A Simple Algorithm for Approximate Partial Point Set Pattern Matching under Rigid Motion

This paper deals with the problem of approximate point set pattern matching in 2D. Given a set P of n points, called sample set, and a query set Q of k points (k <= n), the problem is to find a. match of Q with a subset of P under rigid motion (rotation and/or translation) transformation such that each point in Q lies in the epsilon-neighborhood of a point in P. The epsilon-neighborhood region of a point p(i) is an element of P is an axis-parallel square having each side of length epsilon and p(i) at its centroid. We assume that the point set is well-seperated in the sense that for a given epsilon > 0, each pair of points p, p' is an element of P satisfy at least one of the following two conditions (i) |x(p) - x(p')| >= epsilon, and (ii) |y(p) - y(p')| >= 3 epsilon, and we propose an algorithm for the approximate matching that can find a match (if it exists) under rigid motion in O(n(2)k(2)(klogk + logn)) time. If only translation is considered then the existence of a match can be tested in O(nk(2) log n) time. The salient feature of our algorithm for the rigid motion and translation is that it. avoids the use of intersection of high degree curves.