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.
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Submitted on : Wednesday, June 29, 2011 - 9:36:27 AM
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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⟩

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