A Vectorial Self-Dual Morphological Filter based on Total Variation Minimization

From LRDE

Abstract

We present a vectorial self dual morphological filter. Contrary to many methods, our approach does not require the use of an ordering on vectors. It relies on the minimization of the total variation with Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle L^1} norm as data fidelity on each channel. We further constraint this minimization in order not to create new values. It is shown that this minimization yields a self-dual and contrast invariant filter. Although the above minimization is not a convex problem, we propose an algorithm which computes a global minimizer. This algorithm relies on minimum cost cut-based optimizations.


Bibtex (lrde.bib)

@InProceedings{	  darbon.05.isvc,
  author	= {J\'er\^ome Darbon and Sylvain Peyronnet},
  title		= {A Vectorial Self-Dual Morphological Filter based on Total
		  Variation Minimization},
  booktitle	= {Proceedings of the First International Conference on
		  Visual Computing},
  year		= 2005,
  address	= {Lake Tahoe, Nevada, USA},
  month		= dec,
  pages		= {388--395},
  series	= {Lecture Notes in Computer Science Series},
  publisher	= {Springer-Verlag},
  volume	= 3804,
  abstract	= {We present a vectorial self dual morphological filter.
		  Contrary to many methods, our approach does not require the
		  use of an ordering on vectors. It relies on the
		  minimization of the total variation with $L^1$ norm as data
		  fidelity on each channel. We further constraint this
		  minimization in order not to create new values. It is shown
		  that this minimization yields a self-dual and contrast
		  invariant filter. Although the above minimization is not a
		  convex problem, we propose an algorithm which computes a
		  global minimizer. This algorithm relies on minimum cost
		  cut-based optimizations.}
}