## 3 Methodology
### Iris Measure and Template Detection  
During this stage, the measure and template of the iris are detected. To achieve this, it is necessary to locate the iris boundary, particularly, the boundary of iris and sclera. The flowchart of this stage is shown in Figure 4. (1) First, the eye image is converted from RGB to grayscale. (2) Then the Haar-like feature is applied to the grayscale image to detect the exact eye region with the objective of further narrowing the area of interest. This feature extraction depends on the local feature of the eye, that is, the eye socket appears much darker in grayscale than the area of skin below it. The width of the rectangle window is set to be approximately the horizontal length of the eye, while the height of the window is variable within a certain range. The maximum response of this step corresponds to the eye and the skin area below it. (3) The Gaussian filter is applied to the result of (2), with the goal of smoothing and reducing noise. (4) Then, the canny method is applied as an edge-highlighting technique. (5) The circular Hough transform is employed to locate the iris boundary, due to its circular character. In performing this step, only the vertical gradients (4) are taken for locating the iris boundary [32]. This is based on the consideration that the eyelid edge map will corrupt the circular iris boundary edge map, because the upper and lower iris regions are usually occluded by the eyelids and the eyelashes. The eyelids are usually horizontally aligned. Therefore, the technique of  
Figure 3: The rough localization of eye regions of the image in our database. Half of the face occupies the middle of the image in our database. The eye region is highlighted by the red window, which is slightly smaller than the actual eye region, in order to obtain a clearer display. The right and left eye region can be obtained by dividing the eye region into two parts.  
excluding the horizontal edge map reduces the influence of the eyelids and makes the circle localization more accurate and efficient. (6) Subsequently, we segment a region with dimensions of 1.2\(\times\) radius, horizontally, and 1.5\(\times\) radius, vertically, on both sides from the iris center in the original gray image. The radius and iris center used in this step are the radius and center coordinates of the iris region detected in the last step. These values were chosen so that a complete iris region could be segmented without any damage. This region will be used as a template for the next stage.  
The above operations are applied on the right and left eye regions, respectively, in a ten-frame interval, and ten pairs of iris radius values are extracted. The interval should be chosen to meet two conditions. First, the radius should be accurately determined in the interval. Second, the interval should not influence the next stage because the segmented region will be used for template matching. By the end of the interval, the iris radius value with the largest frequency is determined as the final iris radius. Thus, we have the right iris and left iris, with the radius of \(\mathrm{R_{r}}\) and \(\mathrm{R_{l}}\), respectively.