Analysis of binning of normals for spherical harmonic cross-correlation

Spherical harmonic cross-correlation is a robust registration technique that uses the normals of two overlapping point clouds to bring them into coarse rotational alignment. This registration technique however has a high computational cost as spherical harmonics need to be calculated for every normal. By binning the normals, the computational efficiency is improved as the spherical harmonics can be pre-computed and cached at each bin location. In this paper we evaluate the efficiency and accuracy of the equiangle grid, icosahedron subdivision and the Fibonacci spiral, an approach we propose. It is found that the equiangle grid has the best efficiency as it can perform direct binning, followed by the Fibonacci spiral and then the icosahedron, all of which decrease the computational cost compared to no binning. The Fibonacci spiral produces the highest achieved accuracy of the three approaches while maintaining a low number of bins. The number of bins allowed by the equiangle grid and icosahedron are much more restrictive than the Fibonacci spiral. The performed analysis shows that the Fibonacci spiral can perform as well as the original cross-correlation algorithm without binning, while also providing a significant improvement in computational efficiency.