Representation and reconstruction of fuzzy disks by moments

Sammanfattning

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

Nyckelord

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

Publicerad i

Fuzzy Sets and Systems
2007, volym: 158, nummer: 5, sidor: 517-534
Utgivare: ELSEVIER SCIENCE BV

SLU författare

• Lindblad, Joakim

  • Centre for Image Analysis, Sveriges lantbruksuniversitet
    

Publikationens identifierare

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

Permanent länk till denna sida (URI)

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