Efficient approximate 3-dimensional point set matching using root-mean-square deviation score

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Abstract

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.

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Sasaki, Y., Shibuya, T., Ito, K., & Arimura, H. (2015). Efficient approximate 3-dimensional point set matching using root-mean-square deviation score. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9371, pp. 191–203). Springer Verlag. https://doi.org/10.1007/978-3-319-25087-8_18

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