Interpolating sampled cross-correlation surfaces of images for fine registration

Spatially sampled pictures may be registered to an accuracy of half a pixel by computing the extremum of the cross-correlation surface; when a higher accuracy is required it is necessary to interpolate the cross-correlation surface. It is shown that, when product correlation is used, the interpolation of the cross-correlation surface is equivalent to using the same interpolation process to derive interpolated versions of the reference picture and cross-correlating them with the current picture to establish the surface with arbitrarily fine granularity. When the computationally faster `squared-difference¿ correlation algorithm is used, it is shown that exactly the same registration result may be obtained by augmenting the cross-correlation surface in the vicinity of the extremum prior to interpolation with terms computed from the reference picture. The derivation of the augmentation terms is shown usually to represent a negligible computational load.