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International Conference on Advances in Visual Information Systems

VISUAL 2000: Advances in Visual Information Systems pp 467–476Cite as

Shape Similarity Measures, Properties and Constructions

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1929))

Abstract

This paper formulates properties of similarity measures. We list a number of similarity measures, some of which are not well known (such as the Monge-Kantorovich metric), or newly introduced (re ection metric), and give a set constructions that have been used in the design of some similarity measures.

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References

  1. H. Alt, B. Behrends, and J. Blömer. Approximate matching of polygonal shapes. Annals of Mathematics and Artificial Intelligence, pages 251–265, 1995.

    Google Scholar 

  2. H. Alt, U. Fuchs, G. Rote, and G. Weber. Matching convex shapes with respect to the symmetric difference. In Proc. ESA, pages 320–333. LNCS 1136, Springer, 1996.

    Google Scholar 

  3. H. Alt and M. Godeau. Computing the Fréchet distance between two polygonal curves. International Journal of Computational Geometry & Applications, pages 75–91, 1995.

    Google Scholar 

  4. E. Arkin, P. Chew, D. Huttenlocher, K. Kedem, and J. Mitchel. An effciently computable metric for comparing polygonal shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(3):209–215, 1991.

    Article  Google Scholar 

  5. A. J. Baddeley. An error metric for binary images. In Robust Computer Vision: Quality of Vision Algorithms, Proc. of the Int. Workshop on Robust Computer Vision, Bonn, 1992, pages 59–78. Wichmann

    Google Scholar 

  6. L. P. Chew, M. T. Goodrich, D. P. Huttenlocher, K. Kedem, J. M. Kleinberg, and D. Kravets. Geometric pattern matching under Euclidean motion. Computational Geometry, Theory and Applications, 7:113–124, 1997.

    MATH  MathSciNet  Google Scholar 

  7. P. Chew and K. Kedem. Improvements on approximate pattern matching. In 3rd Scandinav. Workshop Algorithm Theory, LNCS 621, pages 318–325. Springer, 1992.

    Google Scholar 

  8. S. D. Cohen and L. J. Guibas. Partial matching of planar polylines under similarity transformations. In Proc. SODA, pages 777–786, 1997.

    Google Scholar 

  9. G. Cortelazzo, G. A. Mian, G. Vezzi, and P. Zamperoni. Trademark shapes description by string-matching techniques. Pattern Recognition, 27:1005–1018, 1994.

    Article  Google Scholar 

  10. A. Efrat and A. Itai. Improvements on bottleneck matching and related problems using geometry. Proc. SoCG, pages 301–310, 1996.

    Google Scholar 

  11. R. Fagin and L. Stockmeyer. Relaxing the triangle inequality in pattern matching. Int. Journal of Computer Vision, 28(3):219–231, 1998.

    Article  Google Scholar 

  12. R. Fleischer, K. Mehlhorn, G. Rote, E. Welzl, and C. Yap. Simultaneous inner and outer approximation of shapes. Algorithmica, 8:365–389, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  13. D. Fry. Shape Recognition using Metrics on the Space of Shapes. PhD thesis, Harvard University, Department of Mathematics, 1993.

    Google Scholar 

  14. M. Hagedoorn and R. C. Veltkamp. Metric pattern spaces. Technical Report UU-CS-1999-03, Utrecht University, 1999.

    Google Scholar 

  15. M. Hagedoorn and R. C. Veltkamp. Reliable and efficient pattern matching using an affine invariant metric. Int. Journal of Computer Vision, 31(2/3):203–225, 1999.

    Article  Google Scholar 

  16. D. P. Huttenlocher, K. Kedem, and J. M. Kleinberg. On dynamic Voronoi diagrams and the minimum Hausdorff distance for point sets under EuWWW.clidean motion in the plane. In Proc. SoCG, pages 110–120, 1992.

    Google Scholar 

  17. D. P. Huttenlocher, K. Kedem, and M. Sharir. The upper envelope of Voronoi surfaces and its applications. Discrete and Comp. Geometry, 9:267–291, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  18. D. P. Huttenlocher, G. A. Klanderman, and W. J. Rucklidge. Comparing images using the hausdorff distance. IEEE Transactions on Pattern Analysis and Machinen Intelligence, 15:850–863, 1993.

    Article  Google Scholar 

  19. Plato. Meno. Perseus Encyclopedia, Tuft University, http://www.perseus.tufts. edu/Texts/chunk_TOC.grk.html#Plato, 380 B.C.

  20. S. Rachev. The Monge-Kantorovich mass transference problem and its stochastical applications. Theory of Probability and Applications, 29:647–676, 1985.

    Article  MATH  Google Scholar 

  21. Y. Rubner, C. Tomassi, and L Guibas. A metric for distributions with applications to image databases. In Proc. of the IEEE Int. Conf. on Comp. Vision, Bombay, India, pages 59–66, 1998.

    Google Scholar 

  22. W. Rucklidge. Efficient Visual Recognition Using the Hausdorff Distance. LNCS. Springer, 1996.

    MATH  Google Scholar 

  23. S. Schirra. Approximate decision algorithms for approximate congruence. Information Processing Letters, 43:29–34, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  24. L. Schomaker, E. de Leau, and L. Vuurpijl. Using pen-based outlines for object-based annotation and image-based queries. In Visual Information and Information Systems, LNCS 1614, pages 585–592. Springer, 1999.

    Google Scholar 

  25. A. Tversky. Features of similarity. Psychological Review, 84(4):327–352, 1977.

    Article  Google Scholar 

  26. J. Vleugels and R. C. Veltkamp. Efficient image retrieval through vantage objects. In Visual Information and Information Systems, LNCS 1614, pages 575–584. Springer, 1999.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computing Science, Utrecht University, The Netherlands

    Remco C. Veltkamp & Michiel Hagedoorn

Authors
  1. Remco C. Veltkamp
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  2. Michiel Hagedoorn
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Editor information

Editors and Affiliations

  1. Claude Bernard University of Lyon, LISI - 502, INSA de Lyon, 69621, Villeurbanne Cedex, France

    Robert Laurini

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© 2000 Springer-Verlag Berlin Heidelberg

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Veltkamp, R.C., Hagedoorn, M. (2000). Shape Similarity Measures, Properties and Constructions. In: Laurini, R. (eds) Advances in Visual Information Systems. VISUAL 2000. Lecture Notes in Computer Science, vol 1929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40053-2_41

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  • DOI: https://doi.org/10.1007/3-540-40053-2_41

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41177-2

  • Online ISBN: 978-3-540-40053-0

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