Set Connections and Discrete Filtering
Connectivity is a topological notion for sets, often introduced by means of arcs. Classically, discrete geometry transposes to digital sets this arcwise appoach. An alternative, and non topological, axiomatics has been proposed by Serra. It lies on the idea that the union of connected components that intersect is still connected. Such an axiomatics enlarges the range of possible connections, and includes clusters of particles.
The main output of this approach concerns filters. Very powerful new ones have been designed (levelings), and more classical ones have been provided with new properties (openings, strong alternated filters)
The paper presents an overview of set connection and illustrates it by filterings on gray tone images. It is emphazised that all notions introduced here apply equally to both discrete and continuous spaces.
KeywordsComplete Lattice Mathematical Morphology Extended Maximum Digital Space Connected Operator
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