3D rotations : parameter computation and lie-algebra based optimization /
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 boo...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boca Raton, FL :
CRC Press, Taylor & Francis Group,
2020.
|
| Edition: | First edition. |
| Subjects: | |
| Online Access: | Taylor & Francis OCLC metadata license agreement |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Add Tag
Table of Contents:
- Chapter 1. Introduction 1.1 3D ROTATIONS 1.2 ESTIMATION OF ROTATION 1.3 DERIVATIVE-BASED OPTIMIZATION1.4 RELIABILITY EVALUATION OF ROTATION COMPUTATION1.5 COMPUTING PROJECTS 1.6 RELATED TOPICS OF MATHEMATICS Chapter 2. Geometry of Rotation2.1 3D ROTATION 2.2 ORTHOGONAL MATRICES AND ROTATION MATRICES2.3 EULERS THEOREM 2.4 AXIAL ROTATIONS 2.5 SUPPLEMENTAL NOTE 2.6 EXERCISES Chapter 3. Parameters of Rotation3.1 ROLL, PITCH, YAW 3.2 COORDINATE SYSTEM ROTATION 153.3 EULER ANGLES 3.4 RODRIGUES FORMULA 3.5 QUATERNION REPRESENTATION 213.6 SUPPLEMENTAL NOTES 3.7 EXERCISES Chapter 4. Estimation of Rotation I: Isotropic Noise4.1 ESTIMATING ROTATION 4.2 LEAST SQUARES AND MAXIMUM LIKELIHOOD4.3 SOLUTION BY SINGULAR VALUE DECOMPOSITION4.4 SOLUTION BY QUATERNION REPRESENTATION4.5 OPTIMAL CORRECTION OF ROTATION4.6 SUPPLEMENTAL NOTE 4.7 EXERCISES Chapter 5. Estimation of Rotation II: Anisotropic Noise5.1 ANISOTROPIC GAUSSIAN DISTRIBUTIONS5.2 ROTATION ESTIMATION BY MAXIMUM LIKELIHOOD5.3 ROTATION ESTIMATION BY QUATERNION REPRESENTATION5.4 OPTIMIZATION BY FNS 5.5 METHOD OF HOMOGENEOUS CONSTRAINTS5.6 SUPPLEMENTAL NOTE 5.7 EXERCISES Chapter 6. Derivative-based Optimization: Lie Algebra Method6.1 DERIVATIVE-BASED OPTIMIZATION6.2 SMALL ROTATIONS AND ANGULAR VELOCITY6.3 EXPONENTIAL EXPRESSION OF ROTATION6.4 LIE ALGEBRA OF INFINITESIMAL ROTATIONS6.5 OPTIMIZATION OF ROTATION 6.6 ROTATION ESTIMATION BY MAXIMUM LIKELIHOOD6.7 FUNDAMENTAL MATRIX COMPUTATION6.8 BUNDLE ADJUSTMENT 6.9 SUPPLEMENTAL NOTES 6.10 EXERCISES Chapter 7. Reliability of Rotation Computation 7.1 ERROR EVALUATION FOR ROTATION7.2 ACCURACY OF MAXIMUM LIKELIHOOD7.3 THEORETICAL ACCURACY BOUND7.4 KCR LOWER BOUND 7.5 SUPPLEMENTAL NOTES 7.6 EXERCISES Chapter 8. Computing Projects8.1 STEREO VISION EXPERIMENT8.2 OPTIMAL CORRECTION OF STEREO IMAGES8.3 TRIANGULATION OF STEREO IMAGES8.4 COVARIANCE EVALUATION OF STEREO RECONSTRUCTION8.5 LAND MOVEMENT COMPUTATION USING REAL GPS DATA8.6 SUPPLEMENTAL NOTES 8.7 EXERCISES Appendix A Hamiltons Quaternion AlgebraA.1 QUATERNIONS A.2 QUATERNION ALGEBRA A.3 CONJUGATE, NORM, AND INVERSEA.4 QUATERNION REPRESENTATION OF ROTATIONSA.5 COMPOSITION OF ROTATIONSA.6 TOPOLOGY OF ROTATIONS A.7 INFINITESIMAL ROTATIONS A.8 REPRESENTATION OF GROUP OF ROTATIONSA.9 STEREOGRAPHIC PROJECTIONAppendix B Topics of Linear Algebra B.1 LINEAR MAPPING AND BASISB.2 PROJECTION MATRICES B.3 PROJECTION ONTO A LINE AND A PLANEB.4 EIGENVALUES AND SPECTRAL DECOMPOSITIONB.5 MATRIX REPRESENTATION OF SPECTRAL DECOMPOSITIONB.6 SINGULAR VALUES AND SINGULAR DECOMPOSITIONB.7 COLUMN AND ROW DOMAINSAppendix C Lie Groups and Lie Algebras C.1 GROUPS C.2 MAPPINGS AND GROUPS OF TRANSFORMATIONC.3 TOPOLOGY C.4 MAPPINGS OF TOPOLOGICAL SPACESC.5 MANIFOLDS C.6 LIE GROUPS C.7 LIE ALGEBRAS C.8 LIE ALGEBRAS OF LIE GROUPSAnswers Bibliography Index.
3D rotations : parameter computation and lie-algebra based optimization /