Combined blur, translation, scale and rotation invariant image recognition by Radon and pseudo-Fourier–Mellin transforms

The idea of scale and rotation invariant image recognition based on Radon and Fourier–Mellin transforms has been presented recently. In this paper, we extend the previous work and propose a new method to construct a set of combined blur, translation, scale and rotation invariants using Radon and pseudo-Fourier–Mellin transforms, named Radon and pseudo-Fourier–Mellin invariants (RPFMI). The proposed method is robust to additive white noise as a result of summing pixel values to generate projections in the Radon transform step. We also present a mathematical framework of obtaining the Radon and pseudo-Fourier–Mellin transforms of blurred images, and a framework of deriving the combined blur, scale and rotation invariants. Theoretical and experimental results show the superiority of the proposed method and its robustness to additive white noise in comparison with some recent methods.