Cross-Correlation and Rotation Estimation of Local 3D Vector Field Patches

In this paper, we present a method for the fast and accurate computation of the local cross-correlation of 3D vectorial data. Given spherical patches of 3D vector fields, our method computes the full crosscorrelation over all possible rotations and allows an accurate estimation of the rotation offset between two patches. Our approach is based on a novel harmonic representation for 3D vector fields located on spherical surfaces which allows us to apply the convolution theorem and perform a fast correlation in the frequency domain. The theoretical advances presented in this paper can be applied to various computer vision and pattern recognition problems, such as finding corresponding points on vector fields for registration problems, key point detection on vector fields or designing local vector field features.