000			a
999			_c30934 _d30934
008			220527b xxu||||| |||| 00| 0 eng d
020			_a9780367496906
082			_a006.3701512482 _bKAN
100			_aKanatani, Kenichi
245			_a3D rotations : parameter computation and lie-algebra based optimization
260			_bCRC Press, _c2020 _aBoca Raton :
300			_aix, 160 p. ; _bill., _c26 cm
365			_b42.99 _cGBP _d102.80
504			_aIncludes bibliographical references and index.
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.
650			_aComputer vision
650			_aMathematical models
650			_aThree-dimensional modeling
942			_2ddc _cBK