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research-article

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

[+] Author and Article Information
Xiangzhi Wei

Institute of Intelligent Manufacturing and Information Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China
antonwei@sjtu.edu.cn

Jie Zhao

Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
carrotzhao@sjtu.edu.cn

Siqi Qiu

Institute of Intelligent Manufacturing and Information Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China
siqiqiu@sjtu.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4038968 History: Received January 18, 2017; Revised January 04, 2018

Abstract

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 e, 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 e. 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.

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