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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Akutsu, T.: On determining the congruence of point sets in d dimensions. Computational Geometry 9(4), 247–256 (1998)
Alt, H., Guibas, L.: Discrete geometric shapes: Matching, interpolation, and approximation, pp. 121–153. Elsevier Science Publishers B.V. North-Holland (1999)
Alt, H., Mehlhorn, K., Wagener, H., Welzl, E.: Congruence, similarity and symmetries of geometric objects. Discret. Comput. Geom. 3, 237–256 (1988)
Arimura, H., Uno, T., Shimozono, S.: Time and space efficient discovery of maximal geometric graphs. In: Corruble, V., Takeda, M., Suzuki, E. (eds.) DS 2007. LNCS (LNAI), vol. 4755, pp. 42–55. Springer, Heidelberg (2007)
Carpentier, M., Brouillet, S., Pothier, J.: Yakusa: a fast structural database scanning method. Proteins 61(1), 137–151 (2005)
Cho, M., Mount, D.M.: Improved approximation bounds for planar point pattern matching. Algorithmica 50(2), 175–207 (2008)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry: Algorithms and Applications. Springer-Verlag (2000)
de Rezende, P.J., Lee, D.: Point set pattern matching in \(d\)-dimensions. Algorithmica 13(4), 387–404 (1995)
Downey, R.G., Fellows, M.R.: Parameterized complexity. Springer (1999)
Goodrich, M.T., Mitchell, J.S., Orletsky, M.W.: Approximate geometric pattern matching under rigid motions. IEEE Trans. PAMI 21(4), 371–379 (1999)
Kabsch, W.: A solution for the best rotation to relate two sets of vectors. Acta Crystallographica A32(5), 922–923 (1976)
Mäkinen, V., Ukkonen, E.: Point pattern matching. In: Kao, M. (ed.) Encyclopedia of Algorithms, pp. 657–660. Springer (2008)
Nowozin, S., Tsuda, K.: Frequent subgraph retrieval in geometric graph databases. In: 8th IEEE Int’l Conf. on Data Mining, pp. 953–958 (2008)
Pinsky, M., Karlin, S.: An introduction to stochastic modeling. Academic Press (2010)
Schwartz, J.T., Sharir, M.: Identification of partially obscured objects in two and three dimensions by matching noisy characteristic curves. The Int’l J. of Robotics Res. 6(2), 29–44 (1987)
Shibuya, T.: Geometric suffix tree: Indexing protein 3-d structures. Journal of the ACM 57(3), 15 (2010)
Tam, G.K., et al.: Registration of 3d point clouds and meshes: a survey from rigid to nonrigid. IEEE Trans. Vis. Comput. Graphics 19(7), 1199–1217 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
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. SISAP 2015. Lecture Notes in Computer Science(), vol 9371. Springer, Cham. https://doi.org/10.1007/978-3-319-25087-8_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-25087-8_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-25086-1
Online ISBN: 978-3-319-25087-8
eBook Packages: Computer ScienceComputer Science (R0)