Representation and Reconstruction of Fuzzy Disks by Moments
2007 (English)In: Fuzzy sets and systems (Print), ISSN 0165-0114, Vol. 158, no 5, 517-534 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2007. Vol. 158, no 5, 517-534 p.
Image processing, Geometric moments, Shape representation, Shape reconstruction, Parameter estimation, Defuzzification
Computer and Information Science
IdentifiersURN: urn:nbn:se:uu:diva-18180DOI: 10.1016/j.fss.2006.09.017ISI: 000244218500003OAI: oai:DiVA.org:uu-18180DiVA: diva2:45952