Binary, gray-scale, and vector soft mathematical morphology: Extensions, algorithms, and implementations

Abstract

Publisher Summary This chapter discusses standard morphological operations, their algebraic properties, and fuzzy morphology. Soft morphological filters are a relatively new subclass of nonlinear filters. They were introduced to improve the behavior of standard morphological filters in noisy environments. Soft mathematical morphology and the definitions of vector soft morphological operations, their basic properties, and their use in color impulse noise attenuation are provided in the chapter. Several implementations of soft morphological filters and an implementation of vector morphological filters are analyzed in the chapter. Soft morphological operations are based on weighted order statistics. Algorithms for implementation of soft morphological operations include the well-known mergesort and quicksort algorithms for weighted order statistics computation. Fuzzy soft mathematical morphology applies the concepts of soft morphology to fuzzy sets. The definitions and the algebraic properties are illustrated in the chapter through examples and experimental results.