【OpenCV】张正友标定法的 OpenCV 实现

今天看到一篇文章, 把 OpenCV 中实现标定的总体流程, 每个步骤, 调用的每个函数 都讲解清楚了, 直接带路, 张正友相机标定Opencv实现以及标定流程&&标定结果评价&&图像矫正流程解析（附标定程序和棋盘图）.

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以下分析, 适用于 OpenCV 3.1.0

• 以下函数源代码在 imgproc 模块找到

  • cvUndistort2 , see in undistort.cpp

• 以下函数源代码在 calibration 模块找到 calibration.cpp

  • cvFindExtrinsicCameraParams2
  • cvProjectPoints2

cvProjectPoints2 : 三维点到相平面的重投影

//declaration
/* Projects object points to the view plane using
   the specified extrinsic and intrinsic camera parameters */
CVAPI(void) cvProjectPoints2( const CvMat* object_points, const CvMat* rotation_vector,
                              const CvMat* translation_vector, const CvMat* camera_matrix,
                              const CvMat* distortion_coeffs, CvMat* image_points,
                              CvMat* dpdrot CV_DEFAULT(NULL), CvMat* dpdt CV_DEFAULT(NULL),
                              CvMat* dpdf CV_DEFAULT(NULL), CvMat* dpdc CV_DEFAULT(NULL),
                              CvMat* dpddist CV_DEFAULT(NULL),
                              double aspect_ratio CV_DEFAULT(0));

cvUndistort2 : 去畸变校正

CVAPI(void) cvUndistort2( const CvArr* src, CvArr* dst,
                          const CvMat* camera_matrix,
                          const CvMat* distortion_coeffs,
                          const CvMat* new_camera_matrix CV_DEFAULT(0) );

cvFindExtrinsicCameraParams2 : 已知内参求外参

/* Finds extrinsic camera parameters from
   a few known corresponding point pairs and intrinsic parameters */
CVAPI(void) cvFindExtrinsicCameraParams2( const CvMat* object_points,
                                          const CvMat* image_points,
                                          const CvMat* camera_matrix,
                                          const CvMat* distortion_coeffs,
                                          CvMat* rotation_vector,
                                          CvMat* translation_vector,
                                          int use_extrinsic_guess CV_DEFAULT(0) );

• 计算原理

1. 将空间点和图像点齐次化，得到图像点矩阵$m$ 空间点矩阵$M$，
2. 求取矩阵$M$的平均值 $M_c$
3. 计算另一个矩阵 $mm=(M-M_c{)}^T(M-M_c)$
4. 对$mm$进行 SVD 分解, $mm=UWV$
5. $R_t=V$
6. $T_t=-M_c{R}_t$
7. $M_{xy}=V_t{M}^T+T_t$
8. $H=\text{find homography between }m\text{ and }{M}_{xy}$
9. $H=[h_1,h_2,t],\text{then normalization}$
10. $h_1=\frac{h_1}{|h_1|}$
11. $t=\frac{t}{|h_1|+|h_2|}$
12. $h_3=h_1\times h_2$
13. $H=[h_1,h_2,h_3]$
14. $\text{final result, }{R}_f=H\ast R_t,t_f=H\ast T_t+t$
15. LM 迭代优化

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Ref

• OpenCV 3.1.0 Module : Camera Calibration and 3D Reconstruction
• opencv中cvFindExtrinsicCameraParams2函数的算法原理？ - 鱼丸还是粗面的回答 - 知乎 : 嗯, 讲解的很透彻了.