Representation and reconstruction of fuzzy disks by moments

  • Authors:

  • Nataša Sladoje;Joakim Lindblad

  • Affiliations:

  • Centre for Image Analysis, Lägerhyddsv. 3, SE-752 37, SLU, Uppsala, Sweden and Faculty of Engineering, University of Novi Sad, Novi Sad, Serbia and Montenegro;Centre for Image Analysis, Lägerhyddsv. 3, SE-752 37, SLU, Uppsala, Sweden

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2007

Quantified Score

Hi-index 0.21

Visualization

Abstract

In this paper, we analyze the representation and reconstruction of fuzzy disks by using moments. Both continuous and digital fuzzy disks are considered. A fuzzy disk is a convex fuzzy spatial set, where the membership of a point to the fuzzy disk depends only on the distance of the point to the centre of the disk. We show that, for a certain class of membership functions defining a fuzzy disk, there exists a one-to-one correspondence between the set of fuzzy disks and the set of their generalized moment representations. Theoretical error bounds for the accuracy of the estimation of generalized moments of a continuous fuzzy disk from the generalized moments of its digitization and, in connection with that, the accuracy of an approximate reconstruction of a continuous fuzzy disk from the generalized moments of its digitization, are derived. Defuzzification (reduction of a continuous fuzzy disk to a crisp representative) is also considered. A statistical study of generated synthetic objects complements the theoretical results.