Normalized Cross-Correlation using SOFT

We present a novel method to compute the normalized cross-correlation (NCC) of spherical signals such as omnidirectional images for the purpose of image alignment, i.e. orientation estimation, or template tracking. Expanding the reference image and the search template in the spherical harmonics basis, we use the Fourier representation of SO(3) as introduced by Kostelec and Rockmore. We show that the normalized version of the cross-correlation function with regard to orientation can be expressed in terms of standard correlation terms and the NCC can therefore be computed efficiently in O (N³ log²(N)). The approach is validated with experiments on real image sequences in a template matching application.