Morphological filters: An inspiration from natural geometrical erosion and dilation

Abstract

Morphological filters (MFs) are composed of two basic operators: dilation and erosion, inspired by natural geometrical dilation and erosion. MFs locally modify geometrical features of the signal/image using a probe resembling a segment of a function/image that is called structuring element. This chapter analytically explains MFs and their inspirational features from natural geometry. The basic theory of MFs in the binary domain is illustrated, and at the sequence, it has been shown how it is extended to the domain of multivalued functions. Each morphological operator is clarified by intuitive geometrical interpretations. Creative natural inspired analogies are deployed to give a clear intuition to readers about the process of each of them. In this regard, binary and grayscale morphological operators and their properties are well defined and depicted via many examples.