Title :
Characterizing Compactness of Geometrical Clusters Using Fuzzy Measures
Author :
Beliakov, Gleb ; Gang Li ; Huy Quan Vu ; Wilkin, Tim
Author_Institution :
Sch. of Inf. Technol., Deakin Univ., Burwood, VIC, Australia
Abstract :
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.
Keywords :
computational geometry; fuzzy set theory; image processing; trees (mathematics); Sugeno-type fuzzy measures; artificial images; cluster identification; fuzzy measure decomposition; geometrical cluster compactness characterization; image detail preservation; image processing; imaging sensors; intensity variations; minimum spanning trees; spatial organization; spatially cohesive pixel clusters; Context; Image processing; Noise; Rotation measurement; Sea measurements; Size measurement; Smoothing methods; Aggregation functions; cluster compactness; fuzzy measure; image reduction;
Journal_Title :
Fuzzy Systems, IEEE Transactions on
DOI :
10.1109/TFUZZ.2014.2336871