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Research article - Peer-reviewed, 2007

Representation and reconstruction of fuzzy disks by moments

Sladoje N, Lindblad J


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


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

    SLU Authors

    • Lindblad, Joakim

      • Centre for Image Analysis, Swedish University of Agricultural Sciences

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