THE FUNDAMENTALS OF FUZZY MATHEMATICAL MORPHOLOGY PART 1: BASIC CONCEPTS
Bernard De Baets, Etienne E. Kerre, Madan M. Gupta · International Journal of General Systems · 1995
Fuzzy mathematical morphology provides an alternative extension of the binary morphological operations to gray-scale images based on the theory of fuzzy sets. This paper introduces the basic concepts of fuzzy mathematical morphology, starting from the original definitions of the morphological operations by Serra. More specifically, the fuzzy dilation, erosion, closing and opening operations are introduced. Their basic properties such as monotonicity and interaction with union and intersection are discussed in detail. Some important relationships between the fuzzy erosion and fuzzy dilation are established.