Color Fourier–Mellin descriptors for image recognition

• Quaternionic Fourier Mellin moments are rewritten using Clifford algebras.
• Bivector choice is examined and its role emphasized.
• A method to make the proposed descriptors invariant to this parameter is given.
• The descriptors are used in a color image recognition and image retrieval context.
• Better results than other frequency methods are provided.

We propose new sets of Fourier–Mellin descriptors for color images. They are constructed using the Clifford Fourier transform of Batard et al. (2010) [4] 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 favorably compared to standard feature descriptors.