Publications/boutry.15.ismm

Authors

Nicolas Boutry, Thierry Géraud, Laurent Najman

Where

Mathematical Morphology and Its Application to Signal and Image Processing -- Proceedings of the 12th International Symposium on Mathematical Morphology (ISMM)

Place

Reykjavik, Iceland

Type

inproceedings

Publisher

Springer

Projects

Image"Image" is not in the list (Vaucanson, Spot, URBI, Olena, APMC, Tiger, Climb, Speaker ID, Transformers, Bison, ...) of allowed values for the "Related project" property.

Keywords

Image

Date

2015-04-07

Abstract

Latecki et al. introduced the notion of 2D and 3D well-composed images, i.e., a class of images free from the ``connectivities paradox of digital topology. Unfortunately natural and synthetic images are not a priori well-composed. In this paper we extend the notion of ``digital well-composedness to nD setsinteger-valued functions (gray-level images), and interval-valued maps. We also prove that the digital well-composedness implies the equivalence of connectivities of the level set components in nD. Contrasting with a previous result stating that it is not possible to obtain a discrete nD self-dual digitally well-composed function with a local interpolation, we then propose and prove a self-dual discrete (non-local) interpolation method whose result is always a digitally well-composed function. This method is based on a sub-part of a quasi-linear algorithm that computes the morphological tree of shapes.

Documents

• Paper

Bibtex (lrde.bib)

@InProceedings{	  boutry.15.ismm,
  author	= {Nicolas Boutry and Thierry G\'eraud and Laurent Najman},
  title		= {How to Make {$n$D} Functions Digitally Well-Composed in a
		  Self-Dual Way},
  booktitle	= {Mathematical Morphology and Its Application to Signal and
		  Image Processing -- Proceedings of the 12th International
		  Symposium on Mathematical Morphology (ISMM)},
  year		= {2015},
  series	= {Lecture Notes in Computer Science Series},
  volume	= {9082},
  address	= {Reykjavik, Iceland},
  publisher	= {Springer},
  editor	= {J.A. Benediktsson and J. Chanussot and L. Najman and H.
		  Talbot},
  pages		= {561--572},
  abstract	= {Latecki {\it et al.} introduced the notion of 2D and 3D
		  well-composed images, {\it i.e.}, a class of images free
		  from the ``connectivities paradox'' of digital topology.
		  Unfortunately natural and synthetic images are not {\it a
		  priori} well-composed. In this paper we extend the notion
		  of ``digital well-composedness'' to $n$D sets,
		  integer-valued functions (gray-level images), and
		  interval-valued maps. We also prove that the digital
		  well-composedness implies the equivalence of connectivities
		  of the level set components in $n$D. Contrasting with a
		  previous result stating that it is not possible to obtain a
		  discrete $n$D self-dual digitally well-composed function
		  with a local interpolation, we then propose and prove a
		  self-dual discrete (non-local) interpolation method whose
		  result is always a digitally well-composed function. This
		  method is based on a sub-part of a quasi-linear algorithm
		  that computes the morphological tree of shapes.}
}