A Frequency Domain Technique Based on Energy Radial Projections for Robust Estimation of Global 2D Affine Transformations

The contribution of this paper is twofold: (1) it provides a thorough analysis of the frequency domain relationships relating two affine-warped images and (2) based on a fundamental equation between energy radial projections, it presents an original algorithm for estimating the global 2D affine transformation between the two images. It is well known that operating in the frequency domain allows one to separate the estimate of the affine matrix, related to the magnitudes of the Fourier transforms of the two images, from the estimate of the translation vector, related to their phases. Exploiting this property, our algorithm consists of two main steps: (1) the affine matrix is first estimated by solving, with a coarse-to-fine strategy, a suitable minimization problem formulated upon the radial projections of the image energies, and (2) after compensation for the contribution of the affine matrix, the translation vector is then recovered by means of phase correlation. The proposed method is very robust against perspective distortion and, with moderate translational displacements, it may also work when the two images differ along their peripheral areas. Experimental evidence of these characteristics is reported and discussed. The algorithm can be efficiently implemented via FFT and well suits applications requiring unsupervised and/or quasi-real-time estimation of global motion that can be described with 2D affine transformations.