Opencv：手动投影点

Question

我正在尝试从 OpenCV 重现方法 projectPoints() 的行为。

在下面的两张图中，红/绿/蓝轴是用OpenCV的方法得到的，而洋红色/黄色/青色轴是用我自己的方法得到的：

图像1

图像2

使用我的方法，轴的方向似乎很好，但平移不正确。

这是我的代码：

void drawVector(float x, float y, float z, float r, float g, float b, cv::Mat &pose, cv::Mat &cameraMatrix, cv::Mat &dst) {
    //Origin = (0, 0, 0, 1)
    cv::Mat origin(4, 1, CV_64FC1, double(0));
    origin.at<double>(3, 0) = 1;

    //End = (x, y, z, 1)
    cv::Mat end(4, 1, CV_64FC1, double(1));
    end.at<double>(0, 0) = x; end.at<double>(1, 0) = y; end.at<double>(2, 0) = z;

    //multiplies transformation matrix by camera matrix
    cv::Mat mat = cameraMatrix * pose.colRange(0, 4).rowRange(0, 3);

    //projects points
    origin = mat * origin;
    end = mat * end;

    //draws corresponding line
    cv::line(dst, cv::Point(origin.at<double>(0, 0), origin.at<double>(1, 0)),
        cv::Point(end.at<double>(0, 0), end.at<double>(1, 0)),
        CV_RGB(255 * r, 255 * g, 255 * b)); 
}

void drawVector_withProjectPointsMethod(float x, float y, float z, float r, float g, float b, cv::Mat &pose, cv::Mat &cameraMatrix, cv::Mat &dst) {
    std::vector<cv::Point3f> points;
    std::vector<cv::Point2f> projectedPoints;

    //fills input array with 2 points
    points.push_back(cv::Point3f(0, 0, 0));
    points.push_back(cv::Point3f(x, y, z));

    //Gets rotation vector thanks to cv::Rodrigues() method.
    cv::Mat rvec;
    cv::Rodrigues(pose.colRange(0, 3).rowRange(0, 3), rvec);

    //projects points using cv::projectPoints method
    cv::projectPoints(points, rvec, pose.colRange(3, 4).rowRange(0, 3), cameraMatrix, std::vector<double>(), projectedPoints);

    //draws corresponding line
    cv::line(dst, projectedPoints[0], projectedPoints[1],
        CV_RGB(255 * r, 255 * g, 255 * b)); 
}

void drawAxis(cv::Mat &pose, cv::Mat &cameraMatrix, cv::Mat &dst) {
    drawVector(0.1, 0, 0, 1, 1, 0, pose, cameraMatrix, dst);
    drawVector(0, 0.1, 0, 0, 1, 1, pose, cameraMatrix, dst);
    drawVector(0, 0, 0.1, 1, 0, 1, pose, cameraMatrix, dst);

    drawVector_withProjectPointsMethod(0.1, 0, 0, 1, 0, 0, pose, cameraMatrix, dst);
    drawVector_withProjectPointsMethod(0, 0.1, 0, 0, 1, 0, pose, cameraMatrix, dst);
    drawVector_withProjectPointsMethod(0, 0, 0.1, 0, 0, 1, pose, cameraMatrix, dst);
}

我做错了什么？

Answer 1

我只是忘记将结果点除以投影后的最后一个分量：

给定用于拍摄图像的相机矩阵，对于 3d 空间中的任何点 (x, y, z, 1)，其在该图像上的投影计算如下：

//point3D has 4 component (x, y, z, w), point2D has 3 (x, y, z).
point2D = cameraMatrix * point3D;

//then we have to divide the 2 first component of point2D by the third.
point2D /= point2D.z;