Technical Report CS0599

Title: Navigating In Moving Influence Fields
Authors: Y. Pnueli, N. Kiryati, A.M. Bruckstein
Abstract: This paper applies existing Hough transform methods used for detecting straight lines [2] and general two dimensional shapes [3] in images and for straight line fitting [4] to problems of constant velocity motion design in the p~sence of moving objects in two and three dimensions. Hough transform methods solve optimization problems in two stages. In the first, accumulation stage, the cost of each possible solution is calculated. In the second, search stage, the parameter space is searched for the optimal solution. We show that in the appropriate parameter space, the locus of velocities incurring the same cost by the encounter with a given moving object is a straight line passing through the origin. We utilize this fact to achieve an efficient accumulation algorithm. Since the computational complexity of the algorithm is dominated by the accumulation stage this results in an overall efficient algorithm.
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