• OpenCV => 3.2
• 操作系统/平台 => Windows 64 位
• 编译器 => Visual Studio 2015

我目前正在从事我的项目，该项目涉及车辆检测和跟踪以及估计和优化车辆周围的长方体。为此，我已经完成了车辆的检测和跟踪，我需要找到车辆边界框边缘图像点的 3-D 世界坐标，然后估计长方体和项目边缘的世界坐标它返回图像以显示它。

所以，我是计算机视觉和 OpenCV 的新手，但据我所知，我只需要图像上的 4 个点，并且需要知道这 4 个点的世界坐标，然后在 OpenCV 中使用 solvePNP 来获取旋转和平移 vector (我已经有了相机矩阵和畸变系数)。然后，我需要使用 Rodrigues 将旋转 vector 转换为旋转矩阵，然后将其与平移 vector 连接以获得我的外部矩阵，然后将外部矩阵与相机矩阵相乘以获得我的投影矩阵。由于我的 z 坐标为零，因此我需要从投影矩阵中删除第三列，该矩阵给出用于将 2D 图像点转换为 3D 世界点的单应矩阵。现在，我找到了单应性矩阵的逆矩阵，它给出了 3D 世界点到 2D 图像点之间的单应性。之后，我将图像点 [x, y, 1]t 与逆单应矩阵相乘得到 [wX, wY, w]t 并将整个 vector 除以标量 w 得到 [X, Y, 1]给我世界坐标的 X 和 Y 值。

我的代码是这样的:

#include "opencv2/opencv.hpp"
#include <stdio.h>
#include <iostream>
#include <sstream>
#include <math.h> 
#include <conio.h>

using namespace cv;
using namespace std;

Mat cameraMatrix, distCoeffs, rotationVector, rotationMatrix, 
translationVector,extrinsicMatrix, projectionMatrix, homographyMatrix, 
inverseHomographyMatrix;


Point point;
vector<Point2d> image_points;
vector<Point3d> world_points;

int main()
{
FileStorage fs1("intrinsics.yml", FileStorage::READ);

fs1["camera_matrix"] >> cameraMatrix;
cout << "Camera Matrix: " << cameraMatrix << endl << endl;

fs1["distortion_coefficients"] >> distCoeffs;
cout << "Distortion Coefficients: " << distCoeffs << endl << endl;



image_points.push_back(Point2d(275, 204));
image_points.push_back(Point2d(331, 204));
image_points.push_back(Point2d(331, 308));
image_points.push_back(Point2d(275, 308));

cout << "Image Points: " << image_points << endl << endl;

world_points.push_back(Point3d(0.0, 0.0, 0.0));
world_points.push_back(Point3d(1.775, 0.0, 0.0));
world_points.push_back(Point3d(1.775, 4.620, 0.0));
world_points.push_back(Point3d(0.0, 4.620, 0.0));

cout << "World Points: " << world_points << endl << endl;

solvePnP(world_points, image_points, cameraMatrix, distCoeffs, rotationVector, translationVector);
cout << "Rotation Vector: " << endl << rotationVector << endl << endl;
cout << "Translation Vector: " << endl << translationVector << endl << endl;

Rodrigues(rotationVector, rotationMatrix);
cout << "Rotation Matrix: " << endl << rotationMatrix << endl << endl;

hconcat(rotationMatrix, translationVector, extrinsicMatrix);
cout << "Extrinsic Matrix: " << endl << extrinsicMatrix << endl << endl;

projectionMatrix = cameraMatrix * extrinsicMatrix;
cout << "Projection Matrix: " << endl << projectionMatrix << endl << endl;

double p11 = projectionMatrix.at<double>(0, 0),
    p12 = projectionMatrix.at<double>(0, 1),
    p14 = projectionMatrix.at<double>(0, 3),
    p21 = projectionMatrix.at<double>(1, 0),
    p22 = projectionMatrix.at<double>(1, 1),
    p24 = projectionMatrix.at<double>(1, 3),
    p31 = projectionMatrix.at<double>(2, 0),
    p32 = projectionMatrix.at<double>(2, 1),
    p34 = projectionMatrix.at<double>(2, 3);


homographyMatrix = (Mat_<double>(3, 3) << p11, p12, p14, p21, p22, p24, p31, p32, p34);
cout << "Homography Matrix: " << endl << homographyMatrix << endl << endl;

inverseHomographyMatrix = homographyMatrix.inv();
cout << "Inverse Homography Matrix: " << endl << inverseHomographyMatrix << endl << endl;

Mat point2D = (Mat_<double>(3, 1) << image_points[0].x, image_points[0].y, 1);
cout << "First Image Point" << point2D << endl << endl;

Mat point3Dw = inverseHomographyMatrix*point2D;
cout << "Point 3D-W : " << point3Dw << endl << endl;

double w = point3Dw.at<double>(2, 0);
cout << "W: " << w << endl << endl;

Mat matPoint3D;
divide(w, point3Dw, matPoint3D);

cout << "Point 3D: " << matPoint3D << endl << endl;

_getch();
return 0;

我已经获得了四个已知世界点的图像坐标并对其进行了硬编码以进行简化。 image_points 包含四个点的图像坐标，world_points 包含四个点的世界坐标。我将第一个世界点视为世界轴的原点 (0, 0, 0)，并使用已知距离计算其他四个点的坐标。现在，在计算出逆单应矩阵后，我将其与与世界坐标 (0, 0, 0) 相关的 [image_points[0].x, image_points[0].y, 1]t 相乘。然后我将结果除以第三个分量 w 得到 [X, Y, 1]。但是打印出X和Y的值后，发现它们分别不是0、0。哪里做错了？

我的代码的输出是这样的:

Camera Matrix: [517.0036881709533, 0, 320;
0, 517.0036881709533, 212;
0, 0, 1]

Distortion Coefficients: [0.1128663679798094;
-1.487790079922432;
0;
0;
2.300571896761067]

Image Points: [275, 204;
331, 204;
331, 308;
275, 308]

World Points: [0, 0, 0;
1.775, 0, 0;
1.775, 4.62, 0;
0, 4.62, 0]

Rotation Vector:
[0.661476468596541;
-0.02794460022559267;
0.01206996342819649]

Translation Vector:
[-1.394495345140898;
-0.2454153722672731;
15.47126945512652]

Rotation Matrix:
[0.9995533907649279, -0.02011656447351923, -0.02209848058392758;
 0.002297501163799448, 0.7890323093017149, -0.6143474069013439;
 0.02979497438726573, 0.6140222623910194, 0.7887261380159]

Extrinsic Matrix:
[0.9995533907649279, -0.02011656447351923, -0.02209848058392758, 
-1.394495345140898;
 0.002297501163799448, 0.7890323093017149, -0.6143474069013439, 
-0.2454153722672731;
 0.02979497438726573, 0.6140222623910194, 0.7887261380159, 
15.47126945512652]

Projection Matrix:
[526.3071813531748, 186.086785938988, 240.9673682002232, 4229.846989065414;
7.504351145361707, 538.1053336219271, -150.4099339268854, 3153.028471890794;
0.02979497438726573, 0.6140222623910194, 0.7887261380159, 15.47126945512652]

Homography Matrix:
[526.3071813531748, 186.086785938988, 4229.846989065414;
7.504351145361707, 538.1053336219271, 3153.028471890794;
0.02979497438726573, 0.6140222623910194, 15.47126945512652]

Inverse Homography Matrix:
[0.001930136511648154, -8.512427241879318e-05, -0.5103513244724983;
-6.693679705844383e-06, 0.00242178892313387, -0.4917279870709287
-3.451449134581896e-06, -9.595179260534558e-05, 0.08513443835773901]

First Image Point[275;
204;
1]

Point 3D-W : [0.003070864657310213;
0.0004761913292736786;
0.06461112415423849]

W: 0.0646111
Point 3D: [21.04004290792539;
135.683117651025;
1]

最佳答案

你的推理是合理的，但你在最后一个部分犯了一些错误..还是我遗漏了什么？

W 除法前的结果是:

Point 3D-W : 
[0.003070864657310213;
0.0004761913292736786;
0.06461112415423849]

现在我们需要通过将所有坐标除以 W(数组的第 3 个元素)来对其进行归一化，如您在问题中所述。所以:

Point 3D-W Normalized = 
[0.003070864657310213 / 0.06461112415423849;
0.0004761913292736786 / 0.06461112415423849;
0.06461112415423849 / 0.06461112415423849]

结果是:

Point 3D-W Normalized = 
[0.047528420183179314;
 0.007370113668614144;
 1.0]

这该死的接近 [0,0]。

关于c++ - 将 2D 图像坐标转换为 z = 0 的 3D 世界坐标，我们在Stack Overflow上找到一个类似的问题： https://stackoverflow.com/questions/44104633/