We propose new sets of Fourier-Mellin descriptors for color images. They are constructed using the Clifford Fourier Transform of Batard et al. (2010) and are an extension of the classical Fourier-Mellin descriptors for grayscale images. These are invariant under direct similarity transformations (translations, rotations, scale) and marginal treatment of colors images is avoided. An implementation of these features is given and the choice of the bivector (a distinguished color plane which parameterizes the Clifford Fourier Transform) is discussed. The proposed formalism extends and clarifies the notion of direction of analysis as introduced for the quaternionic Fourier-Mellin moments (Guo and Zhu, 2011). Thus, another set of descriptors invariant under this parameter is defined. Our proposals are tested with the purpose of object recognition on well-known color image databases. Their retrieval rates are favourably compared to standard feature descriptors.

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.

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