Locality and Adjacency Stability Constraints for MorphologicalConnected Operators
Journal of Mathematical Imaging and Vision
Set-Theoretical Algebraic Approaches to Connectivityin Continuous or Digital Spaces
Journal of Mathematical Imaging and Vision
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Connectivity on Complete Lattices
Journal of Mathematical Imaging and Vision
Connections for sets and functions
Fundamenta Informaticae - Special issue on mathematical morphology
Computer and Robot Vision
Connected morphological operators for binary images
Connected morphological operators for binary images
Digital Steiner sets and Matheron semi-groups
Image and Vision Computing
Geodesy and connectivity in lattices
Fundamenta Informaticae
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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.