A Metric and Multiscale Color Segmentation Using the Color Monogenic Signal

  • Authors:

  • Guillaume Demarcq;Laurent Mascarilla;Pierre Courtellemont

  • Affiliations:

  • Laboratoire Mathématiques, Images, Applications, Université de La Rochelle, France;Laboratoire Mathématiques, Images, Applications, Université de La Rochelle, France;Laboratoire Mathématiques, Images, Applications, Université de La Rochelle, France

  • Venue:
  • CAIP '09 Proceedings of the 13th International Conference on Computer Analysis of Images and Patterns
  • Year:
  • 2009

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Abstract

In this paper, we use the formalism of Clifford algebras to extend the so-called Monogenic Signal to color images. This extension consists in a function with values in the Clifford algebra 驴5,0 that encodes color as well as geometric structure information. Using geometric calculus, such a mathematical object can be used to extend classical concepts of signal processing (filtering, Fourier Transform...) to color images in a consistent manner. Regarding this paper, a local color phase is introduced, which generalizes the one for grayscale image. As an example of application, we provide a new method for color segmentation. Based on our phase definition and the multiscale aspect of the Color Monogenic Signal, we provide a metric approach using differential geometry which reveals relevant on the Berkeley Image Dataset.