A Color Tree of Shapes with Illustrations on FilteringSimplification, and Segmentation

From LRDE

Abstract

The Tree of Shapes is a morphological tree that provides a high-level, hierarchical, self-dual, and contrast invariant representation of images, suitable for many image processing tasks. When dealing with color images, one cannot use the Tree of Shapes because its definition is ill-formed on multivariate data. Common workarounds such as marginal processing, or imposing a total order on data are not satisfactory and yield many problems (color artifactsloss of invariances, etc.) In this paper, we highlight the need for a self-dual and contrast invariant representation of color images and we provide a method that builds a single Tree of Shapes by merging the shapes computed marginally, while guarantying the most important properties of the ToS. This method does not try to impose an arbitrary total ordering on values but uses only the inclusion relationship between shapes. Eventually, we show the relevance of our method and our structure through some illustrations on filtering, image simplification, and interactive segmentation.

Documents

Bibtex (lrde.bib)

@InProceedings{	  carlinet.15.ismm,
  author	= {Edwin Carlinet and Thierry G\'eraud},
  title		= {A Color Tree of Shapes with Illustrations on Filtering,
		  Simplification, and Segmentation},
  booktitle	= {Mathematical Morphology and Its Application to Signal and
		  Image Processing -- Proceedings of the 12th International
		  Symposium on Mathematical Morphology (ISMM)},
  year		= {2015},
  series	= {Lecture Notes in Computer Science Series},
  volume	= {9082},
  address	= {Reykjavik, Iceland},
  publisher	= {Springer},
  editor	= {J.A. Benediktsson and J. Chanussot and L. Najman and H.
		  Talbot},
  pages		= {363--374},
  abstract	= {The Tree of Shapes is a morphological tree that provides a
		  high-level, hierarchical, self-dual, and contrast invariant
		  representation of images, suitable for many image
		  processing tasks. When dealing with color images, one
		  cannot use the Tree of Shapes because its definition is
		  ill-formed on multivariate data. Common workarounds such as
		  marginal processing, or imposing a total order on data are
		  not satisfactory and yield many problems (color artifacts,
		  loss of invariances, etc.) In this paper, we highlight the
		  need for a self-dual and contrast invariant representation
		  of color images and we provide a method that builds a
		  single Tree of Shapes by merging the shapes computed
		  marginally, while guarantying the most important properties
		  of the ToS. This method does not try to impose an arbitrary
		  total ordering on values but uses only the inclusion
		  relationship between shapes. Eventually, we show the
		  relevance of our method and our structure through some
		  illustrations on filtering, image simplification, and
		  interactive segmentation.}
}