3D Rotations: Parameter Computation and Lie Algebra based Optimization Kanatani Kenichi

3D rotation analysis is widely encountered in everyday problems thanks to the development of computers. This book focuses on the computational analysis of 3D rotation, rather than classical motion analysis. Sensing 3D using cameras and sensors, analyzing and modeling 3D for computer vision and computer graphics, and controlling and simulating robot motion all require 3D rotation computation.

It also pursues statistically optimal computation for maximizing the expected accuracy, as is typical of nonlinear optimization. It regards noise as random variables and models their probability distributions. All concepts are illustrated using computer vision applications as examples.Mathematically, the set of all 3D rotations forms a group denoted by SO(3).

Exploiting this group property, we obtain an optimal solution analytical or numerically, depending on the problem. Our numerical