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

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Combinatorial Image Analysis (IWCIA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6636))

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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.

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References

  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. Bloch, I.: On fuzzy distances and their use in image processing under imprecision. Pattern Recognition Letters 32, 1873–1895 (1999)

    Article  Google Scholar 

  3. Borgefors, G.: Hierarchical Chamfer Matching: A Parametric Edge Matching Algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence 10(6), 849–865 (1988)

    Article  Google Scholar 

  4. Boxer, L.: On Hausdorff-like metrics for fuzzy sets. Pattern Recognition Letters 18, 115–118 (1997)

    Article  Google Scholar 

  5. Brass, P.: On the nonexistence of Hausdorff-like metrics for fuzzy sets. Pattern Recognition Letters 23, 39–43 (2002)

    Article  MATH  Google Scholar 

  6. Chaudhuri, B.B., Rosenfeld, A.: On a metric distance between fuzzy sets. Pattern Recognition Letters 17, 1157–1160 (1996)

    Article  Google Scholar 

  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. 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. Eiter, T., Mannila, H.: Distance measures for point sets and their computation. Acta Informatica 34, 103–133 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  10. Fan, J.: Note on Hausdorff-like metrics for fuzzy sets. Pattern Recognition Letters 19, 739–796 (1998)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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. MPEG7 CE Shape-1 Part B, URL(2010), http://www.imageprocessingplace.com

  14. Ralescu, A., Ralescu, D.: Probability and fuzziness. Information Sciences 34(2), 85–92 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  15. Rosenfeld, A.: Distances between fuzzy sets. Pattern Recognition Letters 3, 229–233 (1985)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  Google Scholar 

  19. Zadeh, L.: Fuzzy sets. Information and control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Centre for Image Analysis, Uppsala University, Sweden

    Vladimir Ćurić

  2. Centre for Image Analysis, Swedish University of Agricultural Sciences, Uppsala, Sweden

    Joakim Lindblad

  3. Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Joakim Lindblad

  4. Faculty of Technical Sciences, University of Novi Sad, Serbia

    Nataša Sladoje

Authors
  1. Vladimir Ćurić
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  2. Joakim Lindblad
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  3. Nataša Sladoje
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, The University of Texas, 1 University Station C0803, 78712-0240, Austin, TX, USA

    Jake K. Aggarwal

  2. Department of Computer and Information Science, State University of New York at Fredonia, 280 Central Ave., 14063, Fredonia, NY, USA

    Reneta P. Barneva

  3. Mathematics Department, SUNY Buffalo State College, 1300 Elmwood Ave., 14222, Buffalo, NY, USA

    Valentin E. Brimkov

  4. Esuela Politécnica Superior, Departamento de Ingenería Informática, Universidad Autónoma de Madrid, c/Tomas y Valiente, 11, 28049, Cantoblanco, Madrid, Spain

    Kostadin N. Koroutchev

  5. Departamento de Física Fundamental, Universidad Nacional de Educación a Distancia, c/ Senda del Rey 9, 28080, Madrid, Spain

    Elka R. Korutcheva

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© 2011 Springer-Verlag Berlin Heidelberg

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Ćurić, V., Lindblad, J., Sladoje, N. (2011). Distance Measures between Digital Fuzzy Objects and Their Applicability in Image Processing. In: Aggarwal, J.K., Barneva, R.P., Brimkov, V.E., Koroutchev, K.N., Korutcheva, E.R. (eds) Combinatorial Image Analysis. IWCIA 2011. Lecture Notes in Computer Science, vol 6636. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21073-0_34

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  • DOI: https://doi.org/10.1007/978-3-642-21073-0_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21072-3

  • Online ISBN: 978-3-642-21073-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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