3D Similarity search by shape approximation

  • Hans-Peter Kriegel
  • Thomas Schmidt
  • Thomas Seidl
Spatial Similarities
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1262)

Abstract

This paper presents a new method for similarity retrieval of 3D surface segments in spatial database systems as used in molecular biology, medical imaging, or CAD. We propose a similarity criterion and algorithm for 3D surface segments which is based on the approximation of segments by using multi-parametric functions. The method can be adjusted to individual requirements of specific applications by choosing appropriate surface functions as approximation models. For an efficient evaluation of similarity queries, we developed a filter function which supports fast searching based on spatial index structures and guarantees no false drops. The evaluation of the filter function requires a new query type with multidimensional ellipsoids as query regions. We present an algorithm to efficiently perform ellipsoid queries on the class of spatial index structures that manage their directory by rectilinear hyperrectangles, such as R-trees or X-trees. Our experiments show both, effectiveness as well as efficiency of our method using a sample application from molecular biology.

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References

  1. [AFS93]
    Agrawal R., Faloutsos C., Swami A.: ‘Efficient Similarity Search in Sequence Databases', Proc. 4th. Int. Conf. on Foundations of Data Organization and Algorithms (FODO'93), Evanston, ILL, in: Lecture Notes in Computer Science, Vol. 730, Springer, 1993, pp. 69–84.Google Scholar
  2. [ALSS 95]
    Agrawal R., Lin K.-I., Sawhney H. S., Shim K.: ‘Fast Similarity Search in the Presence of Noise, Scaling, and Translation in Time-Series Databases', Proc. 21th Int. Conf. on Very Large Databases (VLDB'95), Morgan Kaufmann, 1995, pp. 490–501.Google Scholar
  3. [Ber+77]
    Bernstein F. C., Koetzle T. F., Williams G. J., Meyer E. F., Brice M. D., Rodgers J. R., Kennard O., Shimanovichi T., Tasumi M.: ‘The Protein Data Bank: a Computer-based Archival File for Macromolecular Structures', Journal of Molecular Biology, Vol. 112, 1977, pp. 535–542.Google Scholar
  4. [Ber+97]
    Berchtold S., Böhm C., Braunmüller B., Keim D., Kriegel H.-P.: ‘Fast Parallel Similarity Search in Multimedia Databases', Proc. ACM SIGMOD Int. Conf. on Management of Data, 1997.Google Scholar
  5. [BHKS 93]
    Brinkhoff T., Horn H., Kriegel H.-P., Schneider R.: ‘A Storage and Access Architecture for Efficient Query Processing in Spatial Database Systems', Proc. 3rd Int. Symp. on Large Spatial Databases (SSD'93), Singapore, 1993, Lecture Notes in Computer Science, Vol. 692, Springer, pp. 357–376.Google Scholar
  6. [BKK 96]
    Berchtold S., Keim D., Kriegel H.-P.: ‘The X-tree: An Index Structure for High-Dimensional Data', Proc. 22nd Int. Conf. on Very Large Data Bases (VLDB'96), Mumbai, India, 1996, pp. 28–39.Google Scholar
  7. [BKK 97]
    Berchtold S., Keim D., Kriegel H.-P.: ‘Using Extended Feature Objects for Partial Similarity Retrieval', accepted for publication in VLDB Journal.Google Scholar
  8. [BK 97]
    Berchtold S., Kriegel H.-P: ‘S3: Similarity Search in CAD Database Systems', Proc. ACM SIGMOD Int. Conf. on Management of Data, 1997.Google Scholar
  9. [BKSS 90]
    Beckmann N., Kriegel H.-P, Schneider R., Seeger B.: ‘The R*-tree: An Efficient and Robust Access Method for Points and Rectangles', Proc. ACM SIGMOD Int. Conf. on Management of Data, Atlantic City, NJ, 1990, pp. 322–331.Google Scholar
  10. [BKSS 94]
    Brinkhoff T., Kriegel H.-P., Schneider R., Seeger B.: ‘Efficient Multi-Step Processing of Spatial Joins', Proc. ACM SIGMOD Int. Conf. on Management of Data, 1994, pp. 197–208.Google Scholar
  11. [BR 85]
    Best, M. J., Ritter K.: ‘Linear Programming. Active Set Analysis and Computer Programs', Englewood Cliffs, N.J., Prentice Hall, 1985.Google Scholar
  12. [Fal+94]
    Faloutsos C., Barber R., Flickner M., Hafner J., Niblack W., Petkovic D., Equitz W.: ‘Efficient and Effective Querying by Image Content', Journal of Intelligent Information Systems, Vol. 3, 1994, pp. 231–262.Google Scholar
  13. [FRM 94]
    Faloutsos C., Ranganathan M., Manolopoulos Y.: ‘Fast Subsequence Matching in Time-Series Databases', Proc. ACM SIGMOD Int. Conf. on Management of Data, 1994, pp. 419–429.Google Scholar
  14. [GM 93]
    Gary J. E., Mehrotra R.: ‘Similar Shape Retrieval using a Structural Feature Index', Information Systems, Vol. 18, No. 7, 1993, pp. 525–537.Google Scholar
  15. [Gut 84]
    Guttman A.: ‘R-trees: A Dynamic Index Structure for Spatial Searching', Proc. ACM SIGMOD Int. Conf. on Management of Data, Boston, MA, 1984, pp. 47–57.Google Scholar
  16. [HS 94]
    Holm L., Sander C.: ‘The FSSP database of structurally aligned protein fold families', Nucl. Acids Res. 22, 1994, pp. 3600–3609.Google Scholar
  17. [HS 95]
    Hjaltason G. R., Samet H.: ‘Ranking in Spatial Databases', Proc. 4th Int. Symposium on Large Spatial Databases (SSD'95), Lecture Notes in Computer Science, Vol. 951, Springer, 1995, pp. 83–95.Google Scholar
  18. [Jag 91]
    Jagadish H. V.: ‘A Retrieval Technique for Similar Shapes', Proc. ACM SIGMOD Int. Conf. on Management of Data, 1991, pp. 208–217.Google Scholar
  19. [Kor+96]
    Korn F., Sidiropoulos N., Faloutsos C., Siegel E., Protopapas Z.: ‘Fast Nearest Neighbor Search in Medical Image Databases', Proc. 22nd VLDB Conference, Mumbai, India, 1996, pp. 215–226.Google Scholar
  20. [MG 93]
    Mehrotra R., Gary J. E.: ‘Feature-Based Retrieval of Similar Shapes', Proc. 9th Int. Conf. on Data Engineering, Vienna, Austria, 1993, pp. 108–115.Google Scholar
  21. [OM 88]
    Orenstein J. A., Manola F. A..: ‘PROBE Spatial Data Modeling and Query Processing in an Image Database Application', IEEE Trans. on Software Engineering, Vol. 14, No. 5, 1988, pp. 611–629.Google Scholar
  22. [PTVF 92]
    Press W. H., Teukolsky S. A., Vetterling W. T, Flannery B. P.: ‘Numerical Recipes in C', 2nd ed., Cambridge University Press, 1992.Google Scholar
  23. [RKV 95]
    Roussopoulos N., Kelley S., Vincent F.: ‘Nearest Neighbor Queries', Proc. ACM SIGMOD Int. Conf. on Management of Data, 1995, pp. 71–79.Google Scholar
  24. [SK 95]
    Seidl T., Kriegel H.-P.: ‘A 3D Molecular Surface Representation Supporting Neighborhood Queries', Proc. 4th Int. Symposium on Large Spatial Databases (SSD '95), Portland, Maine, USA, Lecture Notes in Computer Science, Vol. 951, Springer, 1995, pp. 240–258.Google Scholar
  25. [SRF 87]
    Sellis T., Roussopoulos N., Faloutsos C.: ‘The R+-Tree: A Dynamic Index for Multi-Dimensional Objects', Proc. 13th Int. Conf. on Very Large Databases, Brighton, England, 1987, pp 507–518.Google Scholar
  26. [TC 91]
    Taubin G., Cooper D. B.: ‘Recognition and Positioning of Rigid Objects Using Algebraic Moment Invariants', in Geometric Methods in Computer Vision, Vol. 1570, SPIE, 1991, pp. 175–186.Google Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Hans-Peter Kriegel
    • 1
  • Thomas Schmidt
    • 1
  • Thomas Seidl
    • 1
  1. 1.Institute for Computer ScienceUniversity of MunichMünchenGermany

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