Cayley Transformation and Numerical Stability of Calibration Equation

	Cayley Transformation and Numerical Stability of Calibration Equation
	Wu, F. C.; Wang, Z. H.; Hu, Z. Y.
发表期刊	INTERNATIONAL JOURNAL OF COMPUTER VISION
	2009-04-01
卷号	82 期号:2 页码:156-184
文章类型	Article
摘要	The application of Cayley transformation to enhance the numerical stability of camera calibration is investigated. First, a new calibration equation, called the standard calibration equation, is introduced using the Cayley transformation and its analytical solution is obtained. The standard calibration equation is equivalent to the classical calibration equation, but it exhibits remarkable better numerical stability. Second, a one-parameter calibration family, called the Cayley calibration family which is equivalent to the standard calibration equation, is obtained using also the Cayley transformation and it is found that this family is composed of those infinite homographies whose rotation has the same axis with the rotation between the two given views. The condition number of equations in the Cayley calibration family varies with the parameter value, and an algorithm to determine the best parameter value is provided. Third, the generalized Cayley calibration families equivalent to the standard calibration equation are also introduced via generalized Cayley transformations. An example of the generalized Cayley transformations is illustrated, called the S-Cayley calibration family. As in the Cayley calibration family, the numerical stability of equations in a generalized Cayley calibration family also depends on the parameter value. In addition, a more generic calibration family is also proposed and it is proved that the standard calibration equation, the Cayley calibration family and the S-Cayley calibration family are all some special cases of this generic calibration family.
关键词	Camera Calibration The Absolute Conic Calibration Equation Cayley Transformation Numerical Stability
WOS标题词	Science & Technology ; Technology
关键词[WOS]	ONE-DIMENSIONAL OBJECTS ; CAMERA CALIBRATION ; SELF-CALIBRATION ; MOVING CAMERA ; ALGORITHM
收录类别	SCI
语种	英语
WOS研究方向	Computer Science
WOS类目	Computer Science, Artificial Intelligence
WOS记录号	WOS:000263421200003
引用统计	被引频次：9[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.ia.ac.cn/handle/173211/2953
专题	多模态人工智能系统全国重点实验室_机器人视觉
作者单位	Chinese Acad Sci, Inst Automat, Natl Lab Pattern Recognit, Beijing 100190, Peoples R China
第一作者单位	模式识别国家重点实验室
推荐引用方式 GB/T 7714	Wu, F. C.,Wang, Z. H.,Hu, Z. Y.. Cayley Transformation and Numerical Stability of Calibration Equation[J]. INTERNATIONAL JOURNAL OF COMPUTER VISION,2009,82(2):156-184.
APA	Wu, F. C.,Wang, Z. H.,&Hu, Z. Y..(2009).Cayley Transformation and Numerical Stability of Calibration Equation.INTERNATIONAL JOURNAL OF COMPUTER VISION,82(2),156-184.
MLA	Wu, F. C.,et al."Cayley Transformation and Numerical Stability of Calibration Equation".INTERNATIONAL JOURNAL OF COMPUTER VISION 82.2(2009):156-184.