An Efficiently Computable Metric for Comparing Polygonal Shapes

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 is based on the L2 distance between the turning functions of the two polygons. It works for both convex and nonconvex polygons and runs in time O(mn log mn) where m is the number of vertices in one polygon and n is the number of vertices in the other. We also present some examples to show that the method produces answers that are intuitively reasonable.