DocumentCode :
1564532
Title :
Continuous Choquet integrals with respect to random sets
Author :
Gader, Paul D.
Author_Institution :
Dept. of Comput. & Inf. Sci. & Eng., Florida Univ., Gainesville, FL, USA
Volume :
2
fYear :
2003
Firstpage :
1281
Abstract :
An interpretation of continuous Choquet integrals with respect to random sets is given in the context of image filtering and shape detection. In this context, random sets represent random shapes defined on the plane. Random sets are characterized by their capacity functionals. Capacity functionals are fuzzy measures. Thus, input images can be integrated with respect to random sets. In this paper, input images are represented as fuzzy sets. The integration is interpreted in the context of mathematical morphology as the average a generalization morphological dilation or erosion. Specifically, the integrals represent the average probability that sets either intersect or are contained in the random sets, the average being over the alpha cuts of the input image. This interpretation has the potential for deriving new learning algorithms for using Choquet integrals in shape detection.
Keywords :
fuzzy set theory; image processing; integral equations; learning (artificial intelligence); mathematical morphology; probability; alpha cuts; average probability; capacity functionals; continuous choquet integral interpretation; erosion; fuzzy measures; fuzzy sets; generalization morphological dilation; image filtering; input images; learning algorithm; mathematical morphology; random sets; random shapes; shape detection; Algebra; Fuzzy logic; Fuzzy sets; Fuzzy systems; Information filtering; Information filters; Information science; Morphology; Q measurement; Shape;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Fuzzy Systems, 2003. FUZZ '03. The 12th IEEE International Conference on
Print_ISBN :
0-7803-7810-5
Type :
conf
DOI :
10.1109/FUZZ.2003.1206615
Filename :
1206615
Link To Document :
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