The precision of the template matching - basic and rened - and the de-formable template matching is accurate almost independent of resolution and they are very fast for low resolution images. The precision of the heuristic double thresholding worsens when decreasing resolution. The edges con-fusing the color-based template method is smoothed out to some extent, consequently the performance is improved. Interpreting the results, the de-formable template matching method should be chosen if one focus on high accuracy. On the other hand, if one require as less computation time as possible, the basic template matching should be utilized.
19.2 Performance of Bayesian Eye Trackers
A Bayesian approach for eye tracking is presented in chapter 14. The eye is tracked from a video sequence utilizing the active contour method [36][64]
and particle ltering, but extended with constraints, robust statistics, and a novel renement method - Deformable template matching.
A few examples of the tracker is depicted in the theory part in gure 14.8. Tracking the eyes during blinking is a challenging task. An example of this phenomena is illustrated in gure 19.3. The extension of the contour method, increases the robustness to outliers and relaxes the importance of the hypotheses along the contour around the eyelids. The resulting estimate of the iris center is seen, in bottom right gure 19.3, to be ne.
The performance of the active contour methods are evaluated by averag-ing over 10 runs of the video frame sequences. Figure 19.4 depicts the error as a function of the number of particles used, for low resolution and high resolution images respectively. The errors of the three dierent active con-tour algorithms are shown; basic, with EM renement, and with deformable template renement. In addition, the constraints regarding the mentioned methods are evaluated.
The proposed constraints on the active contour generally improves the accuracy of the t. However, utilizing the constraints with more than 50 par-ticles in high-resolution images, worsens the precision. This is caused by the fact that the contour shape changes with the gaze direction; in the extreme directions of gaze, the contour is deformed to an extent which is penalized by the constraints. Thus, there is no need to constraint the deformation, when the number of particles is suciently large on high-resolution images.
The constraints should therefore be utilized on low-resolution images, and to avoid a break down of the algorithm due to poor data. In contrast, the constraints on the deformable template never worsens the accuracy. The two
150 CHAPTER 19. EYE TRACKING
Figure 19.3: The active contour algorithm utilizes particle ltering. (Top left:) A frame challenging the eye trackers; eye blinking. (Top right:) A set of particles is drawn from a prediction prior. (Bottom left:) By evaluation of the hypotheses regarding the particles, a new re-sampled set of particles is obtained. This is the estimated posterior state distribution. (Bottom right:) The current state is then found by taking the sample mean of the estimated posterior probability. Notice that the algorithm is capable to estimate the center of iris, despite the fact that a major part of the iris is occluded by the eyelid.
19.2. PERFORMANCE OF BAYESIAN EYE TRACKERS 151
No. of particles
Mean Error [mm]
AC w/ Cons.
No. of particles
Mean Error [mm]
AC w/ Cons.
No. of particles Hi−res Data
No. of particles Lo−res Data
AC AC w/ EM AC w/ DT
Figure 19.4: Performance of the active contour averaged across 10 runs of each method.
(Top gures:) The error of the active contour algorithms as a function of the number of particles and resolution. Constraining the shape deformation clearly improves the accuracy of the contour method in low-resolution and high-resolution images with few particles.
Utilizing the constraints with more than 50 particles in high-resolution images, worsens the precision. In general, the deformable template renement has the best precision.
(Bottom gures:) The framerate of the methods are evaluated as the number of frames processed pr. second. The framerate is highly dependent on the number of particles, and the basic contour is considerably faster than the rened versions. On the other hand, the number of particles needed is reduced signicantly by use of renement.
152 CHAPTER 19. EYE TRACKING error curves converges to the same value when the number of particles is increased. Contrary to the iris, the pupil is not partly occluded except when blinking. Therefore, the method is more accurate although the number of particles is lower.
The renement by the deformable template outperforms the EM method - Even when comparing low-resolution image to EM renement on high-resolution images. The cost is an increased number of computations, which is resolution dependent. The basic, or even EM rened, active contour is faster than the deformable renement utilizing few particles in high-resolution data.
Conversely, increasing the number of particles or by use of low-resolution images, this renement is not signicant slower.
In general the methods perform better in high-resolution images com-pared to low-resolution images, where the dependency on the number of particles is increased. The cost of increasing the number of particles is an increased number of computations - leading to a lower framerate. The de-formable template is, however, only dependent on the resolution. Hence, the framerate is increased when the number of pixels is decreased.
Corneal reections caused naturally by illumination challenges the eye tracking methods. Typically, this phenomenon inuences on the accuracy - The estimate is biased to some extent. A frame sequence exemplifying handling of corneal reections is shown in gure 19.5. The light conditions result in strong reections in bottom left gure. By weighing the hypotheses as proposed in section 14.6 and utilizing robust statistics regarding the de-formable template, increases the robustness and accuracy of the estimate of the iris center. An illustrative example is found in gure 14.4.
19.2.1 Ability to Handle Eye Movements
The particles are drawn from a narrower distribution in frame sequences where the center location of iris is nearly static. In this case, sudden eye movements may confuse the contour method. The re-sampling of particles, broadens the state distribution and thus recovering the t in a few frames.
The performance of the contour method under dynamic and static states is shown in gure 19.6. The performance is certainly aected by eye move-ments, when utilizing few particles. The error of the dynamic frames is in general a bit larger, but vanishes when the number of particles is increased.
The deformable template has, surprisingly, a lower error in these frames. This is caused by the fact, that the error is in average larger in the extremes of the gaze direction; the eye is typically static in these states. Hence, the error function is biased to some extent. The inuence on the low-resolution data is less compared to the high-resolution. This is due to the relative smaller