Fuzzy convexity and connectivity

Abstract

In image analysis and pattern recognition fuzzy sets play the role of a good model for segmentation and classifications tasks when the regions and the classes cannot be strictly defined. Shape analysis is of great importance for different applications of image processing, for instance in the recognition of pathological objects on X-ray or microscopic images. Pure mathematical notions like convexity and connectivity play an essential role in shape analysis. In practical image processing, the notions of convexity and connectivity as defined in any textbook in mathematics are rarely encountered, moreover it is not easy to define what exactly a convex discrete arrangement of pixels mean. Also, in real vision systems, whether machine or human, imprecisions are inherent in the spatial and intensity characterisation of the image, there are also effects of noise in sensory transduction and of limits of sampling frequency. Unlike computer systems, human beings are more flexible. In general, they can easily say whether a pattern looks convex or not, or they can specify easily the connected components on a grey-scale or a colour image. Therefore the terms approximate convexity and approximate connectivity based on fuzzy set theory have been introduced. © Springer-Verlag 2001.