Journal of Mathematical Imaging and Vision

, Volume 40, Issue 3, pp 269–284

The Color Monogenic Signal: Application to Color Edge Detection and Color Optical Flow

  • Guillaume Demarcq
  • Laurent Mascarilla
  • Michel Berthier
  • Pierre Courtellemont
Article

Abstract

The aim of this paper is to define an extension of the analytic signal for a color image. We generalize the construction of the so-called monogenic signal to mappings with values in the vectorial part of the Clifford algebra ℝ5,0. Solving a Dirac equation in this context leads to a multiscale signal (relatively to the Poisson scale-space) which contains both structure and color information. The color monogenic signal can be used in a wide range of applications. Two examples are detailed: the first one concerns a multiscale geometric segmentation with respect to a given color; the second one is devoted to the extraction of the optical flow from moving objects of a given color.

Keywords

Color monogenic signal Analytic and monogenic signal Clifford algebras Color segmentation Color optical flow 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Guillaume Demarcq
    • 1
  • Laurent Mascarilla
    • 1
  • Michel Berthier
    • 1
  • Pierre Courtellemont
    • 1
  1. 1.Laboratoire Mathématiques, Images, Applications (MIA)Université de La RochelleLa Rochelle CedexFrance

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