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.
Keywords3D point set matching RMSD Geometric transformation One-to-one correspondence Branch and bound Probabilistic analysis
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- 2.Alt, H., Guibas, L.: Discrete geometric shapes: Matching, interpolation, and approximation, pp. 121–153. Elsevier Science Publishers B.V. North-Holland (1999)Google Scholar
- 7.de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry: Algorithms and Applications. Springer-Verlag (2000)Google Scholar
- 9.Downey, R.G., Fellows, M.R.: Parameterized complexity. Springer (1999)Google Scholar
- 12.Mäkinen, V., Ukkonen, E.: Point pattern matching. In: Kao, M. (ed.) Encyclopedia of Algorithms, pp. 657–660. Springer (2008)Google Scholar
- 13.Nowozin, S., Tsuda, K.: Frequent subgraph retrieval in geometric graph databases. In: 8th IEEE Int’l Conf. on Data Mining, pp. 953–958 (2008)Google Scholar
- 14.Pinsky, M., Karlin, S.: An introduction to stochastic modeling. Academic Press (2010)Google Scholar