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. (c) 2006 Elsevier B.V. All rights reserved

Keywords

Image processing; Geometric moments; Shape representation; Shape reconstruction; Parameter estimation; Defuzzification

Published in

Fuzzy Sets and Systems
2007, Volume: 158, number: 5, pages: 517-534
Publisher: ELSEVIER SCIENCE BV

SLU Authors

• Lindblad, Joakim

  • Centre for Image Analysis, Swedish University of Agricultural Sciences
    

Publication Identifiers

DOI: https://doi.org/10.1016/j.fss.2006.09.017

Permanent link to this page (URI)

https://res.slu.se/id/publ/17132