Mathematical Morphological Distributive Concepts over Unions and Intersections

Mathematical Morphological concepts outline techniques for analysing and processing geometric structures based on set theory. In this paper, we present proofs of our theorems on morphological distributive properties over Unions and Intersections with respect to Dilation and Erosion. These results provide new realizations of Dilation, Erosion and conclude that they are distributive over Unions but non-distributive over Intersections.