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

This work presents a new method for estimating planar roto-translations that 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 robust against noise, and it can be very accurate; estimation errors on the rotational angle range from a few hundredths to a few tenths of a degree, depending on the noise level. In the presence of not-too-large translational displacements, it may work, though with less accuracy, in the case of cropped images as well. Experimental evidence of this performance is presented, and the mathematical reasons behind these characteristics are explained in depth. Another remarkable feature of the algorithm consists in that it works in Cartesian coordinates, bypassing the need to transform data from the Cartesian to the polar domain, which, typically, is a numerically delicate and computationally onerous task. The proposed technique can become an effective tool for unsupervised estimation of roto-translations by means of implementations based on FFT algorithms.