Feature Based Defuzzification at Increased Spatial Resolution

  • Joakim Lindblad
  • Nataša Sladoje
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4040)


Defuzzification of fuzzy spatial sets by feature distance minimization, recently proposed as an alternative to crisp segmentation, is studied further. Fully utilizing information available in a fuzzy (discrete) representation of a continuous shape, we present an improved defuzzification method, such that the crisp discrete representation of a fuzzy set is generated at an increased spatial resolution, compared to the resolution of the fuzzy set. The correspondence between a fuzzy and a crisp set is established through a distance between their representations based on selected features, where the different resolutions of the images to compare are taken into account. The performance of the method is tested on both synthetic and real images.


fuzzy sets defuzzification multigrid resolution distance measure feature estimates 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bogomolny, A.: On the perimeter and area of fuzzy sets. Fuzzy Sets and Systems 23, 257–269 (1987)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Chanussot, J., Nyström, I., Sladoje, N.: Shape signatures of fuzzy sets based on distance from the centroid. Pattern Recognition Letters 26(6), 735–746 (2005)CrossRefGoogle Scholar
  3. 3.
    Leekwijck, W.V., Kerre, E.: Defuzzification: Criteria and classification. Fuzzy Sets and Systems 108, 159–178 (1999)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of state calculations by fast computing machines. Journal of Chemical Physics 21(6), 1087–1092 (1953)CrossRefGoogle Scholar
  5. 5.
    Pal, S., Rosenfeld, A.: Image enhancement and thresholding by optimization of fuzzy compactness. Pattern Recognition Letters 7, 77–86 (1988)MATHCrossRefGoogle Scholar
  6. 6.
    Rondeau, L., Ruelas, R., Levrat, L., Lamotte, M.: A defuzzification method respecting the fuzzification. Fuzzy Sets and Systems 86, 311–320 (1997)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Roventa, E., Spircu, T.: Averaging procedures in defuzzification processes. Fuzzy Sets and Systems 136, 375–385 (2003)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    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
  9. 9.
    Sladoje, N., Lindblad, J., Nyström, I.: Defuzzification of discrete objects by optimizing area and perimeter similarity. In: Kittler, J., Petrou, M., Nixon, M. (eds.) Proc. of 17th International Conference on Pattern Recognition (ICPR 2004), Cambridge, UK, vol. 3, pp. 526–529. IEEE Comp. Society, Los Alamitos (2004)CrossRefGoogle Scholar
  10. 10.
    Sladoje, N., Lindblad, J., Nyström, I.: Defuzzification of spatial fuzzy sets by feature distance minimization (submitted, 2005)Google Scholar
  11. 11.
    Sladoje, N., Nyström, I., Saha, P.: Measurements of digitized objects with fuzzy borders in 2D and 3D. Image and Vision Computing 23, 123–132 (2005)CrossRefGoogle Scholar
  12. 12.
    Udupa, J.K., Grevera, G.J.: Go digital, go fuzzy. Pattern Recognition Letters 23, 743–754 (2002)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Joakim Lindblad
    • 1
  • Nataša Sladoje
    • 2
  1. 1.Centre for Image AnalysisSwedish University of Agricultural SciencesUppsalaSweden
  2. 2.Faculty of EngineeringUniversity of Novi SadNovi SadSerbia and Montenegro

Personalised recommendations