Length estimators for digitized contours
Computer Vision, Graphics, and Image Processing
A fuzzy medial axis transformation based on fuzzy disks
Pattern Recognition Letters
Graphical Models and Image Processing
Fuzzy geometry: an updated overview
Information Sciences: an International Journal
A Survey on Content-Based Retrieval for Multimedia Databases
IEEE Transactions on Knowledge and Data Engineering
On Using Functions to Describe the Shape
Journal of Mathematical Imaging and Vision
Digital Straight Line Segments
IEEE Transactions on Computers
The fuzzy geometry of image subsets
Pattern Recognition Letters
Representation and reconstruction of fuzzy disks by moments
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Fuzzy Sets and Systems
SMI 2011: Full Paper: Geometric models with weigthed topology
Computers and Graphics
Feature based defuzzification at increased spatial resolution
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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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 @a-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 @a-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 @a-cuts) outperforms the others.