000			06349cam a2200577Ki 4500
001			9781003037675
003			FlBoTFG
005			20220724194542.0
006			m o d
007			cr cnu|||unuuu
008			200826s2020 flu ob 000 0 eng d
040			_aOCoLC-P _beng _erda _epn _cOCoLC-P
020			_a9781003037675 _q(electronic bk.)
020			_a1003037674 _q(electronic bk.)
020			_a9781000071658 _q(electronic bk. : EPUB)
020			_a1000071650 _q(electronic bk. : EPUB)
020			_z9780367471330
020			_a9781000070347 _q(electronic bk. : Mobipocket)
020			_a1000070344 _q(electronic bk. : Mobipocket)
020			_a9781000070668 _q(electronic bk. : PDF)
020			_a1000070662 _q(electronic bk. : PDF)
020			_z9780367496906
035			_a(OCoLC)1190777059
035			_a(OCoLC-P)1190777059
050		4	_aTA1634
072		7	_aCOM _x012000 _2bisacsh
072		7	_aCOM _x012040 _2bisacsh
072		7	_aCOM _x014000 _2bisacsh
072		7	_aUB _2bicssc
082	0	4	_a006.3/701512482 _223
100	1		_aKanatani, Kenʼichi, _d1947- _eauthor.
245	1	0	_a3D rotations : _bparameter computation and lie-algebra based optimization / _cby Kenichi Kanatani.
250			_aFirst edition.
264		1	_aBoca Raton, FL : _bCRC Press, Taylor & Francis Group, _c2020.
300			_a1 online resource (x, 157 pages).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
500			_a"A Chapman & Hall Book"
520			_a3D 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.
505	0		_aChapter 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.
588			_aOCLC-licensed vendor bibliographic record.
650		0	_aComputer vision _xMathematical models.
650		0	_aThree-dimensional modeling _xMathematical models.
650		7	_aCOMPUTERS / Computer Graphics / General _2bisacsh
650		7	_aCOMPUTERS / Computer Graphics / Game Programming & Design _2bisacsh
650		7	_aCOMPUTERS / Computer Science _2bisacsh
856	4	0	_3Read Online _uhttps://www.taylorfrancis.com/books/9781003037675
856	4	2	_3OCLC metadata license agreement _uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
942			_2lcc _cEBK
999			_c18791 _d18791