A frequency domain technique based on energy radial projections for robustestimation of global 2D affine transformations

The contribution of this paper is twofold: (1) it provides a thorough analy sis 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 tran sformation between the two images. It is well known that operating in the f requency domain allows one to separate the estimate of the affine matrix, r elated 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 ma trix is first estimated by solving, with a coarse-to-fine strategy, a suita ble minimization problem formulated upon the radial projections of the imag e energies, and (2) after compensation for the contribution of the affine m atrix, the translation vector is then recovered by means of phase correlati on. The proposed method is very robust against perspective distortion and, with moderate translational displacements, it may also work when the two im ages differ along their peripheral areas. Experimental evidence of these ch aracteristics is reported and discussed. The algorithm can be efficiently i mplemented via FFT and well suits applications requiring unsupervised and/o r quasi-real-time estimation of global motion that can be described with 2D affine transformations. (C) 2001 Academic Press.