3D Rotations: Parameter Computation and Lie-Algebra Based Optimization
暫譯: 3D 旋轉：參數計算與李代數基礎的優化
Kanatani, Kenichi
- 出版商: CRC
- 出版日期: 2020-08-04
- 售價: $3,950
- 貴賓價: 9.5 折 $3,753
- 語言: 英文
- 頁數: 167
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 0367471337
- ISBN-13: 9780367471330
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商品描述
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.
商品描述(中文翻譯)
3D 旋轉分析在日常問題中因電腦的發展而廣泛應用。利用相機和感測器感知 3D，分析和建模 3D 用於電腦視覺和電腦圖形，以及控制和模擬機器人運動，都需要進行 3D 旋轉計算。本書專注於 3D 旋轉的計算分析，而非傳統的運動分析。它將噪聲視為隨機變數並對其概率分佈進行建模。它還追求統計上最佳的計算，以最大化期望準確度，這是非線性優化的典型特徵。所有概念均以電腦視覺應用作為例子進行說明。
在數學上，所有 3D 旋轉的集合形成一個稱為 SO(3) 的群。利用這一群的性質，我們根據問題獲得最佳解，無論是解析的還是數值的。我們的數值方案稱為「李代數方法」，基於 SO(3) 的李群結構。
本書還為希望編碼本書中所呈現理論的讀者提出計算專案，描述必要的 3D 模擬設置，並提供真實的 GPS 3D 測量數據。為了幫助對抽象數學不太熟悉的讀者，本書在卷末附錄中提供了四元數代數、矩陣分析、李群和李代數的簡要概述。
作者簡介
Kenichi Kanatani received his B.E., M.S., and Ph.D. in applied mathematics from the University of Tokyo in 1972, 1974, and 1979, respectively. After serving as Professor of computer science at Gunma University, Gunma, Japan, and Okayama University, Okayama, Japan, he retired in 2013 and is now Professor Emeritus of Okayama University.He was a visiting researcher at the University of Maryland, U.S. (1985-1986, 1988-1989, 1992), the University of Copenhagen, Denmark (1988), the University of Oxford, U.K. (1991), INRIA at Rhone Alpes, France (1988), ETH, Switzerland (2013), the Uni-versity of Paris-Est, France (2014), Link ̈oping University, Sweden (2015), and NationalTaiwan Normal University (2019).He is the author of K. Kanatani, Group-Theoretical Methods in Image Understanding(Springer, 1990), K. Kanatani, Geometric Computation for Machine Vision(Oxford Uni-versity Press, 1993), K. Kanatani, Statistical Optimization for Geometric Computation: Theory and Practice(Elsevier, 1996; reprinted Dover, 2005), K. Kanatani, Understand-ing Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision andGraphics(CRC Press, 2015), K. Kanatani, Y. Sugaya, Y. Kanazawa, Ellipse Fitting forComputer Vision: Implementation and Applications(Morgan-Claypool, 2016), and K.Kanatani, Y. Sugaya, Y. Kanazawa, Guide to 3D Vision Computation: Geometric Anal-ysis and Implementation(Springer, 2016).He received many awards including the best paper awards from IPSJ (1987), IEICE(2005), and PSIVT (2009). He is a Fellow of IEEE, IAPR, and IEICE.1
作者簡介(中文翻譯)
Kenichi Kanatani於1972年、1974年和1979年分別在東京大學獲得應用數學的學士、碩士和博士學位。在擔任日本群馬大學和岡山大學的計算機科學教授後，他於2013年退休，現為岡山大學名譽教授。他曾在美國馬里蘭大學（1985-1986、1988-1989、1992）、丹麥哥本哈根大學（1988）、英國牛津大學（1991）、法國INRIA（1988）、瑞士ETH（2013）、法國巴黎東大學（2014）、瑞典林雪平大學（2015）以及國立台灣師範大學（2019）擔任訪問研究員。他是以下著作的作者：K. Kanatani, Group-Theoretical Methods in Image Understanding（Springer, 1990）、K. Kanatani, Geometric Computation for Machine Vision（Oxford University Press, 1993）、K. Kanatani, Statistical Optimization for Geometric Computation: Theory and Practice（Elsevier, 1996；重印於Dover, 2005）、K. Kanatani, Understanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics（CRC Press, 2015）、K. Kanatani, Y. Sugaya, Y. Kanazawa, Ellipse Fitting for Computer Vision: Implementation and Applications（Morgan-Claypool, 2016），以及K. Kanatani, Y. Sugaya, Y. Kanazawa, Guide to 3D Vision Computation: Geometric Analysis and Implementation（Springer, 2016）。他獲得了多項獎項，包括IPSJ（1987）、IEICE（2005）和PSIVT（2009）的最佳論文獎。他是IEEE、IAPR和IEICE的會士。
