使用OpenCV计算2D图像点的3D世界坐标

Question

我正在开发iOS应用程序。我根据《掌握OpenCV》一书使用相机矩阵。在我的场景中，我有一个已知的盒子。我知道它的真实尺寸，也知道它的角落像素的确切位置。使用这些信息，我计算出相机的旋转和平移向量。通过这些参数，我能够计算出相机的位置。我通过将3D世界坐标投影回图像来检查我的计算，并获得非常准确的结果。

在我的情况下，世界原点是盒子底线的中间部分。盒子从一侧打开。照片是沿着那个方向拍摄的，所以我可以看到盒子里面的内容。

现在，我有一个物体在盒子里面。我非常清楚地知道这个物体角落的图像坐标（2D）。我知道角落的真实高度（真正的Y，而且Y不等于0）。如何计算物体角落的世界X和Z坐标？

以下是我的代码：

#include "opencv2/core/core.hpp"
#include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/calib3d/calib3d.hpp"
#include "opencv2/highgui/highgui.hpp"

#include <iostream>
#include <ctype.h>

using namespace cv;
using namespace std;


Point2f point;
vector<vector<Point2f>> objectPoints(1);
vector<vector<Point2f>> boxPoints(1);

Point3f calc3DPointOutOf2DwithYknown(double u, double v, float worldY, double fx, double fy, double cx, double cy, Mat tvec, Mat rotMat)
{
    Point3f tmpPoint;

    // This fiunction I need to complete
    return tmpPoint;
}

int main( int argc, char** argv )
{

    ///////// Loading image
    Mat sourceImage = imread("/Users/Ilan/Xcode/LK Test/LK Test/images/box_center640X480.jpg");

    namedWindow( "Source", 1 );

    ///// Setting box corners /////
    point = Point2f((float)102,(float)367.5);  //640X480
    boxPoints[0].push_back(point);
    circle( sourceImage, boxPoints[0][0], 3, Scalar(0,255,0), -1, 8);

    point = Point2f((float)83,(float)90.5);  //640X480
    boxPoints[0].push_back(point);
    circle( sourceImage, boxPoints[0][1], 3, Scalar(0,255,0), -1, 8);

    point = Point2f((float)520,(float)82.5);  //640X480
    boxPoints[0].push_back(point);
    circle( sourceImage, boxPoints[0][2], 3, Scalar(0,255,0), -1, 8);

    point = Point2f((float)510.5,(float)361);  //640X480
    boxPoints[0].push_back(point);
    circle( sourceImage, boxPoints[0][3], 3, Scalar(0,255,0), -1, 8);

    ///// Setting object corners /////
    point = Point2f((float)403.5,(float)250);  //640X480
    objectPoints[0].push_back(point);
    circle( sourceImage, objectPoints[0][0], 3, Scalar(0,255,0), -1, 8);

    point = Point2f((float)426.5,(float)251.5);  //640X480
    objectPoints[0].push_back(point);
    circle( sourceImage, objectPoints[0][1], 3, Scalar(0,255,0), -1, 8);

    imshow("Source", sourceImage);

    vector<vector<Point3f>> worldBoxPoints(1);
    Point3f tmpPoint;

    tmpPoint = Point3f((float)-100,(float)0,(float)0);
    worldBoxPoints[0].push_back(tmpPoint);
    tmpPoint = Point3f((float)-100,(float)-150,(float)0);
    worldBoxPoints[0].push_back(tmpPoint);
    tmpPoint = Point3f((float)100,(float)-150,(float)0);
    worldBoxPoints[0].push_back(tmpPoint);
    tmpPoint = Point3f((float)100,(float)0,(float)0);
    worldBoxPoints[0].push_back(tmpPoint);

    std::cout << "There are " << boxPoints[0].size() << " roomPoints and " << worldBoxPoints[0].size() << " worldRoomPoints." << std::endl;

    cv::Mat cameraMatrix1(3,3,cv::DataType<double>::type);
    cv::setIdentity(cameraMatrix1);

    cv::Mat distCoeffs1(4,1,cv::DataType<double>::type);
    distCoeffs1.at<double>(0) = 0;
    distCoeffs1.at<double>(1) = 0;
    distCoeffs1.at<double>(2) = 0;
    distCoeffs1.at<double>(3) = 0;


    //Taken from Mastring OpenCV
    double fx = 6.24860291e+02 * ((float)(sourceImage.cols)/352.);
    double fy = 6.24860291e+02 * ((float)(sourceImage.rows)/288.);
    double cx = (float)(sourceImage.cols)/2.;
    double cy = (float)(sourceImage.rows)/2.;

    cameraMatrix1.at<double>(0, 0) = fx;
    cameraMatrix1.at<double>(1, 1) = fy;
    cameraMatrix1.at<double>(0, 2) = cx;
    cameraMatrix1.at<double>(1, 2) = cy;

    std::cout << "After calib cameraMatrix --- 1: " << cameraMatrix1 << std::endl;
    std::cout << "After calib distCoeffs: --- 1" << distCoeffs1 << std::endl;

    cv::Mat rvec1(3,1,cv::DataType<double>::type);
    cv::Mat tvec1(3,1,cv::DataType<double>::type);

    cv::solvePnP(worldBoxPoints[0], boxPoints[0], cameraMatrix1, distCoeffs1, rvec1, tvec1);

    std::cout << "rvec --- 1: " << rvec1 << std::endl;
    std::cout << "tvec --- 1: " << tvec1 << std::endl;

    cv::Mat rvecM1(3,3,cv::DataType<double>::type);
    cv::Rodrigues(rvec1,rvecM1);

    std::cout << "cameraRotation --- 1 : " << rvecM1 << std::endl;
    std::cout << "cameraPosition --- 1 : " << (rvecM1.t())*((-1.0)*tvec1) << std::endl;

    std::vector<cv::Point2f> projectedPoints1;
    cv::projectPoints(worldBoxPoints[0], rvec1, tvec1, cameraMatrix1, distCoeffs1, projectedPoints1);

    for(unsigned int i = 0; i < projectedPoints1.size(); ++i)
    {
        std::cout << "box point --- 1: " << boxPoints[0][i] << " Projected to --- 1: " << projectedPoints1[i] << std::endl;
    }

    vector<vector<Point3f>> worldObjectPoints(1);

    tmpPoint = calc3DPointOutOf2DwithYknown(objectPoints[0][0].x, objectPoints[0][0].y, /*the real Y of the object*/ -40.0, fx, fy, cx, cy, tvec1, rvecM1);
    worldObjectPoints[0].push_back(tmpPoint);

    tmpPoint = calc3DPointOutOf2DwithYknown(objectPoints[0][1].x, objectPoints[0][1].y, /*the real Y of the object*/ -40.0, fx, fy, cx, cy, tvec1, rvecM1);
    worldObjectPoints[0].push_back(tmpPoint);

    cv::projectPoints(worldObjectPoints[0], rvec1, tvec1, cameraMatrix1, distCoeffs1, projectedPoints1);
    for(unsigned int i = 0; i < projectedPoints1.size(); ++i)
    {
        std::cout << "object point --- 1: " << objectPoints[0][i] << " Projected to --- 1: " << projectedPoints1[i] << std::endl;
    }

    waitKey(0);

    return 0;
}

所以，我想实现calc3DPointOutOf2DwithYknown函数。当然，根据我的理解，参数已经设置好了。如果我需要其他参数，我会使用其他方法。

非常感谢你， Ilan

- user2743760

Answer 1

我成功地自己解决了这个问题。如果有人需要帮助，这是代码：

Point3f calc3DPointOutOf2DwithYknown(double u, double v, float worldY, double fx, double fy, double cx, double cy, Mat tvec, Mat rotMat)
{
    Point3f tmpPoint;

    float r1 = rotMat.at<double>(0,0);
    float r2 = rotMat.at<double>(0,1);
    float r3 = rotMat.at<double>(0,2);

    float r4 = rotMat.at<double>(1,0);
    float r5 = rotMat.at<double>(1,1);
    float r6 = rotMat.at<double>(1,2);

    float r7 = rotMat.at<double>(2,0);
    float r8 = rotMat.at<double>(2,1);
    float r9 = rotMat.at<double>(2,2);

    float t1 = tvec.at<double>(0,0);
    float t2 = tvec.at<double>(1,0);
    float t3 = tvec.at<double>(2,0);

    float xt = (u/fx) - (cx/fx);
    float yt = (v/fy) - (cy/fy);

    float K1 = xt*r8*worldY + xt*t3 - r2*worldY - t1;
    float K2 = xt*r9 - r3;
    float K3 = r1 - xt*r7;


    float worldZ = (yt*r7*K1 + yt*K3*r8*worldY + yt*K3*t3 - r4*K1 - K3*r5*worldY - K3*t2)/
                    (r4*K2 + K3*r6 - yt*r7*K2 - yt*K3*r9);

    float worldX = (K1 + worldZ*K2)/K3;


    tmpPoint = Point3f(worldX, worldY, worldZ);

    return tmpPoint;
}

- user2743760