Characterizing compactness of geometrical clusters using fuzzy measures

Beliakov, Gleb, Li, Gang, Vu, Huy Quan and Wilkin, Tim 2015, Characterizing compactness of geometrical clusters using fuzzy measures, IEEE transactions on fuzzy systems, vol. 23, no. 4, pp. 1030-1043, doi: 10.1109/TFUZZ.2014.2336871.

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Title Characterizing compactness of geometrical clusters using fuzzy measures
Author(s) Beliakov, GlebORCID iD for Beliakov, Gleb
Li, GangORCID iD for Li, Gang
Vu, Huy Quan
Wilkin, TimORCID iD for Wilkin, Tim
Journal name IEEE transactions on fuzzy systems
Volume number 23
Issue number 4
Start page 1030
End page 1043
Total pages 14
Publisher IEEE
Place of publication Piscataway, N.J.
Publication date 2015-08
ISSN 1063-6706
Keyword(s) Science & Technology
Computer Science, Artificial Intelligence
Engineering, Electrical & Electronic
Computer Science
Aggregation functions
cluster compactness
fuzzy measure
image reduction
Summary Certain tasks in image processing require the preservation of fine image details, while applying a broad operation to the image, such as image reduction, filtering, or smoothing. In such cases, the objects of interest are typically represented by small, spatially cohesive clusters of pixels which are to be preserved or removed, depending on the requirements. When images are corrupted by the noise or contain intensity variations generated by imaging sensors, identification of these clusters within the intensity space is problematic as they are corrupted by outliers. This paper presents a novel approach to accounting for spatial organization of the pixels and to measuring the compactness of pixel clusters based on the construction of fuzzy measures with specific properties: monotonicity with respect to the cluster size; invariance with respect to translation, reflection, and rotation; and discrimination between pixel sets of fixed cardinality with different spatial arrangements. We present construction methods based on Sugeno-type fuzzy measures, minimum spanning trees, and fuzzy measure decomposition. We demonstrate their application to generating fuzzy measures on real and artificial images.
Language eng
DOI 10.1109/TFUZZ.2014.2336871
Field of Research 080108 Neural, Evolutionary and Fuzzy Computation
0801 Artificial Intelligence And Image Processing
0906 Electrical And Electronic Engineering
0102 Applied Mathematics
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2015, IEEE
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