Morphological operators characterized by neighborhood graphs

Mathematical Morphology is a theory that studies the decomposition of lattice operators in terms of some families of elementary lattice operators. When the lattices considered have a sup-generating family, the elementary operators can be characterized by structuring functions. The representation of structuring functions by neighborhood graphs is a powerful model for the construction of image operators. This model, that is a conceptual improvement of the one proposed by Vincent, permits a natural polymorphic extension of classical softwares for image processing by Mathematical Morphology. These systems constitute a complete framework for implementations of connected filters, that are one of the most modern and powerful approaches for image segmentation, and of operators that extract information from populations of objects in images. In this paper, besides presenting the formulation of the model, we present the polymorphic extension of a system for morphological image processing and some applications of it in image analysis.