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Introducing the Dahu Pseudo-Distance

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Abstract

The minimum barrier (MB) distance is defined as the minimal interval of gray-level values in an image along a path between two points, where the image is considered as a vertex-valued graph. Yet this definition does not fit with the interpretation of an image as an elevation map, i.e. a somehow continuous landscape. In this paper, based on the discrete set-valued continuity setting, we present a new discrete definition for this distance, which is compatible with this interpretation, while being free from digital topology issues. Amazingly, we show that the proposed distance is related to the morphological tree of shapeswhich in addition allows for a fast and exact computation of this distance. That contrasts with the classical definition of the MB distance, where its fast computation is only an approximation.

Documents

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Bibtex (lrde.bib)

@InProceedings{	  geraud.17.ismm,
  author	= {Thierry G\'eraud and Yongchao Xu and Edwin Carlinet and
		  Nicolas Boutry},
  title		= {Introducing the {D}ahu Pseudo-Distance},
  booktitle	= {Mathematical Morphology and Its Application to Signal and
		  Image Processing -- Proceedings of the 13th International
		  Symposium on Mathematical Morphology (ISMM)},
  year		= {2017},
  editor	= {J. Angulo and S. Velasco-Forero and F. Meyer},
  volume	= {10225},
  series	= {Lecture Notes in Computer Science},
  pages		= {55--67},
  month		= may,
  address	= {Fontainebleau, France},
  publisher	= {Springer},
  abstract	= {The minimum barrier (MB) distance is defined as the
		  minimal interval of gray-level values in an image along a
		  path between two points, where the image is considered as a
		  vertex-valued graph. Yet this definition does not fit with
		  the interpretation of an image as an elevation map, i.e. a
		  somehow continuous landscape. In this paper, based on the
		  discrete set-valued continuity setting, we present a new
		  discrete definition for this distance, which is compatible
		  with this interpretation, while being free from digital
		  topology issues. Amazingly, we show that the proposed
		  distance is related to the morphological tree of shapes,
		  which in addition allows for a fast and exact computation
		  of this distance. That contrasts with the classical
		  definition of the MB distance, where its fast computation
		  is only an approximation.}
}