Clifford Fourier Transform for Color Image Processing

Abstract : The aim of this paper is to define a Clifford Fourier transform that is suitable for color image spectral analysis. There have been many attempts to define such a transformation using quaternions or Clifford algebras. We focus here on a geometric approach using group actions. The idea is to generalize the usual definition based on the characters of abelian groups by considering group morphisms from $R^2$ to spinor groups Spin(3) and Spin(4). The transformation we propose is parameterized by a bivector and a quadratic form, the choice of which is related to the application to be treated. A general definition for 4D signal defined on the plane is also given; for particular choices of spinors it coincides with the definitions of S.Sangwine and T. Bülow.
Complete list of metadatas

Cited literature [14 references]  Display  Hide  Download
Contributor : Christophe Saint-Jean <>
Submitted on : Wednesday, June 29, 2011 - 9:36:27 AM
Last modification on : Wednesday, November 29, 2017 - 10:30:00 AM


Files produced by the author(s)


  • HAL Id : hal-00332912, version 3



Thomas Batard, Michel Berthier, Christophe Saint-Jean. Clifford Fourier Transform for Color Image Processing. Bayro-Corrochano, Eduardo; Scheuermann, Gerik. Geometric Algebra Computing, Springer Verlag, pp.135-162, 2010, Engineering and Computer Science. ⟨hal-00332912v3⟩



Record views


Files downloads