Basic Morphological Operators Applied On Partitions

This document describes morphological operators designed for partition images. Two approaches are addressed. In the first one, each cell of the partition is considered independently of the others and various anti-extensive operators can be defined on it. However, these operators can be applied directly on the whole partition. There is no need to extract each cell to transform it. The second approach, on the contrary, considers a partition as a representation of a Delaunay graph. Morphological operators can be defined on this graph. This document explains how these operators can be implemented directly on the partition image. These operators have been implemented with the MAMBA Image library.