In this paper, we present a complete set of hybrid
similarity invariants under the Analytical Fourier-Mellin
Transform (AFMT) framework, and apply it to invariant face
recognition. Because the magnitude and phase spectra are not
processed separately, this invariant descriptor is complete. In order to simplify the invariant feature data for recognition and discrimination, a 2D-PCA approach is introduced into this complete invariant descriptor. The experimental results indicate that the presented invariant descriptor is complete and similarityinvariant. Its compact representation through the 2D-PCA preserves the essential structure of an object. Furthermore, we apply this compact form into ORL, Yale and BioID face databases for experimental verification, and achieve the desired results