Lindblad, Joakim
- Centre for Image Analysis, Swedish University of Agricultural Sciences
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
UKÄ Subject classification
Computer graphics and computer vision
Publication identifier
- DOI: https://doi.org/10.1016/j.fss.2006.09.017
Permanent link to this page (URI)
https://res.slu.se/id/publ/17132