Complete invariants for robust face recognition

In this paper, we propose two complete sets of similarity invariant descriptors under the Fourier–Mellin transform and the analytical Fourier–Mellin transform (AFMT) frameworks, respectively. The magnitude and phase spectra are jointly processed in our case, and the presented invariants are complete and can be used to reconstruct the image. Their numerical properties are also revealed through image reconstruction. In order to simplify the invariant feature data for recognition and discrimination, a 2D-PCA approach is incorporated into the presented complete invariant descriptor. The obtained compact representation through the 2D-PCA preserves the essential structure of the objects in an image. We tested this compact form on the ORL, Yale and BioID face databases for experimental verification, and achieved a face verification under similarity transforms with a much inferior equal error rate (EER) compared to when the 2D-PCA-based compact form is used without complete invariants.