Quasi Fourier-Mellin Transform for Affine Invariant Features

Fourier-Mellin transform (FMT) has been widely used for the extraction of rotation- and scale-invariant features. However, affine transform is a more reasonable approximation model for real viewpoint change. Due to shearing, the integral along the angular direction in the calculation of FMT cannot be used to extract the inherent features of an image undergoing affine transform. To eliminate the effect of shearing, whitening transform should be conducted on the integral along the radial direction. FMT can hardly be modified by conventional whitening-based methods with low computational cost due to additional processes. In this paper, two factors are constructed and embedded into FMT. Quasi Fourier-Mellin transform (QFMT) is proposed. The embedding of these factors is equivalent to whitening transform and can eliminate the effect of shearing in the affine transform. In particular, QFMT can also be calculated by integrating along the radial direction followed by integrating along the angular direction, as in FMT. Based on QFMT, the quasi Fourier-Mellin descriptor (QFMD) is constructed for the extraction of affine invariant features. Some experiments have also been conducted to test the performance of the proposed method.