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EyeSeeCam is a novel head mounted camera that is continuously oriented to the user's point of regard by the eye movement signals of a mobile video-based eye tracking device. We have devised a new eye tracking algorithm for EyeSeeCam which has low computational complexity and lends enough robustness in the detection of pupil centre. Accurate determination of the location of the centre of the pupil and processing speed are the most crucial requirements in such a real-time video-based eye-tracking system. However, occlusion of the pupil by artifacts such as eyelids, eyelashes, glints and shadows in the image of the eye and changes in the illumination conditions pose significant problems in the determination of pupil centre. Apart from robustness and accuracy, real-time eye-tracking applications demand low computational complexity as well. In our algorithm, the Fast Radial Symmetry Detector is used to give a rough estimate of the location of the pupil. An edge operator is used to produce the edge image. Unwanted artifacts are deleted in a series of logical steps. Then, Delaunay Triangulation is used to extract the pupil boundary from the edge image, based on the fact that the pupil is a convex hull. A luminance contrast filter is used to obtain an ellipse fit at the subpixel level. The ellipse fitting function is based on a non iterative least squares minimization approach. The pupil boundary was detected accurately in 96% of the cases, including those in which the pupil was occluded by more than half its size. The proposed algorithm is also robust against drastic changes in the environment, i.e., eye tracking in a closed room versus eye tracking in sunlight.