Fuzzy Sets and Mathematical Morphology
Isabelle Bloch · 2013
Since mathematical morphology relies mainly on set theoretical concepts and algebraic properties, it appears as a natural set of tools to be extended to fuzzy sets for handling spatial information. This chapter limits its presentation to truly fuzzy approaches, in which fuzzy sets are transformed using fuzzy structuring elements. It focuses on the four basic operations of mathematical morphology- erosion, dilation, opening and closing - from which numerous other operations can be derived. The chapter recalls the basic notions of fuzzy sets theory. The two main classes of approaches are detailed. Links between both approaches and the conditions for their equivalence are established in the chapter. It gives a few examples on how spatial relations can be built from fuzzy mathematical morphology. Controlled Vocabulary Terms algebra; fuzzy set theory; mathematical morphology