No abstract

It is shown that if each pair of curves 7i, ~'j, i ~ j, intersect one another in at most two points, then the boundary of K =1.)~"= 1Ki contains at most max(2, 6m-12) intersection points of the curves y,, and this bound cannot be improved. As a corollary, we obtain a similar upper bound for the number of points of local nonconvexity in the union of rn Minkowski sums of planar convex sets. Following a basic approach suggested by Lozano Perez and Wesley, this can be applied to planning a collision-free translational motion of a convex polygon B amidst several (convex) polygonal obstacles A 1 ..... Am. Assuming that the number of corners of B is fixed, the algorithm presented here runs in time O(n log2n), where n is the total number of comers of the Ai's.

No abstract

Model-based recognition is concerned with comparing a shape A, which is stored as a model for some particular object, with a shape B, which is found to exist in an image. If A and B are close to being the same shape, then a vision system should report a match and return a measure of how good that match is. To be useful this measure should satisfy a number of properties, including: (1) it should be a metric, (2) it should be invariant under translation, rotation, and change-of-scale, (3) it should be reasonably easy to compute, and (4) it should match our intuition (i.e., answers should be similar to those that a person might give). We develop a method for comparing polygons that has these properties. The method works for both convex and nonconvex polygons and runs in time O(mn log inn) where m is the number of vertices in one polygon and n is the number of vertices in the other.some examples to-ekaw that the method produces answers that are intuitively reasonable.