Theoretical Foundations of Spatially-Variant Mathematical Morphology Part II: Gray-Level Images

In this paper, we develop a spatially-variant (SV) mathematical morphology theory for gray-level signals and images in the euclidean space. The proposed theory preserves the geometrical concept of the structuring function, which provides the foundation of classical morphology and is essential in signal and image processing applications. We define the basic SV gray-level morphological operators (that is, SV gray-level erosion, dilation, opening, and closing) and investigate their properties. We demonstrate the ubiquity of SV gray-level morphological systems by deriving a kernel representation for a large class of systems, called V-systems, in terms of the basic SV gray-level morphological operators. A V-system is defined to be a gray-level operator, which is invariant under gray-level (vertical) translations. Particular attention is focused on the class of SV flat gray-level operators. The kernel representation for increasing V-systems is a generalization of Maragos' kernel represe...

• Type: Journal
• Year: 2008
• Where: PAMI
• Authors: Nidhal Bouaynaya, Dan Schonfeld
• Keywords: Gray-level Morphological Operators, Gray-level Operators, PAMI 2008, SV Gray-level Erosion