Distance Measures between Digital Fuzzy Objects and Their Applicability in Image Processing

  • Vladimir Ćurić
  • Joakim Lindblad
  • Nataša Sladoje
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6636)

Abstract

We present two different extensions of the Sum of minimal distances and the Complement weighted sum of minimal distances to distances between fuzzy sets. We evaluate to what extent the proposed distances show monotonic behavior with respect to increasing translation and rotation of digital objects, in noise free, as well as in noisy conditions. Tests show that one of the extension approaches leads to distances exhibiting very good performance. Furthermore, we evaluate distance based classification of crisp and fuzzy representations of objects at a range of resolutions. We conclude that the proposed distances are able to utilize the additional information available in a fuzzy representation, thereby leading to improved performance of related image processing tasks.

Keywords

Fuzzy sets set distance registration classification 

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References

  1. 1.
    Bloch, I., Maitre, H.: Fuzzy distances and image processing, In: Proc. of the ACM Symposium on Applied Computing, Tennessee, USA, pp. 570–573 (1995)Google Scholar
  2. 2.
    Bloch, I.: On fuzzy distances and their use in image processing under imprecision. Pattern Recognition Letters 32, 1873–1895 (1999)CrossRefGoogle Scholar
  3. 3.
    Borgefors, G.: Hierarchical Chamfer Matching: A Parametric Edge Matching Algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence 10(6), 849–865 (1988)CrossRefGoogle Scholar
  4. 4.
    Boxer, L.: On Hausdorff-like metrics for fuzzy sets. Pattern Recognition Letters 18, 115–118 (1997)CrossRefGoogle Scholar
  5. 5.
    Brass, P.: On the nonexistence of Hausdorff-like metrics for fuzzy sets. Pattern Recognition Letters 23, 39–43 (2002)CrossRefMATHGoogle Scholar
  6. 6.
    Chaudhuri, B.B., Rosenfeld, A.: On a metric distance between fuzzy sets. Pattern Recognition Letters 17, 1157–1160 (1996)CrossRefGoogle Scholar
  7. 7.
    Ćurić, V., Lindblad, J., Sladoje, N., Sarve, H.: Set distances and their performance in binary image registration (2010) (submitted for publication)Google Scholar
  8. 8.
    Dubuisson, M., Jain, A.: A Modified Hausdorff Distance for Object Matching. In: Proc. of International Conference on Pattern Recognition, Jerusalem, Israel, pp. 566–568 (1994)Google Scholar
  9. 9.
    Eiter, T., Mannila, H.: Distance measures for point sets and their computation. Acta Informatica 34, 103–133 (1997)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Fan, J.: Note on Hausdorff-like metrics for fuzzy sets. Pattern Recognition Letters 19, 739–796 (1998)Google Scholar
  11. 11.
    Fudos, I., Palios, L., Pitoura, E.: Geometric-Similarity Retrieval in Large Image Bases. In: International Conference on Data Engineering, pp. 441–450. IEEE, Los Alamitos (2002)CrossRefGoogle Scholar
  12. 12.
    Lindblad, J., Ćurić, V., Sladoje, N.: On set distances and their application in image analysis. In: Proc. of International Symposium on Image and Signal Processing and Analysis (ISPA), pp. 449–545. IEEE, Salzburg (2009)Google Scholar
  13. 13.
    MPEG7 CE Shape-1 Part B, URL(2010), http://www.imageprocessingplace.com
  14. 14.
    Ralescu, A., Ralescu, D.: Probability and fuzziness. Information Sciences 34(2), 85–92 (1984)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Rosenfeld, A.: Distances between fuzzy sets. Pattern Recognition Letters 3, 229–233 (1985)CrossRefMATHGoogle Scholar
  16. 16.
    Sladoje, N., Lindblad, J.: High-precision boundary length estimation by utilizing gray-level information. IEEE Transaction on Pattern Analysis and Machine Intelligence 31(2), 357–363 (2009)CrossRefGoogle Scholar
  17. 17.
    Sladoje, N., Lindblad, J.: Estimation of moments of digitized objects with fuzzy borders. In: Roli, F., Vitulano, S. (eds.) ICIAP 2005. LNCS, vol. 3617, pp. 188–195. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. 18.
    Sladoje, N., Nyström, I., Saha, K.P.: Measurements of digitized objects with fuzzy borders in 2D and 3D. Image Vision Computing 23(2), 123–132 (2005)CrossRefGoogle Scholar
  19. 19.
    Zadeh, L.: Fuzzy sets. Information and control 8, 338–353 (1965)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Vladimir Ćurić
    • 1
  • Joakim Lindblad
    • 2
    • 3
  • Nataša Sladoje
    • 4
  1. 1.Centre for Image AnalysisUppsala UniversitySweden
  2. 2.Centre for Image AnalysisSwedish University of Agricultural SciencesUppsalaSweden
  3. 3.Mathematical InstituteSerbian Academy of Sciences and ArtsBelgradeSerbia
  4. 4.Faculty of Technical SciencesUniversity of Novi SadSerbia

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