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

In this paper, we study approximate point subset match (APSM) problem with minimum RMSD score under translation, rotation, and one-to-one correspondence in d-dimension. Since this problem seems computationally much harder than the previously studied APSM problems with translation only or distance evaluation only, 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. Next, we present another algorithm that runs fast with high probability when a set of parameters are fixed. Experimental results on real 3-D molecular data sets showed that our branch-and-bound algorithm achieved significant speed-up over the naive algorithm still keeping the advantage of generating all answers.