Connectivity on Complete Lattices
Journal of Mathematical Imaging and Vision
A multiscale approach to connectivity
Computer Vision and Image Understanding
Journal of Mathematical Imaging and Vision
Geodesy and connectivity in lattices
Fundamenta Informaticae
A New Fuzzy Connectivity Measure for Fuzzy Sets
Journal of Mathematical Imaging and Vision
An Axiomatic Approach to Hyperconnectivity
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Hyperconnectivity, Attribute-Space Connectivity and Path Openings: Theoretical Relationships
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Adjacency stable connected operators and set levelings
Image and Vision Computing
Hyperconnected Attribute Filters Based on k-Flat Zones
IEEE Transactions on Pattern Analysis and Machine Intelligence
Hi-index | 0.01 |
In this paper the notion of hyperconnectivity, which is an extension of connectivity is explored in the lattice theoretical framework. It is shown that a fourth axiom is needed when moving from connections to hyperconnections, in order to define hyperconnected components meaningfully, which is important for the definition of, e.g., viscous levellings. New hyperconnectivity openings, which are the hyperconnected equivalents of connectivity openings are then defined. It then shown that all algebraic openings which are translation and grey-scale invariant can be described as hyperconnected attribute filters. This means that hyperconnectivity lies at the heart of a vast range of morphological filters.