Hierarchical image simplification and segmentation based on Mumford-Shah-salient level line selection

Authors

Yongchao Xu, Thierry Géraud, Laurent Najman

Journal

Pattern Recognition Letters

Type

article

Projects

Olena

Keywords

Image

Date

2016-05-20

Abstract

Hierarchies, such as the tree of shapes, are popular representations for image simplification and segmentation thanks to their multiscale structures. Selecting meaningful level lines (boundaries of shapes) yields to simplify image while preserving intact salient structures. Many image simplification and segmentation methods are driven by the optimization of an energy functional, for instance the celebrated Mumford-Shah functional. In this paper, we propose an efficient approach to hierarchical image simplification and segmentation based on the minimization of the piecewise-constant Mumford-Shah functional. This method conforms to the current trend that consists in producing hierarchical results rather than a unique partition. Contrary to classical approaches which compute optimal hierarchical segmentations from an input hierarchy of segmentations, we rely on the tree of shapes, a unique and well-defined representation equivalent to the image. Simply put, we compute for each level line of the image an attribute function that characterizes its persistence under the energy minimization. Then we stack the level lines from meaningless ones to salient ones through a saliency map based on extinction values defined on the tree-based shape space. Qualitative illustrations and quantitative evaluation on Weizmann segmentation evaluation database demonstrate the state-of-the-art performance of our method.

Documents

• Paper

Bibtex (lrde.bib)

@Article{	  xu.16.prl,
  author	= {Yongchao Xu and Thierry G\'eraud and Laurent Najman},
  title		= {Hierarchical image simplification and segmentation based
		  on {M}umford-{S}hah-salient level line selection},
  journal	= {Pattern Recognition Letters},
  year		= {2016},
  month		= nov,
  volume	= {83},
  number	= {3},
  pages		= {278--286},
  doi		= {10.1016/j.patrec.2016.05.006},
  abstract	= {Hierarchies, such as the tree of shapes, are popular
		  representations for image simplification and segmentation
		  thanks to their multiscale structures. Selecting meaningful
		  level lines (boundaries of shapes) yields to simplify image
		  while preserving intact salient structures. Many image
		  simplification and segmentation methods are driven by the
		  optimization of an energy functional, for instance the
		  celebrated Mumford-Shah functional. In this paper, we
		  propose an efficient approach to hierarchical image
		  simplification and segmentation based on the minimization
		  of the piecewise-constant Mumford-Shah functional. This
		  method conforms to the current trend that consists in
		  producing hierarchical results rather than a unique
		  partition. Contrary to classical approaches which compute
		  optimal hierarchical segmentations from an input hierarchy
		  of segmentations, we rely on the tree of shapes, a unique
		  and well-defined representation equivalent to the image.
		  Simply put, we compute for each level line of the image an
		  attribute function that characterizes its persistence under
		  the energy minimization. Then we stack the level lines from
		  meaningless ones to salient ones through a saliency map
		  based on extinction values defined on the tree-based shape
		  space. Qualitative illustrations and quantitative
		  evaluation on Weizmann segmentation evaluation database
		  demonstrate the state-of-the-art performance of our
		  method.}
}