DOI link for Grayscale Morphology
Grayscale Morphology book
Mathematical morphology represents image objects as sets in a Euclidean space. In morphological analysis, the set is the primary notion and a function is viewed as a particular case of a set [e.g., an N-dimensional, multivalued function can be viewed as a set in an (N + 1)-dimensional space]. From this viewpoint then, any function-or set-processing system is viewed as a set mapping, a transformation, from one class of sets into another. The extension of the morphological transformations from binary to grayscale processing by Serra , Sternberg , and Haralick, Sternberg, and Zhuang , introduced a natural morphological generalization of the dilation and erosion operations. Heijmans  further showed how to use binary morphological operators and thresholding techniques to build a large class of grayscale morphological operators.