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Pattern Recognition Letters
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On a metric distance between fuzzy sets
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A defuzzification method respecting the fuzzification
Fuzzy Sets and Systems
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Fuzzy Sets and Systems
Defuzzification: criteria and classification
Fuzzy Sets and Systems
Set defuzzification and choquet integral
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On the nonexistence of Hausdorff-like metrics for fuzzy sets
Pattern Recognition Letters
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ICIAP '97 Proceedings of the 9th International Conference on Image Analysis and Processing-Volume I - Volume I
Averaging procedures in defuzzification processes
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Defuzzification of Discrete Objects by Optimizing Area and Perimeter Similarity
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 3 - Volume 03
High-Precision Boundary Length Estimation by Utilizing Gray-Level Information
IEEE Transactions on Pattern Analysis and Machine Intelligence
Measurements of digitized objects with fuzzy borders in 2D and 3D
Image and Vision Computing
Estimation of moments of digitized objects with fuzzy borders
ICIAP'05 Proceedings of the 13th international conference on Image Analysis and Processing
Feature based defuzzification in ℤ2 and ℤ3 using a scale space approach
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Feature based defuzzification at increased spatial resolution
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
The fuzzy geometry of image subsets
Pattern Recognition Letters
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Computer Vision and Image Understanding
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We present a novel defuzzification method, i.e., a mapping from the set of fuzzy sets to the set of crisp sets, and we suggest its application to image processing. Spatial fuzzy sets are, e.g., useful as information preserving representations of objects in images. Defuzzification of such a spatial fuzzy set can be seen as a crisp segmentation procedure. With the aim to provide preservation of selected quantitative features of the fuzzy set, we define the defuzzification of a fuzzy set to be a crisp set which is as close as possible to the fuzzy set, where the distance measure on the set of fuzzy sets, that we propose for defuzzification, incorporates selected local and global features of the fuzzy sets. The distance measure is based on the Minkowski distance between feature representations of the sets. The distance minimization, performed in the suggested defuzzification method, provides preservation of the selected quantitative features of the fuzzy set. The method utilizes the information contained in the fuzzy representation for defining a mapping from the set of fuzzy sets to the set of crisp sets. If the fuzzy set is a representation of an unknown crisp original set, such that the selected features of the original set are preserved in the fuzzy representation, then the defuzzified set may be seen as an approximate reconstruction of the crisp original. We present four optimization algorithms, exhibiting different properties, for finding the crisp set closest to a given discrete fuzzy set. A number of examples, using both synthetic and real images, illustrate the main properties of the proposed method. An evaluation of both theoretical aspects of the method, and its results, is given.