Color representation and processes with Clifford algebra

Abstract

In the literature, colour information of pixels of an image has been represented by different structures. Recently algebraic entities such as quaternions or Clifford algebras have been used to perform image processing for example. We propose to review several contributions for colour image processing by using the Quaternion algebra and the Clifford algebra. First, we illustrate how this formalism can be used to define colour alterations with algebraic operations. We generalise linear filtering algorithms already defined with quaternions and review a Clifford color edge detector. Clifford algebras appear to be an efficient mathematical tool to investigate the geometry of nD images. It has been shown for instance how to use quaternions for colour edge detection or to define an hypercomplex Fourier transform. The aim of the second part of this chapter is to present an example of applications, namely the Clifford Fourier transform of Clifford algebras to colour image processing.