Shape matching under rigid motion

Abstract

We present improved algorithms to match two polygonal shapes P and Q to approximate their maximum overlap. Let n be their total number of vertices. Our first algorithm finds a translation that approximately maximizes the overlap area of P and Q under translation in O(n 2 ε −3) time. The error is additive and it is at most ε • min{area(P), area(Q)} with probability 1 − n −O(1). We also obtain an algorithm that approximately maximizes the overlap of P and Q under rigid motion in O(n 3 ε −4) time. The same error bound holds with probability 1 − n −O(1). We also show how to improve the running time to O(n + ε −3) for the translation case when one of the polygons is convex.