An Axiomatic Approach to Hyperconnectivity

  • Authors:

  • Michael H. Wilkinson

  • Affiliations:

  • Institute for Mathematics and Computing Science, University of Groningen, Groningen, 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

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Abstract

In this paper the notion of hyperconnectivity, first put forward by Serra as an extension of the notion of connectivity is explored theoretically. Hyperconnectivity operators, which are the hyperconnected equivalents of connectivity openings are defined, which supports both hyperconnected reconstruction and attribute filters. The new axiomatics yield insight into the relationship between hyperconnectivity and structural morphology. The latter turns out to be a special case of the former, which means a continuum of filters between connected and structural exists, all of which falls into the category of hyperconnected filters.