3D Rotations: Parameter Computation and Lie Algebra based Optimization

3D rotation analysis is crucial for computer vision and graphics, robotics, and sensing. This book focuses on computational analysis of 3D rotation, modeling noise as random variables, and optimizing computation for maximum accuracy. It utilizes computer vision applications and provides computing projects for readers to code the theories.

Format: Paperback / softback
Length: 157 pages
Publication date: 01 March 2022
Publisher: Taylor & Francis Ltd

The analysis of 3D rotation has become increasingly prevalent in everyday problems due to the advancements in computer technology. This analysis involves the use of cameras and sensors to sense 3D environments, the analysis and modeling of 3D data for computer vision and computer graphics, as well as the control and simulation of robot motion. This book specifically focuses on the computational analysis of 3D rotation, rather than classical motion analysis. It treats noise as random variables and models their probability distributions. Moreover, it aims to achieve statistically optimal computation for maximizing the expected accuracy, a common approach in nonlinear optimization.

To illustrate these concepts, computer vision applications are used as examples throughout the book. Mathematically, the set of all 3D rotations forms a group called SO(3). By leveraging this group property, an optimal solution can be obtained analytically or numerically, depending on the specific problem. Our numerical scheme, known as the Lie algebra method, is based on the Lie group structure of SO(3).

Furthermore, this book provides computing projects for readers who wish to implement the theories presented. It includes detailed descriptions of the necessary 3D simulation settings and provides real GPS 3D measurement data. To assist readers who may not have a strong background in abstract mathematics, an appendix is provided at the end of the volume, offering a brief overview of quaternion algebra, matrix analysis, Lie groups, and Lie algebras.

Weight: 308g
Dimension: 254 x 178 (mm)
ISBN-13: 9780367496906