Estimation of moments of digitized objects with fuzzy borders

Authors:
Nataša Sladoje;Joakim Lindblad
Affiliations:
Centre for Image Analysis, Swedish University of Agricultural Sciences and Uppsala University, Uppsala, Sweden;Centre for Image Analysis, Swedish University of Agricultural Sciences and Uppsala University, Uppsala, Sweden
Venue:
ICIAP'05 Proceedings of the 13th international conference on Image Analysis and Processing
Year:
2005

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Abstract

Error bounds for estimation of moments from a fuzzy representation of a shape are derived, and compared with estimations from a crisp representation. It is shown that a fuzzy membership function based on the pixel area coverage provides higher accuracy of the estimates, compared to binary Gauss digitization at the same spatial image resolution. Theoretical results are confirmed by a statistical study of disks and squares, where the moments of the shape, up to order two, are estimated from its fuzzy discrete representation. The errors of the estimates decrease both with increased size of a shape (spatial resolution) and increased membership resolution (number of available grey-levels).