Efficient Approximate 3-Dimensional Point Set Matching Using Root-Mean-Square Deviation Score

Yoichi SASAKI  Tetsuo SHIBUYA  Kimihito ITO  Hiroki ARIMURA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A   No.9   pp.1159-1170
Publication Date: 2019/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.1159
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: Optimization
3D point set matching,  RMSD,  geometric transformation,  one-to-one correspondence,  branch and bound,  probabilistic analysis,  

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In this paper, we study the approximate point set matching (APSM) problem with minimum RMSD score under translation, rotation, and one-to-one correspondence in d-dimension. Since most of the previous works about APSM problems use similality scores that do not especially care about one-to-one correspondence between points, such as Hausdorff distance, we cannot easily apply previously proposed methods to our APSM problem. So, we focus on speed-up of exhaustive search algorithms that can find all approximate matches. First, we present an efficient branch-and-bound algorithm using a novel lower bound function of the minimum RMSD score for the enumeration version of APSM problem. Then, we modify this algorithm for the optimization version. Next, we present another algorithm that runs fast with high probability when a set of parameters are fixed. Experimental results on both synthetic datasets and real 3-D molecular datasets showed that our branch-and-bound algorithm achieved significant speed-up over the naive algorithm still keeping the advantage of generating all answers.