Abstract

The factorization method described in this series of reports requires an algorithm to track the motion of features in an image stream. Given the small inter-frame displacement made possible by the factorization approach, the best tracking method turns out to be the one proposed by Lucas and Kanade in 1981. The method defines the measure of match between fixed-size feature windows in the past and current frame as the sum of squared intensity differences over the windows. The displacement is then defined as the one that minimizes this sum. For small motions, a linearization of the image intensities leads to a Newton-Raphson style minimization. In this report, after rederiving the method in a physically intuitive way, we answer the crucial question of how to choose the feature windows that are best suited for tracking. Our selection criterion is based directly on the definition of the tracking algorithm, and expresses how well a feature can be tracked. As a result, the criterion is optimal by construction. We show by experiment that the performance of both the selection and the tracking algorithm are adequate for our factorization method, and we address the issue of how to detect occlusions. In the conclusion, we point out specific open questions for future research. Chapter 1

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