A Brief Account of the Relations between Gray-Scale Mathematical Morphologies

Mathematical morphology was originally conceived as a set theoretic approach for the processing of binary images. Approaches that extend classical binary morphology to gray-scale images are either based on umbras, thresholds, level sets, or fuzzy sets. Complete lattices form a general framework for all of these approaches. This paper discusses and compares several approaches to gray-scale mathematical morphology including the threshold, umbra, and level set approaches as well as fuzzy approaches.