Globally optimal rotation alignment of spherical surfaces with associated scalar values

Abstract

Abstract. We propose a new approach to global optimization algorithm based on controlled random search techniques for rotational alignment of spherical surfaces with associated scalar values. To reduce the distortion in correspondence and increase efficiency, the spherical surface is first re-sampled using a geodesic sphere. The rotation in space is represented using the modified Rodrigues parameters.Correspondence between two spherical surfaces is implemented in the parametric domain. We applied the methods to the alignment of beam patterns computed from the outer ear shapes of bats. The proposed method is compared with other approaches such as alignment based on principal component analysis (PCA), exhaustive search in the discrete space of rotations defined by Euler angles and direct search using uniform samples over the rotation group SO(3). Experimental results demonstrate that the proposed rotation alignment obtained using the proposed algorithm has a high degree of precision and give the best result among the other four approaches.

Optimal angular sampling for 3D volume matching and faster fitting of 3D structures into cryogenic electron microscopy data

“…In electron microscopy the goal is to match 3D density maps. In sonar systems we obtain a scalar function of directions and frequencies, which is often defined on a sphere [24].…”