The aim of this paper is to propose two different approaches for color object recognition, both using the recently defined color Clifford Fourier transform. The first one deals with so-called Generalized Fourier Descriptors, the definition of which relies on plane motion group actions. The proposed color extension leads to more compact descriptors, with lower complexity and better recognition rates, than the already existing descriptors based on the processing of the r, g and b channels separately (later referred as marginal processing). The second approach concerns color phase correlation for color images. The idea here is to generalize in the Clifford framework the usual means of measuring correlation from the well-known shift theorem. Both methods necessitate to choose a bivector B of R_{4,0} which corresponds to an analysis plane in the color space. The relevance of proposed methods for classification purposes is discussed on several color image database. In particular, the influence of parameter B is studied regarding the type of images.