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Shape signaturs of fuzzy star-shaped sets based on distance from the centroid
Signal and Image Laboratory (LIS, Grenoble).
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, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis.
2005 (English)In: Pattern Recognition Letters, ISSN 0167-8655, Vol. 26, no 6, p. 735-746Article in journal (Refereed) Published
Abstract [en]

We extend the shape signature based on the distance of the boundary points from the shape centroid, to the case of fuzzy sets. The analysis of the transition from crisp to fuzzy shape descriptor is first given in the continuous case. This is followed by a study of the specific issues induced by the discrete representation of the objects in a computer.

We analyze two methods for calculating the signature of a fuzzy shape, derived from two ways of defining a fuzzy set: first, by its membership function, and second, as a stack of its α-cuts. The first approach is based on measuring the length of a fuzzy straight line by integration of the fuzzy membership function, while in the second one we use averaging of the shape signatures obtained for the individual α-cuts of the fuzzy set. The two methods, equivalent in the continuous case for the studied class of fuzzy shapes, produce different results when adjusted to the discrete case. A statistical study, aiming at characterizing the performances of each method in the discrete case, is done. Both methods are shown to provide more precise descriptions than their corresponding crisp versions. The second method (based on averaged Euclidean distance over the α-cuts) outperforms the others.

Place, publisher, year, edition, pages
Elsevier, 2005. Vol. 26, no 6, p. 735-746
Keywords [en]
fuzzy shape representation, shape signature, discrete geometry, membership function, radial integral
National Category
Computer Vision and Robotics (Autonomous Systems)
Research subject
Computerized Image Processing
Identifiers
URN: urn:nbn:se:uu:diva-73917DOI: 10.1016/j.patrec.2004.09.025OAI: oai:DiVA.org:uu-73917DiVA, id: diva2:101828
Available from: 2005-07-19 Created: 2005-07-19 Last updated: 2018-12-02

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Nyström, IngelaSladoje, Natasa

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