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Minimum Hausdorff distance under rigid motions and comparison of protein structures

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Abstract

Hausdorff distance between two compact sets, defined as the maximum distance from a point of one set to another set, has many application in computer science. It is a good measure for the similarity of two sets. This paper proves that the shape distance between two compact sets in R n defined by minimum Hausdorff distance under rigid motions is a distance. The authors introduce similarity comparison problems in protein science, and propose that this measure may have good application to comparison of protein structure as well. For calculation of this distance, the authors give one dimensional formulas for problems (2, n), (3, 3), and (3, 4). These formulas can reduce time needed for solving these problems. The authors did some numerical experiments for (2, n). On these sets of data, this formula can reduce time needed to one fifteenth of the best algorithms known on average. As n increases, it would save more time.

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References

  1. F. P. Preparata and M. I. Shamos, Computational Geometry: An Introduction, Springer-Verlag, New York, 1985.

    Google Scholar 

  2. H. Alt and L. Guibas, Discrete geometric shapes: Matching, interpolation, and approximation, Handbook of Computational Geometry (ed. by J. R. Sack and J. Urrutia), Elsevier Science, 1999, 121–154.

  3. S. Seeger and X. Laboureux, Feature extraction and registration: An overview, Principles of 3D Image Analysis and Synthesis (ed. by Bernd Girod, Gnther Greiner, Heinrich Niemann), Kluwer Academic Publishers, 2002, 153–166.

  4. W. J. Rucklidge, Efficiently locating objects using the Hausdorff distance, International Journal of Computer Vision, 1997, 24(3): 251–270.

    Article  Google Scholar 

  5. D. Sim, O. Kwon, and R. Park, Object matching algorithms using robust Hausdorff distance measures, IEEE Transactions on Image Processing, 1999, 8(3): 425–429.

    Article  Google Scholar 

  6. D. P. Hunttenlocher, G. A. Klanderman, and W. J. Rucklidge, Comparing images using the Hausdorff distance, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1993, 15(9): 850–863.

    Article  Google Scholar 

  7. L. Holm and C. Sander, Mapping the protein universe, Science, 1996, 273: 595–602.

    Article  Google Scholar 

  8. M. S. Johnson, A. Sali, and T. L. Blundell, Phylogenetic relationships from three-dimensional protein structures, Methods Enzymol., 1990, 183: 670–690.

    Article  Google Scholar 

  9. W. A. Koppensteiner, P. Lackner, M. Wiederstein, and M. J. Sippl, Characterization of novel proteins based on known protein structres, J. Mol. Biol. 2000, 296(4): 1139–1152.

    Article  Google Scholar 

  10. A. M. Edwards, B. Kus, R. Jansen, D. Greenbaum, J. Greenblatt, and M. Gerstein, Bridging structural biology and genomics: Assessing protein interaction data with known complexes, Trends Genet. 2002, 18: 529–536.

    Article  Google Scholar 

  11. I. Halperin, B. Ma, H. Wolfson, and R. Nussinov, Principles of docking: An overview of search algorithms and a guide to scoring functions, Proteins: Structure, Functions, and Genetics, 2002, 47: 409–443.

    Article  Google Scholar 

  12. I. N. Shindyalov and P. E. Bourne, Protein structure alignment by incremental combinatorial extension (CE) of the optimal path, Protein Engineering, 1998, 11(9): 739–747.

    Article  Google Scholar 

  13. L. Holm and C. Sander, Protein structure comparison by alignment of distance matrices, J. Mol. Biol., 1993, 233(1): 123–138.

    Article  Google Scholar 

  14. E. Krissinel and K. Henrick, Secondary-structure matching (SSM), a new tool for fast protein structure alignment in three dimensions, Acta Crystallogr. D Biol. Crystallogr., 2004, 60 (Pt12 Pt1): 2256–2268.

    Article  Google Scholar 

  15. D. P. Huttenlocher and K. Kedem, Computing the minimum Hausdorff distance for point sets under translation, Proceedings of the Sixth Annual Symposium for Computing Geometry, 1990, 340–349.

  16. G. Rote, Computing the minimum Hausdorff distance between two point sets on a line under translation, Information Processing Letters, 1991, 38: 123–127.

    Article  MATH  MathSciNet  Google Scholar 

  17. M. Ben-Or, Lower bounds for algebraic computation trees, in Proc. 15th Annual ACM Symp. on Theory of Computing, 1983, 80–86.

  18. B. H. Li, Y. F. Shen, and B. Li, A new algorithm for computing the minimum Hausdorff distance between two point sets on a line under translation, Information Processing Letters, 2008, 106(2): 52–58.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Key Laboratory of Mathematics Mechanization and Center of Bioinformatics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Banghe Li, Bo Li & Yuefeng Shen

  2. Graduate University of Chinese Academy of Sciences, Beijing, 100049, China

    Bo Li & Yuefeng Shen

Authors
  1. Banghe Li
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  2. Bo Li
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  3. Yuefeng Shen
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Corresponding author

Correspondence to Banghe Li.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant No. 10771206 and by 973 Project (2004CB318000) of China.

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Li, B., Li, B. & Shen, Y. Minimum Hausdorff distance under rigid motions and comparison of protein structures. J Syst Sci Complex 22, 560–586 (2009). https://doi.org/10.1007/s11424-009-9188-0

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  • DOI: https://doi.org/10.1007/s11424-009-9188-0

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