Efficient Approximate 3-Dimensional Point Set Matching Using Root-Mean-Square Deviation Score
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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: Amato G., Connor R., Falchi F., Gennaro C. (eds) Similarity Search and Applications. Lecture Notes in Computer Science, vol 9371. Springer, Cham
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.
Keywords3D point set matching RMSD Geometric transformation One-to-one correspondence Branch and bound Probabilistic analysis
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