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We propose a novel eye and face tracking algorithm using active infrared (IR) illumination. Most eye trackers based on active IR illumination require bright pupil images to successfully detect eyes in image sequences. However, due to factors such as eye closure, head rotation, variation in illumination and occlusion, most trackers tend to fail in these situations where pupil shows weak reflections. Our proposed method overcomes these limitations by making use of the dark-bright pupil difference images as well as using adaptive thresholding techniques. The core computational module of the algorithm is based on the Kalman filter and adaptive template matching to find and update the most probable eye position in the current frame. Our eye tracker can robustly detect faces and track eyes in a sequence of images under variable lighting conditions and face orientations. Experiments show good performance in challenging image sequences with low quality and occluded images with the subject showing considerable head movements.