## 4 Experimental Results
### Results of Pupil Localization  
The accuracy of the proposed pupil detection algorithm was tested on static eye images on the dataset we built. The dataset consists of 5795 eye images with a resolution of 300 \(\times\) 150 pixels for samples without wearing corrective lenses and 400 \(\times\) 200 pixels for samples wearing lenses. All images were from our video database. The pupil location was manually labeled as the ground truth data for analysis. In order to appreciate the accuracy of the pupil detection algorithm, the Euclidean distance \(\mathrm{D}_{\mathrm{P}}^{(\mathrm{E})}\) between the detected and the manually labeled pupil coordinates, as well as the distance \(\mathrm{D}_{\mathrm{P}}^{(\mathrm{x})}\) and \(\mathrm{D}_{\mathrm{P}}^{(\mathrm{y})}\) on both axes of the coordinate system was calculated for the entire dataset. The detection rate measured in individual directions had a certain reference value, as the mobility of eyes has two degrees of freedom. The accuracy of the pupil localization could be measured by calculating the percentage of the eye pupil images for which the pixel error was lower than a threshold in pixels. We compared our pupil detection method with the classical Starburst [33] algorithm and circular Hough transform (CHT) [36]. The performance of pupil localization with different algorithms is illustrated in Table 3. The accuracy rates of the following statistical indicators were used: \"\(\mathrm{D}_{\mathrm{P}}^{(\mathrm{E})}<5\)\" and \"\(\mathrm{D}_{\mathrm{P}}^{(\mathrm{E})}<10\)\" corresponded to the detection rate, at 5 and 10 pixels, in Euclidean distance; \"\(\mathrm{D}_{\mathrm{P}}^{(\mathrm{x})}<4\)\" or \"\(\mathrm{D}_{\mathrm{P}}^{(\mathrm{y})}<2\)\" represented the percentage of the eye pupil images for which the pixel error was lower than 4 pixels in horizontal direction or 2 pixels in vertical direction. As we can see, the performance of the Starburst algorithm was much poorer, which was due to the detection of the pupil contour points, using the iterative feature-based technique. In this step, the candidate feature points that belonged to the contour points were determined along the rays that extended radially away from the starting point, until a threshold \(\varnothing=20\) was exceeded. For our database, there were many disturbing contour points detected, especially the limbus. This could cause the final stage to find the best-fitting ellipse for a subset of candidate feature points by using the RANSAC method to misfit the limbus. The performance of the CHT was acceptable, but it was highly dependent on the estimate of the range of the radius of the pupil. There might have been overlaps between the radius of the pupil and the limbus for different samples, which made the algorithm invalid for some samples. While our method shows a good detection result overall. Actually, the overall detection rate was an average result. Poor detection in some samples had lowered the overall performance. Listed below, are some cases in locating the pupil, as shown in Figure 9. Some correct detection results are shown in Figure 9a, which shows that our algorithm could get a good detect effect in most cases, even if there was interference from glasses. Some typical examples of errors are described in Figure 9b. The errors could be attributed to the following factors--(1) a large part of the pupil was covered by the eyelids so that the exposed pupil contour, together with a part of eyelid contour, were fitted to an ellipse when the model was fitted, as shown in set 1 of Figure 9b; (2) the pupil was extremely small, so the model fitting was prone to be similar to the result discussed in factor 1, as shown in set 2 of Figure 9b; (3) the difference within the iris region was not so apparent that the canny filter could not get a good edge of the pupil, thus, leading to poor results, as shown in set 3 of Figure 9b; (4) the failure detection caused by the phantom effects when the fast-moving occluder was close to the eyeball, as shown in set 4 of Figure 9b.