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 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. © 2010 Springer-Verlag London Limited.
CITATION STYLE
Batard, T., Berthier, M., & Saint-Jean, C. (2010). Clifford-fourier transform for color image processing. In Geometric Algebra Computing: in Engineering and Computer Science (pp. 135–162). Springer London. https://doi.org/10.1007/978-1-84996-108-0_8
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