On the practical estimability of planar roto-translations with the locus Δ(K)=0

It is well-known that, by working in the frequency domain, the estimation of a planar roto-translation is separable into two distinct tasks. One may first estimate the rotational component from the magnitudes of the Fourier transforms and then, after compensating for rotation, one may easily estimate the translational component, e.g., by using phase correlation techniques. In our previous work, from the Fourier transforms of two relatively roto-translated signals, we devised the function Δ(k) whose locus Δ(k)=0 proved to be a very effective tool capable of yielding extremely robust estimates of the rotation angle. In the present paper we explain how to extend those results to practical cases in which images have a finite support and may differ owing to missing corners. An example of use of the locus Δ(k)=0 in a practical case is reported and commented