Introducing Multivariate Connected Openings and Closings

From LRDE

Abstract

The component trees provide a high-level, hierarchicaland contrast invariant representations of images, suitable for many image processing tasks. Yet their definition is ill-formed on multivariate data, e.g., color imagesmulti-modality images, multi-band images, and so on. Common workarounds such as marginal processing, or imposing a total order on data are not satisfactory and yield many problems, such as artifacts, loss of invariances, etc. In this paper, inspired by the way the Multivariate Tree of Shapes (MToS) has been defined, we propose a definition for a Multivariate min-tree or max-tree. We do not impose an arbitrary total ordering on values; we use only the inclusion relationship between components. As a straightforward consequence, we thus have a new class of multivariate connected openings and closings.

Documents

Publications/carlinet.19.ismm.inc

Bibtex (lrde.bib)

@InProceedings{	  carlinet.19.ismm,
  author	= {Edwin Carlinet and Thierry G\'eraud},
  title		= {Introducing Multivariate Connected Openings and Closings},
  booktitle	= {Mathematical Morphology and Its Application to Signal and
		  Image Processing -- Proceedings of the 14th International
		  Symposium on Mathematical Morphology (ISMM)},
  year		= 2019,
  editor	= {},
  volume	= {},
  series	= {Lecture Notes in Computer Science Series},
  address	= {Saarbr\"ucken, Germany},
  publisher	= {Springer},
  pages		= {1--12},
  month		= {July},
  abstract	= {The component trees provide a high-level, hierarchical,
		  and contrast invariant representations of images, suitable
		  for many image processing tasks. Yet their definition is
		  ill-formed on multivariate data, e.g., color images,
		  multi-modality images, multi-band images, and so on. Common
		  workarounds such as marginal processing, or imposing a
		  total order on data are not satisfactory and yield many
		  problems, such as artifacts, loss of invariances, etc. In
		  this paper, inspired by the way the Multivariate Tree of
		  Shapes (MToS) has been defined, we propose a definition for
		  a Multivariate min-tree or max-tree. We do not impose an
		  arbitrary total ordering on values; we use only the
		  inclusion relationship between components. As a
		  straightforward consequence, we thus have a new class of
		  multivariate connected openings and closings.}
}