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Given two planar sets A and B, we examine the problem of determining the smallest ϵ such that there is a Euclidean motion (rotation and translation) of A that brings each member of A within distance ϵ of some member of B. We establish upper bounds on the combinatorial complexity of this subproblem in model-based computer vision, when the sets A and B contain points, line segments, or (filled-in) polygons. We also show how to use our methods to substantially improve on existing algorithms for finding the minimum Hausdorff distance under Euclidean motion.
Chew et al. (Wed,) studied this question.