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3D Rotations
3D Rotations
📖 Book - PDF

3D Rotations

Parameter Computation and Lie Algebra based Optimization
Kenichi Kanatani
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157 pages
language
English
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📖 Book - PDF

3D Rotations

Parameter Computation and Lie Algebra based Optimization
Kenichi Kanatani
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About This Book

3D rotation analysis is widely encountered in everyday problems thanks to the development of computers. 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. This book focuses on the computational analysis of 3D rotation, rather than classical motion analysis. It regards noise as random variables and models their probability distributions. It also pursues statistically optimal computation for maximizing the expected accuracy, as is typical of nonlinear optimization. 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 scheme, which we call the "Lie algebra method, " is based on the Lie group structure of SO(3).

This book also proposes computing projects for readers who want to code the theories presented in this book, describing necessary 3D simulation setting as well as providing real GPS 3D measurement data. To help readers not very familiar with abstract mathematics, a brief overview of quaternion algebra, matrix analysis, Lie groups, and Lie algebras is provided as Appendix at the end of the volume.

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Information

Publisher
CRC Press
Year
2020
ISBN
9781000071658
Topic
Computer Science
Subtopic
Computer Graphics
Edition
1

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