Cayley Transformation and Numerical Stability of Calibration Equation
Cayley Transformation and Numerical Stability of Calibration Equation
复制标题
标定方程的凯莱变换和数值稳定性
DOI：
10.1007/s11263-008-0193-x
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发表时间：
2009-04
影响因子：
19.5
通讯作者：
Hu, Z. Y.
中科院分区：
文献类型：
--
作者：
Wu, F. C.;Wang, Z. H.;Hu, Z. Y.
研究了利用凯莱变换提高摄像机标定数值稳定性的方法。首先，利用凯莱变换，引入一个新的校准方程，称为标准校准方程，并得到其解析解。标准校准方程与经典校准方程等价，但具有更好的数值稳定性。其次，一个单参数校准家庭，称为凯莱校准家庭，这是等价于标准的校准方程，也使用凯莱变换，它被发现，这个家庭是由那些无限的单应性，其旋转具有相同的轴之间的旋转两个给定的视图。Cayley校准族中方程的条件数随参数值的变化而变化，并给出了确定最佳参数值的算法。第三，通过广义Cayley变换，引入了与标准定标方程等价的广义Cayley定标族。给出了广义Cayley变换的一个例子，称为S-Cayley校准族。与Cayley校准族一样，广义Cayley校准族中方程的数值稳定性也依赖于参数值。此外，还提出了一个更一般的校准族，并证明了标准校准方程、Cayley校准族和S-Cayley校准族都是该校准族的一些特例。
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.
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影响因子：
3.8
作者：
M. C. Seiler;F. A. Seiler
通讯作者：
M. C. Seiler;F. A. Seiler
DOI：
10.1109/34.574792
发表时间：
1997-02
期刊：
IEEE Trans. Pattern Anal. Mach. Intell.
影响因子：
--
作者：
R. Hartley
通讯作者：
R. Hartley
DOI：
10.1023/b:visi.0000029664.99615.94
发表时间：
2004-11-01
影响因子：
19.5
作者：
Lowe, DG
通讯作者：
Lowe, DG
DOI：
10.1007/3-540-61123-1_183
发表时间：
1996-04
期刊：
--
影响因子：
--
作者：
P. Sturm;B. Triggs
通讯作者：
P. Sturm;B. Triggs
DOI：
10.1109/tpami.2004.21
发表时间：
2004-07-01
影响因子：
23.6
作者：
Zhang, ZY
通讯作者：
Zhang, ZY