An Improved Algorithm for Point Set Pattern Matching under Rigid Motion

Abstract

This paper presents a simple algorithm for the partial point set pattern matching in 2D. Given a set P of n points, called sample set, and a query set Q of k points (n ≥ k), the problem is to find a matching of Q with a subset of P under rigid motion. In other words, whether each point in Q is matched with corresponding point in P under translation and/or rotation. The proposed algorithm requires O(n2) space and O(n2logn) preprocessing time, and the worst case query time complexity is O(kαlogn), where α is the maximum number of equidistant pairs of points. For a set of n points, α may be O(n4/3) in the worst case. Experimental results on random point sets and fingerprint databases show that it needs much less time in actual practice. The algorithm is then extended for checking the existence of a matching among two sets of line segments under rigid motion in O(knlogn) time, and locating a query polygon among a set of sample polygons in O(kn) time under rigid motion.