Ruminations on Tarjan's Union-Find algorithm and connected operators

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Abstract

This papers presents a comprehensive and general form of the Tarjan's union-find algorithm dedicated to connected operators. An interesting feature of this form is to introduce the notion of separated domains. The properties of this form and its flexibility are discussed and highlighted with examples. In particular, we give clues to handle correctly the constraint of domain-disjointness preservation and, as a consequence, we show how we can rely on “union-find” to obtain algorithms for self-dual filters approaches and levelings with a marker function.


Bibtex (lrde.bib)

@InProceedings{	  geraud.05.ismm,
  author	= {Thierry G\'eraud},
  title		= {Ruminations on {T}arjan's {U}nion-{F}ind algorithm and
		  connected operators},
  booktitle	= {Proceedings of the 7th International Symposium on
		  Mathematical Morphology (ISMM'05)},
  year		= 2005,
  volume	= 30,
  pages		= {105--116},
  abstract	= {This papers presents a comprehensive and general form of
		  the Tarjan's union-find algorithm dedicated to connected
		  operators. An interesting feature of this form is to
		  introduce the notion of separated domains. The properties
		  of this form and its flexibility are discussed and
		  highlighted with examples. In particular, we give clues to
		  handle correctly the constraint of domain-disjointness
		  preservation and, as a consequence, we show how we can rely
		  on ``union-find'' to obtain algorithms for self-dual
		  filters approaches and levelings with a marker function.},
  address	= {Paris, France},
  month		= apr,
  publisher	= {Springer},
  series	= {Computational Imaging and Vision}
}