The Set‐Theoretic Framework
Jean‐Charles Pinoli · 2014
The set-theoretic framework is of key importance for studying the stricto sensu geometrical frameworks that is useful for mathematical imaging. In the set-theoretic framework, a binary image is regarded as made up of distinct subsets of pixels with the same value, that is to say either 0 or 1, and objects are represented by sets and subsets for the mathematical imaging purpose. This chapter discusses main notations and approaches such as pixels and objects, pixel and object separation, local finiteness and set transformations for image processing and analysis (IPA). It also discusses main applications of the IPA. The applications are object partition and object components, set-theoretic separation of objects and object removal, counting of separate objects and spatial supports border effects.