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

Abstract

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 ε-neighborhood of a point in P. The ε-neighborhood region of a point p _i  ∈ P is an axis-parallel square having each side of length ε and p _i at its centroid. We assume that the point set is well-seperated in the sense that for a given ε> 0, each pair of points p, p′ ∈ P satisfy at least one of the following two conditions (i) |x(p) − x(p′)| ≥ ε, and (ii) |y(p) − y(p′)| ≥ 3ε, 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(n k ² logn) 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.