A noise-robust frequency domain technique for estimating planar roto-translations

This work presents a new method for estimating planar roto-translations tha t operates in the frequency domain and, as such, is not based on features. Since the proposed technique uses all the image information, it is very rob ust against noise, and it can he very accurate; estimation errors on the ro tational angle range from a few hundredths to a few tenths of a degree, dep ending on the noise level. In the presence of not-too-large translational d isplacements, it may work, though with less accuracy, in the case of croppe d images as well. Experimental evidence of this performance is presented, a nd the mathematical reasons behind these characteristics are explained in d epth. Another remarkable feature of the algorithm consists in that it works in Cartesian coordinates, bypassing the need to transform data from the Ca rtesian to the polar domain, which, typically, is a numerically delicate an d computationally onerous task. The proposed technique can become an effect ive tool for unsupervised estimation of roto-translations by means of imple mentations based on FFT algorithms.