Salient Level Lines Selection Using the Mumford-Shah Functional

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Abstract

Many methods relying on the morphological notion of shapes, (i.e., connected components of level sets) have been proved to be very useful for pattern analysis and recognition. Selecting meaningful level lines (boundaries of level sets) yields to simplify images while preserving salient structures. Many image simplification and/or segmentation methods are driven by the optimization of an energy functional, for instance the Mumford-Shah functional. In this article, we propose an efficient shape-based morphological filtering that very quickly compute to a locally (subordinated to the tree of shapes) optimal solution of the piecewise-constant Mumford-Shah functional. Experimental results demonstrate the efficiency, usefulness, and robustness of our method, when applied to image simplification, pre-segmentation, and detection of affine regions with viewpoint changes.

Documents

Bibtex (lrde.bib)

@InProceedings{	  xu.13.icip,
  author	= {Yongchao Xu and Thierry G\'eraud and Laurent Najman},
  title		= {Salient Level Lines Selection Using the {Mumford-Shah}
		  Functional},
  booktitle	= {Proceedings of the 20th International Conference on Image
		  Processing (ICIP)},
  year		= 2013,
  address	= {Melbourne, Australia},
  month		= sep,
  pages		= {1227--1231},
  organization	= {IEEE},
  abstract	= {Many methods relying on the morphological notion of
		  shapes, (i.e., connected components of level sets) have
		  been proved to be very useful for pattern analysis and
		  recognition. Selecting meaningful level lines (boundaries
		  of level sets) yields to simplify images while preserving
		  salient structures. Many image simplification and/or
		  segmentation methods are driven by the optimization of an
		  energy functional, for instance the Mumford-Shah
		  functional. In this article, we propose an efficient
		  shape-based morphological filtering that very quickly
		  compute to a locally (subordinated to the tree of shapes)
		  optimal solution of the piecewise-constant Mumford-Shah
		  functional. Experimental results demonstrate the
		  efficiency, usefulness, and robustness of our method, when
		  applied to image simplification, pre-segmentation, and
		  detection of affine regions with viewpoint changes.}
}