Morphological operators for image sequences

Abstract

This paper presents a unifying approach to the problem of morphologically processing image sequences (or, equivalently, vector-valued images) by means of lattice theory, thus providing a mathematical foundation for vector morphology. Lattice theory is an abstract algebraic tool that has been extensively used as a theoretical framework for scalar morphology (i.e., mathematical morphology applied on single images). Two approaches to vector morphology are discussed. According to the first approach, vector morphology is viewed as a natural extension of the well-known scalar morphology. This approach formalizes and generalizes Wilson’s matrix morphology and shows that the latter is a direct consequence of marginal vector ordering. The derivation of the second approach is more delicate and requires careful treatment. This approach is a direct consequence of a vector transformation followed by marginal ordering. When the vector transformation is the identity transformation, the two approaches are equivalent. A number of examples demonstrate the applicability of the proposed theory in a number of image processing and analysis problems. © 1994 Academic Press. All rights reserved.