Shape matching under rigid motion

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 Õ(n2ε−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 Õ(n3ε−4) time. The same error bound holds with probability 1 − n−O(1). We also show how to improve the running time to Õ(n + ε−3) for the translation case when one of the polygons is convex. ∗Research supported by the Research Grant Council, Hong Kong, China (project no. 611711). †Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong. Emails: [email protected], [email protected] This is the Pre-Published Version