Smooth Representation of Belief in Rotation Matching: Cryo-EM, Quaternions, and Neural Nets
Inspired by the problem of applying machine learning methods to the
point-cloud rotation matching problem, we have undertaken a detailed examination of recent work on this subject. We have been concerned particularly with understanding the apparent appearance of troubling behavior when quaternions are employed in the process of learning the global rotation needed to align 3D point clouds. We conclude that many of the concerns that have been put forward are readily resolvable using a novel and very simple algebraic expression, and that the noted behaviors have little to do with any apparent defects in the use of quaternions in machine learning for point cloud matching.