Morphological Filtering in Shape Spaces : Applications using Tree-Based Image Representations

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Abstract

Connected operators are filtering tools that act by merging elementary regions of an image. A popular strategy is based on tree-based image representations: for exampleone can compute a shape-based attribute on each node of the tree and keep only the nodes for which the attribute is sufficiently strong. This operation can be seen as a thresholding of the tree, seen as a graph whose nodes are weighted by the attribute. Rather than being satisfied with a mere thresholding, we propose to expand on this idea, and to apply connected filters on this latest graph. Consequently, the filtering is done not in the space of the image, but on the space of shapes build from the image. Such a processing is a generalization of the existing tree-based connected operators. Indeed, the framework includes classical existing connected operators by attributes. It also allows us to propose a class of novel connected operators from the leveling family, based on shape attributes. Finally, we also propose a novel class of self-dual connected operators that we call morphological shapings.

Documents

Bibtex (lrde.bib)

@InProceedings{	  xu.12.icpr,
  author	= {Yongchao Xu and Thierry G\'eraud and Laurent Najman},
  title		= {Morphological Filtering in Shape Spaces : Applications
		  using Tree-Based Image Representations},
  booktitle	= {Proceedings of the 21st International Conference on
		  Pattern Recognition (ICPR)},
  year		= 2012,
  address	= {Tsukuba Science City, Japan},
  month		= nov,
  pages		= {485--488},
  publisher	= {IEEE Computer Society},
  abstract	= {Connected operators are filtering tools that act by
		  merging elementary regions of an image. A popular strategy
		  is based on tree-based image representations: for example,
		  one can compute a shape-based attribute on each node of the
		  tree and keep only the nodes for which the attribute is
		  sufficiently strong. This operation can be seen as a
		  thresholding of the tree, seen as a graph whose nodes are
		  weighted by the attribute. Rather than being satisfied with
		  a mere thresholding, we propose to expand on this idea, and
		  to apply connected filters on this latest graph.
		  Consequently, the filtering is done not in the space of the
		  image, but on the space of shapes build from the image.
		  Such a processing is a generalization of the existing
		  tree-based connected operators. Indeed, the framework
		  includes classical existing connected operators by
		  attributes. It also allows us to propose a class of novel
		  connected operators from the leveling family, based on
		  shape attributes. Finally, we also propose a novel class of
		  self-dual connected operators that we call morphological
		  shapings.}
}