本文来自公众号：机器人视觉
完成双目相机标定以后，获得双目相机的参数矩阵

包括左右相机的内参数矩阵、左右相机的畸变系数矩阵、右相机相对于左相机的旋转矩阵与平移矩阵

已知左右相机图像中的对应点坐标，获取目标在双目视觉传感器下三维坐标的流程如下：

1、将双目相机标定参数整理如下：

//左相机内参数矩阵
float leftIntrinsic[3][3] = { 3061.6936, -0.8869, 641.3042,
0, 3058.8751, 508.9555,
0, 0, 1 };

//左相机畸变系数
float leftDistortion[1][5] = { -0.0133, 0.6503, 0.0029, -0.0049, -16.8704 };
//左相机旋转矩阵
float leftRotation[3][3] = { 1, 0, 0,
0, 1, 0,
0, 0, 1 };
//左相机平移向量
float leftTranslation[1][3] = { 0, 0, 0 };

//右相机内参数矩阵
float rightIntrinsic[3][3] = { 3069.2482, -0.8951, 620.5357,
0, 3069.2450, 532.7122,
0, 0, 1 };
//右相机畸变系数
float rightDistortion[1][5] = { -0.0593, 3.4501, 0.0003, -8.5614, -58.3116 };
//右相机旋转矩阵
float rightRotation[3][3] = { 0.9989, 0.0131, -0.0439,
-0.0121, 0.9996, 0.0233,
0.0441, -0.0228, 0.9987};
//右相机平移向量
float rightTranslation[1][3] = {-73.8389, 2.6712, 3.3792};

2、二维像素坐标与相机坐标系下三维坐标转换

//************************************
// Description: 根据左右相机中成像坐标求解空间坐标
// Method:    uv2xyz
// FullName:  uv2xyz
// Parameter: Point2f uvLeft
// Parameter: Point2f uvRight
// Returns:   cv::Point3f
//************************************
Point3f uv2xyz(Point2f uvLeft, Point2f uvRight)
{
	//  [u1]      |X|					  [u2]      |X|
	//Z*|v1| = Ml*|Y|					Z*|v2| = Mr*|Y|
	//  [ 1]      |Z|					  [ 1]      |Z|
	//			  |1|								|1|
	Mat mLeftRotation = Mat(3, 3, CV_32F, leftRotation);
	Mat mLeftTranslation = Mat(3, 1, CV_32F, leftTranslation);
	Mat mLeftRT = Mat(3, 4, CV_32F);//左相机M矩阵
	hconcat(mLeftRotation, mLeftTranslation, mLeftRT);
	Mat mLeftIntrinsic = Mat(3, 3, CV_32F, leftIntrinsic);
	Mat mLeftM = mLeftIntrinsic * mLeftRT;
	//cout<<"左相机M矩阵 = "<<endl<<mLeftM<<endl;

	Mat mRightRotation = Mat(3, 3, CV_32F, rightRotation);
	Mat mRightTranslation = Mat(3, 1, CV_32F, rightTranslation);
	Mat mRightRT = Mat(3, 4, CV_32F);//右相机M矩阵
	hconcat(mRightRotation, mRightTranslation, mRightRT);
	Mat mRightIntrinsic = Mat(3, 3, CV_32F, rightIntrinsic);
	Mat mRightM = mRightIntrinsic * mRightRT;
	//cout<<"右相机M矩阵 = "<<endl<<mRightM<<endl;

	//最小二乘法A矩阵
	Mat A = Mat(4, 3, CV_32F);
	A.at<float>(0, 0) = uvLeft.x * mLeftM.at<float>(2, 0) - mLeftM.at<float>(0, 0);
	A.at<float>(0, 1) = uvLeft.x * mLeftM.at<float>(2, 1) - mLeftM.at<float>(0, 1);
	A.at<float>(0, 2) = uvLeft.x * mLeftM.at<float>(2, 2) - mLeftM.at<float>(0, 2);

	A.at<float>(1, 0) = uvLeft.y * mLeftM.at<float>(2, 0) - mLeftM.at<float>(1, 0);
	A.at<float>(1, 1) = uvLeft.y * mLeftM.at<float>(2, 1) - mLeftM.at<float>(1, 1);
	A.at<float>(1, 2) = uvLeft.y * mLeftM.at<float>(2, 2) - mLeftM.at<float>(1, 2);

	A.at<float>(2, 0) = uvRight.x * mRightM.at<float>(2, 0) - mRightM.at<float>(0, 0);
	A.at<float>(2, 1) = uvRight.x * mRightM.at<float>(2, 1) - mRightM.at<float>(0, 1);
	A.at<float>(2, 2) = uvRight.x * mRightM.at<float>(2, 2) - mRightM.at<float>(0, 2);

	A.at<float>(3, 0) = uvRight.y * mRightM.at<float>(2, 0) - mRightM.at<float>(1, 0);
	A.at<float>(3, 1) = uvRight.y * mRightM.at<float>(2, 1) - mRightM.at<float>(1, 1);
	A.at<float>(3, 2) = uvRight.y * mRightM.at<float>(2, 2) - mRightM.at<float>(1, 2);

	//最小二乘法B矩阵
	Mat B = Mat(4, 1, CV_32F);
	B.at<float>(0, 0) = mLeftM.at<float>(0, 3) - uvLeft.x * mLeftM.at<float>(2, 3);
	B.at<float>(1, 0) = mLeftM.at<float>(1, 3) - uvLeft.y * mLeftM.at<float>(2, 3);
	B.at<float>(2, 0) = mRightM.at<float>(0, 3) - uvRight.x * mRightM.at<float>(2, 3);
	B.at<float>(3, 0) = mRightM.at<float>(1, 3) - uvRight.y * mRightM.at<float>(2, 3);

	Mat XYZ = Mat(3, 1, CV_32F);
	//采用SVD最小二乘法求解XYZ
	solve(A, B, XYZ, DECOMP_SVD);

	//cout<<"空间坐标为 = "<<endl<<XYZ<<endl;

	//世界坐标系中坐标
	Point3f world;
	world.x = XYZ.at<float>(0, 0);
	world.y = XYZ.at<float>(1, 0);
	world.z = XYZ.at<float>(2, 0);

	return world;
}

//************************************
// Description: 将世界坐标系中的点投影到左右相机成像坐标系中
// Method:    xyz2uv
// FullName:  xyz2uv
// Parameter: Point3f worldPoint
// Parameter: float intrinsic[3][3]
// Parameter: float translation[1][3]
// Parameter: float rotation[3][3]
// Returns:   cv::Point2f
//************************************
Point2f xyz2uv(Point3f worldPoint, float intrinsic[3][3], float translation[1][3], float rotation[3][3])
{
	//    [fx s x0]							[Xc]		[Xw]		[u]	  1		[Xc]
	//K = |0 fy y0|       TEMP = [R T]		|Yc| = TEMP*|Yw|		| | = —*K *|Yc|
	//    [ 0 0 1 ]							[Zc]		|Zw|		[v]	  Zc	[Zc]
	//													[1 ]
	Point3f c;
	c.x = rotation[0][0] * worldPoint.x + rotation[0][1] * worldPoint.y + rotation[0][2] * worldPoint.z + translation[0][0] * 1;
	c.y = rotation[1][0] * worldPoint.x + rotation[1][1] * worldPoint.y + rotation[1][2] * worldPoint.z + translation[0][1] * 1;
	c.z = rotation[2][0] * worldPoint.x + rotation[2][1] * worldPoint.y + rotation[2][2] * worldPoint.z + translation[0][2] * 1;

	Point2f uv;
	uv.x = (intrinsic[0][0] * c.x + intrinsic[0][1] * c.y + intrinsic[0][2] * c.z) / c.z;
	uv.y = (intrinsic[1][0] * c.x + intrinsic[1][1] * c.y + intrinsic[1][2] * c.z) / c.z;

	return uv;
}

3、由像素坐标获取三维坐标

	Point2f l = (638, 393);
	Point2f r = (85, 502);
	Point3f worldPoint;
	worldPoint = uv2xyz(l, r);
	cout << "空间坐标为:" << endl << uv2xyz(l, r) << endl;

更换点对测试

	Point2f l = (857, 666);
	Point2f r = (303, 775);
	//Point2f l = (1014, 445);
	//Point2f r = (523, 387);
	Point3f worldPoint;
	worldPoint = uv2xyz(l, r);
	cout << "空间坐标为:" << endl << uv2xyz(l, r) << endl;
	system("pause");

更换点对测试：

	Point2f l = (931, 449);
	Point2f r = (370, 555);
	Point3f worldPoint;
	worldPoint = uv2xyz(l, r);
	cout << "空间坐标为:" << endl << uv2xyz(l, r) << endl;
	system("pause");

线结构光传感器标定（相机标定+结构光标定）完整流程（一）
https://blog.csdn.net/qq_27353621/article/details/120787942
UR机器人手眼标定（二）
https://blog.csdn.net/qq_27353621/article/details/121603215
双目相机标定（三）
https://blog.csdn.net/qq_27353621/article/details/121031972
公众号：机器人视觉