Efficient computation of commutative anisotropic convolution on the 2-sphere

Zubair Khalid, Rodney A. Kennedy, Parastoo Sadeghi
2012 2012 6th International Conference on Signal Processing and Communication Systems  
Recently, the commutative anisotropic convolution has been defined for signals defined on the 2sphere. Here, we present exact and efficient methods for computation of commutative convolution of two signals defined on the sphere. For fast computation of commutative convolution, we first review the use of existing efficient techniques developed to evaluate SO(3) convolution. By employing the factoring of a rotation into two rotations, followed by the separation of variables, we propose a fast
more » ... propose a fast algorithm for the efficient computation of commutative convolution. In terms of computational complexity, our proposed algorithm provides a saving of O(N ) over the existing algorithms, where the convolution output is evaluated on O(N 2 ) samples on the 2-sphere. Through numerical experiments, we also verify the improvement in the computational complexity.
doi:10.1109/icspcs.2012.6507990 dblp:conf/icspcs/KhalidKS12 fatcat:oisua3yscfbhdok23s26wvgoia