Hyperconnectivity, Attribute-Space Connectivity and Path Openings: Theoretical Relationships

Authors:
Michael H. Wilkinson
Affiliations:
Institute for Mathematics and Computing Science, University of Groningen, AK, The Netherlands 9700
Venue:
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Year:
2009

Citing 13
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Abstract

In this paper the relationship of hyperconnected filters with path openings and attribute-space connected filters is studied. Using a recently developed axiomatic framework based on hyperconnectivity operators, which are the hyperconnected equivalents of connectivity openings, it is shown that path openings are a special case of hyperconnected area openings. The new axiomatics also yield insight into the relationship between hyperconnectivity and attribute-space connectivity. It is shown any hyperconnectivity is an attribute-space connectivity, but that the reverse is not true.