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Representation and Reconstruction of Fuzzy Disks by Moments
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis.
2007 (English)In: Fuzzy sets and systems (Print), ISSN 0165-0114, E-ISSN 1872-6801, Vol. 158, no 5, 517-534 p.Article in journal (Refereed) Published
Abstract [en]

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.
Keyword [en]
Image processing, Geometric moments, Shape representation, Shape reconstruction, Parameter estimation, Defuzzification
National Category
Computer and Information Science
Identifiers
URN: urn:nbn:se:uu:diva-18180DOI: 10.1016/j.fss.2006.09.017ISI: 000244218500003OAI: oai:DiVA.org:uu-18180DiVA: diva2:45952
Available from: 2007-12-20 Created: 2007-12-20 Last updated: 2017-12-08Bibliographically approved

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Sladoje, NatasaLindblad, Joakim

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