Circle-Point Containment, Monte Carlo Method for Shape Matching Based on Feature Points Using the Technique of Sparse Uniform Grids

Shape matching using their critical feature points is useful in mechanical processes such as precision measure of manufactured parts and automatic assembly of parts. In this paper, we present a practical algorithm for measuring the similarity of two point sets A and B: Given an allowable tolerance ε, our target is to determine the feasibility of placing A with respect to B such that the maximum of the minimum distance from each point of A to its corresponding matched point in B is no larger than ε. For sparse and small point sets, an improved algorithm is achieved based on a sparse grid, which is used as an auxiliary structure for building the correspondence relationship between A and B. For large point sets, allowing a trade-off between efficiency and accuracy, we approximate the problem as computing the directed Hausdorff distance from A to B, and provide a two-phase nested Monte Carlo method for solving the problem. Experimental results are presented to validate the proposed algorithms.