In this thesis, we focus on color image recognition using a new geometric approach in the frequency domain. Most existing methods only process grayscale images through descriptors defined from the usual Fourier transform. The extension of these methods to multichannel images such as color images usually consists in reproducing the same processing for each channel. To avoid this marginal processing,we study and compare the different generalizations of color Fourier transforms. This work leads us to use the Clifford Fourier transform for color images defined in the framework of geometric algebra. A detailed study of it leads us to define a fast algorithm and to propose a phase correlation for colorimages. In a second step, with the aim of generalizing Fourier descriptors of the literature with thisFourier transform, we study their properties, including invariance to translation, rotation and scale.This work leads us to propose three new descriptors called “generalized color Fourier descriptors”(GCFD) invariant in translation and in rotation.The proposed methods are evaluated on usual image databases to estimate the contribution of color frequency content compared with grayscale and marginal methods. The results obtained usingan SVM classifier show the potential of the proposed methods ; the GCFD are more compact, have less computational complexity and give better recognition rates. We also propose heuristics for choosing the parameter of the color Clifford Fourier transform.This thesis is a first step towards a generalization of frequency methods to multichannel images.
