Hypercomplex Wiener-Khintchine theorem with application to color image correlation

The auto-correlation and cross-correlation function have been generalized to color images, but only by explicit evaluation of a double summation over the whole image for each pixel of the correlation result. Practical use of any correlation method on images of reasonable spatial resolution requires realization using a Fourier transform. A formula for computing the cross-correlation of a pair of images (and hence the auto-correlation of a single image) is presented, based on a previously published hypercomplex Fourier transform.