三维姿态:关于solvePnP与cvPOSIT
转载自:https://blog.csdn.net/abc20002929/article/details/8520063
之所以写:
场景:给定物体3D点集与对应的图像2D点集,之后进行姿态计算(即求旋转与位移矩阵)。
在翻阅opencv api时看到这2个函数输出都是旋转与位移,故做简单分析并记录于此。
官方解释:
solvePnP(http://docs.opencv.org/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html#solvepnp)
Finds an object pose from 3D-2D point correspondences.
bool solvePnP(InputArray objectPoints, InputArray imagePoints, InputArray cameraMatrix, InputArray distCoeffs, OutputArray rvec, OutputArray tvec,bool useExtrinsicGuess=false, int flags=ITERATIVE )
cvPOSIT(http://www.opencv.org.cn/index.php/Cv照相机定标和三维重建#POSIT)
执行POSIT算法
void cvPOSIT( CvPOSITObject* posit_object, CvPoint2D32f* image_points, double focal_length, CvTermCriteria criteria, CvMatr32f rotation_matrix, CvVect32f translation_vector );
理解:
相同点:
1.输入都是3D点集和对应的2D点集,其中cvPOSIT的3D点包含在posit_object结构中
2.输出均包括旋转矩阵和位移向量
不同点:solvePnP有摄像机的一些内参
solvePnP源码:void cv::solvePnP( InputArray _opoints, InputArray _ipoints, InputArray _cameraMatrix, InputArray _distCoeffs, OutputArray _rvec, OutputArray _tvec, bool useExtrinsicGuess ) { Mat opoints = _opoints.getMat(), ipoints = _ipoints.getMat(); int npoints = std::max(opoints.checkVector(3, CV_32F), >opoints.checkVector(3, CV_64F)); CV_Assert( npoints >= 0 && npoints == std::max(ipoints.checkVector(2, CV_32F), ipoints.checkVector(2, CV_64F)) ); _rvec.create(3, 1, CV_64F); _tvec.create(3, 1, CV_64F); Mat cameraMatrix = _cameraMatrix.getMat(), distCoeffs = _distCoeffs.getMat(); CvMat c_objectPoints = opoints, c_imagePoints = ipoints; CvMat c_cameraMatrix = cameraMatrix, c_distCoeffs = distCoeffs; CvMat c_rvec = _rvec.getMat(), c_tvec = _tvec.getMat(); cvFindExtrinsicCameraParams2(&c_objectPoints, &c_imagePoints, &c_cameraMatrix,
c_distCoeffs.rows*c_distCoeffs.cols ? &c_distCoeffs : 0,
&c_rvec, &c_tvec, useExtrinsicGuess );
}
结论:可以看到,除了前面的一堆数据类型检查和转化外,其实solvePnP调用的是cvFindExtrinsicCameraParams2通过已知的内参进行未知外参求解,是一个精确解;而cvPOSIT是用仿射投影模型近似透视投影模型下,不断迭代计算出来的估计值(在物体深度变化相对于物体到摄像机的距离比较大的时候,这种算法可能不收敛)。
3d坐标->2d坐标,毫米到像素的转换主要体现在fx、fy、cx、cy上,这些量均以像素为单位来表示实际物理长度(mm)。而单位像素有多少个毫米,受sensor面板感光颗粒(单个物理像素)尺寸影响。
solvePnP输出的rvec是旋转向量,可以通过Rodrigues转换成旋转矩阵,有需要可以再转到欧拉角:
static Vec3f rotationMatrixToEulerAngles(Mat &R)
{
float sy = sqrt(R.at<double>(0,0) * R.at<double>(0,0) + R.at<double>(1,0) * R.at<double>(1,0) );
bool singular = sy < 1e-6; // If
float x, y, z;
if (!singular)
{
x = atan2(R.at<double>(2,1) , R.at<double>(2,2));
y = atan2(-R.at<double>(2,0), sy);
z = atan2(R.at<double>(1,0), R.at<double>(0,0));
}
else
{
x = atan2(-R.at<double>(1,2), R.at<double>(1,1));
y = atan2(-R.at<double>(2,0), sy);
z = 0;
}
return Vec3f(x, y, z)*180/3.14159;
}
void test()
{
...
Mat Rv,R,T;
cv::solvePnP(objPts,imgPts,cameraMatrix,Mat(),Rv,T);
//旋转向量转旋转矩阵
Rodrigues(Rv,R);
//旋转矩阵转欧拉角
Vec3f angles = rotationMatrixToEulerAngles(R);
...
}