如何将世界坐标转换为相机图像坐标？

Question

我正在尝试模拟虚拟相机！

我想计算 3D 点在相机图像平面中的投影。参考 this formula，我正在将 3D 世界点转换为 2D 相机坐标，就像这样。

Point2d World2CameraCoOrdinate(Point3d point3D,const  Affine3d mCameraRT,
                 const Affine3d mCameraIntrinsics,const int width,const int height) 
{
    cout <<"Input World CoOrdinates 3D: " <<point3D<<endl;  

    Affine3d viewProjectionMatrix = mCameraIntrinsics * mCameraRT;

    point3D = viewProjectionMatrix * point3D;

    Point2d ptCamCoOrdinates;

    float winX = (( point3D.x + 1 ) / 2.0) * width ;
    float winY = (( 1 - point3D.y ) / 2.0) * height ;

    ptCamCoOrdinates=Point2d(winX,winY);

    cout <<"Output Camera Co Ordinates 2D: " <<ptCamCoOrdinates<<endl;  

    return ptCamCoOrdinates;
}

但我无法正确计算它并且我正在使用 OpenCV VTK 来验证结果！

VTK 渲染图像点 2D：408,150

估计的 2D 相机点：800053，-147570

这是我的完整源代码：

#include <iostream>
#include <fstream>
#include <string>

#include <Windows.h>
#include <gl/GL.h>
#include <gl/GLU.h>

#pragma comment( lib, "opengl32.lib" )  
#pragma comment( lib, "glu32.lib" )  

#include <opencv2/opencv.hpp>
#include <opencv2/plot.hpp>
#include <opencv2/viz.hpp>

using namespace std;
using namespace cv;

bool bViewFromCamera = false;

void keyboard_callback(const viz::KeyboardEvent &event, void* cookie)
{
  if ( event.action == 0 &&!event.symbol.compare("s") )
    bViewFromCamera = !bViewFromCamera;
}

Point2d World2CameraCoOrdinate(Point3d point3D,const  Affine3d mCameraRT,
                 const Affine3d mCameraIntrinsics,const int width,const int height) 
{
    cout <<"Input World CoOrdinates 3D: " <<point3D<<endl;  

    Affine3d viewProjectionMatrix = mCameraIntrinsics * mCameraRT;

    point3D = viewProjectionMatrix * point3D;

    Point2d ptCamCoOrdinates;

    float winX = (( point3D.x + 1 ) / 2.0) * width ;
    float winY = (( 1 - point3D.y ) / 2.0) * height ;

    ptCamCoOrdinates=Point2d(winX,winY);

    cout <<"Output Camera Co Ordinates 2D: " <<ptCamCoOrdinates<<endl;  

    return ptCamCoOrdinates;
}

int _tmain(int argc, _TCHAR* argv[])
{

    const int   IMAGE_WIDTH=1176,
                IMAGE_HEIGHT=482;

    const double    fx=1239.911,            
                    fy=1239.911,            
                    cx=519.909,
                    cy=246.656;
    double camMatarray[9] = {fx, 0., cx,
                            0., fy, cy, 
                            0., 0., 1.};
    Matx33d CameraMatrix = Matx33d( fx,  0, cx,
                                     0, fy, cy,
                                     0,  0,  1);


    Point3d pt3dSignPosition_Actual(-1.0,-0.50,5.0),
            Pt3D_Camera;
    Point2d Pt2D_CameraCoOrdinate;

    /// Create 3D windows
    viz::Viz3d Window_3D("World 3D Frame");
    Window_3D.setWindowSize(Size(IMAGE_WIDTH,IMAGE_HEIGHT));
    Window_3D.setBackgroundColor(); // black by default
    Window_3D.registerKeyboardCallback(&keyboard_callback);

    Mat RotationVector=Mat::zeros(1,3,CV_64F);
    Mat TranslationVector=Mat::zeros(3,1,CV_64F);

    while(!Window_3D.wasStopped())
    {
        /// Render points as 3D cubes
        Affine3d point_pose(Mat::eye(3,3,CV_64F), pt3dSignPosition_Actual);

        viz::WCube cube_widget(Point3f(-0.125,-0.125,0.0), Point3f(0.125,0.125,-0.001), true, viz::Color::blue());
                        cube_widget.setRenderingProperty(viz::LINE_WIDTH, 2.0);
        Window_3D.showWidget("Cube"+string("1"), cube_widget, point_pose);

        // Create a sphere widget
        viz::WSphere sw(Point3d( pt3dSignPosition_Actual), 0.01f);
        // Cast sphere widget to cloud widget
        viz::WCloud cw = sw.cast<viz::WCloud>();
        /// Modify it, and it will be modified in the window.
        cw.setColor(viz::Color::red());

        // Display it in a window
        Window_3D.showWidget("SphereCloudWidget", cw);

        Affine3d cam_pose = (Mat::eye(3,3,CV_64F), Point3d(0.0,0.0,0.0));

        viz::WCameraPosition cpw(0.125); // Coordinate axes
        viz::WCameraPosition cpw_frustum(CameraMatrix, 0.3,viz::Color::yellow()); // Camera frustum


        if ( bViewFromCamera )
        {
            Window_3D.setViewerPose(cam_pose);

            //For Verifying the Screen Co Ordinates

            Mat mScreenCapture(Size(IMAGE_WIDTH,IMAGE_HEIGHT),CV_8UC3);

            //use fast 4-byte alignment (default anyway) if possible
            glPixelStorei(GL_PACK_ALIGNMENT, (mScreenCapture.step & 3) ? 1 : 4);

            //set length of one complete row in destination data (doesn't need to equal mScreenCapture.cols)
            glPixelStorei(GL_PACK_ROW_LENGTH, mScreenCapture.step/mScreenCapture.elemSize());

            glReadPixels(0, 0, mScreenCapture.cols, mScreenCapture.rows, GL_BGR_EXT, GL_UNSIGNED_BYTE, mScreenCapture.data);

            cv::flip(mScreenCapture, mScreenCapture, 0);

            Pt2D_CameraCoOrdinate = World2CameraCoOrdinate(pt3dSignPosition_Actual,cam_pose,CameraMatrix,IMAGE_WIDTH,IMAGE_HEIGHT);

            circle(mScreenCapture,Pt2D_CameraCoOrdinate,2,Scalar(0,255,0),2);

            imshow("mScreenCapture",mScreenCapture);
        }
        else
        {
            Window_3D.showWidget("CPW", cpw, cam_pose);
            Window_3D.showWidget("CPW_FRUSTUM", cpw_frustum, cam_pose);
        }

        Window_3D.spinOnce(100, true);
        Window_3D.removeAllWidgets();
    }

    Window_3D.close();
    waitKey();
    return 0;
}

Answer 1

好的，明白了！

1) VTK 相机参数未初始化properly.Only 图像大小设置正确，所有其他参数（如焦距、主点）都设置为输入图像的一些默认值！

2) 生成的相机 2D 图像坐标采用归一化设备坐标 (NDC)。即标准化为 Depth/Z 轴，如下所示！

Point2d World2CameraCoOrdinate(Point3d point3D,const  Affine3d mCameraRT,
                 const Affine3d mCameraIntrinsics,const int width,const int height) 
{
    Affine3d viewProjectionMatrix = mCameraIntrinsics* mCameraRT;

    point3D = viewProjectionMatrix * point3D;

    point3D.x/=point3D.z;
    point3D.y/=point3D.z;
    point3D.z/=point3D.z;

    Point2d ptCamCoOrdinates(point3D.x,point3D.y);

    return ptCamCoOrdinates;
}

如何将世界坐标转换为相机图像坐标？

How to Convert World Coordinates to Camera Image Coordinates?

c++

3d

camera

opencv

vtk