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Perimeter and Area Estimations of Digitized Objects with Fuzzy Borders

  • Nataša Sladoje
  • Ingela Nyström
  • Punam K. Saha
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)

Abstract

Fuzzy segmentation methods have been developed in order to reduce the negative effects of the unavoidable loss of data in the digitization process. These methods require the development of new image analysis methods, handling grey-level images. This paper describes the first step in our work on developing shape analysis methods for fuzzy images: the investigation of several measurements on digitized objects with fuzzy borders. The performance of perimeter, area, and the P 2 A measure estimators for digitized disks and digitized squares with fuzzy borders is analyzed. The method we suggest greatly improves the results obtained from crisp (hard) segmentation, especially in the case of low resolution images.

Keywords

Fuzzy shape representation measurement accuracy precision 

References

  1. 1.
    Bogomolny, A.: On the perimeter and area of fuzzy sets. Fuzzy Sets and Systems 23, 257–269 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Borgefors, G.: Distance transformations in digital images. Computer Vision, Graphics, and Image Processing 34, 344–371 (1986)CrossRefGoogle Scholar
  3. 3.
    Coeurjolly, D., Klette, R.: A comparative evaluation of length estimators. In: Proceedings of International Conference on Pattern Recognition (ICPR 2002, August 2002, vol. IV, pp. 330–334. IEEE Computer Society, Los Alamitos (2002)Google Scholar
  4. 4.
    Dorst, L., Smeulders, A.W.M.: Length estimators for digitized contours. Computer Vision, Graphics, and Image Processing 40, 311–333 (1987)CrossRefGoogle Scholar
  5. 5.
    Kulpa, Z.: Area and perimeter measurement of blobs in discrete binary pictures. Computer Graphics and ImageProcessing 6, 434–454 (1977)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Rosenfeld, A., Haber, S.: The perimeter of a fuzzy subset. Pattern Recognition 18, 125–130 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Saha, P.K., Udupa, J.K.: Relative fuzzy connectedness among multiple objects: Theory, algorithms, and applications in image segmentation. Computer Vision and Image Understanding 82(1), 42–56 (2001)zbMATHCrossRefGoogle Scholar
  8. 8.
    Sladoje, N., Nyström, I., Saha, P.K.: Measuring perimeter and area in low resolution images using a fuzzy approach. In: Bigun, J., Gustavsson, T. (eds.) SCIA 2003. LNCS, vol. 2749, pp. 853–860. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Yang, X.: Some properties of convex fuzzy sets. Fuzzy Sets and Systems 72, 129–132 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Zadeh, L.: Fuzzy sets. Information and Control 8, 338–353 (1965)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Nataša Sladoje
    • 1
  • Ingela Nyström
    • 1
  • Punam K. Saha
    • 2
  1. 1.Centre for Image AnalysisUppsalaSweden
  2. 2.MIPG, Dept. of RadiologyUniversity of PennsylvaniaPhiladelphiaUSA

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