Estimation of Moments of Digitized Objects with Fuzzy Borders

  • Nataša Sladoje
  • Joakim Lindblad
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3617)


Error bounds for estimation of moments from a fuzzy representation of a shape are derived, and compared with estimations from a crisp representation. It is shown that a fuzzy membership function based on the pixel area coverage provides higher accuracy of the estimates, compared to binary Gauss digitization at the same spatial image resolution. Theoretical results are confirmed by a statistical study of disks and squares, where the moments of the shape, up to order two, are estimated from its fuzzy discrete representation. The errors of the estimates decrease both with increased size of a shape (spatial resolution) and increased membership resolution (number of available grey-levels).


Fuzzy sets moments accuracy multigrid resolution 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Nataša Sladoje
    • 1
  • Joakim Lindblad
    • 1
  1. 1.Centre for Image AnalysisSwedish University of Agricultural Sciences and Uppsala UniversityUppsalaSweden

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