum. They are also referred to as the 0.8 GST (pupil) (complex representation of the) structure tensor because Hough (pupil) <=x) Integro−differential (pupil) they represent the ordinary structure tensor fully, with the 0.6 GST (sclera) advantage that eigenvalues and eigenvectors of Sw can Hough (sclera) Integro−differential (sclera) be read out directly from I20;I11. This representation 0.4 is increasingly preferred in fingerprint analysis as it CDF (Prob nd conveniently allows a generalization of the structure 0.2 tensor, offering efficient detection of singularities such 0 as core and delta [10], [11]. It can be also demonstrated 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 that jI20j · I11 (Schwartz inequality). Normalized distance (nd) The Generalized Structure Tensor (GST) DISTANCE BETWEEN CENTRES Assuming that the inner/outer boundaries of the iris 1 can be modeled as circles, they can be detected by means of the Generalized Structure Tensor, [9], which is 0.8 essentially template matching in the tensor domain, and <=x) 0.6 can be conveniently expressed using complex version of the structure tensor, i.e. P 0.4 i2'e 2 I20 = (¸1 ¡ ¸2) e 1 = c (p)(fx (p) + ify (p)) CDF (Prob nd p ¯ ¯ 0.2 P ¯ 2¯ I11 = ¸1 + ¸2 = jc (p)j ¯(fx (p) + ify (p)) ¯ p 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 where c(p) is defined as the complex version of the Normalized distance (nd) structure tensor response of a circle1: Fig. 3. Pupil and sclera segmentation accuracy (test set). ¡i2' ¡ 2 2¢γ ¡ x2+y2 = 2σ2 c (p) = e e1 x + y e ( ) ( 2 ) Here γ and σ2 determine the radius of the circle and the precision of the filter (width of the circular boundary manually, depending on the database (15-70 pixels for the region). It can be shown that a high response in jI20j and CASIA-IrisV3 Interval). A peak in the response of jI20j zero argument of I20 is obtained at a point, if there are will be obtained when the radius of the circular filter fits edges at the prescribed (same) distance from that point that of the pupil boundary, as can be seen in Figure 2, and there is an agreement in terms of local orientations left. To improve detection, and to discard spurious peaks, (structure tensors) with those of a circle. It can also be a threshold to the argument of I20 is also imposed (+/-3 shown that when this happens, the Schwartz inequality degrees in this work), so peaks with argument higher than holds with equality, i.e. jI20j = I11. the threshold are discarded. After detecting the pupil boundary, another circular III. PROPOSED SYSTEM filter is used to search for the sclera boundary. The We propose the use of the GST for iris segmentation minimum radius of this filter is dynamically adjusted following the process described next (summarized in depending on the pupil radius, and the maximum radius Figure 2). is set to 140. For better accuracy, we search for the We first search for the pupil boundary with a circular maximum value of jI20j only within a small region around filter of variable radius. The range of radius values is set the center of the pupil, since the two circles are assumed 1In the ordinary structure tensor c(p) is a Gaussian defining the extent as being concentric to a certain extent [4].