C++ &引用；“手动”；在openCV中取消图像失真

EDIT：我通过查看的文档（并在下面的代码中对其进行了更改）解决了我的问题，但我不完全确定我在这里做什么。如果有人愿意解释前后转换，我将不胜感激。

我正在使用来自的摄像机校准仪。打印畸变矩阵和相机矩阵中的系数，我现在只想使用这些值来消除干扰，如文档中所述[由于声誉低而删除链接]

问题是它不起作用，但当我将“手动”创建的矩阵输入到cv:：undistort时，它就起作用了！ 我做错了什么

int main(void)
{
cv::Mat distortMat = (cv::Mat_<double>(1, 5) << -0.0688081, 0.101627, -0.000487848, -0.00172756, -0.0388046);
cv::Mat cameraMatrix = (cv::Mat_<double>(3, 3) << 893.035, 0, 623.697, 0, 895.748, 526.612, 0, 0, 1);

cv::Mat img = cv::imread("photo.jpg", 1);
cv::cvtColor(img, img, CV_BGR2GRAY);
img.convertTo(img, CV_8UC1);
cv::Mat uPhoto = img.clone();

double k1 = distortMat.at<double>(0, 0);
double k2 = distortMat.at<double>(0, 1);
double p1 = distortMat.at<double>(0, 2);
double p2 = distortMat.at<double>(0, 3);
double k3 = distortMat.at<double>(0, 4);
double  fx = cameraMatrix.at<double>(0, 0);
double  cx = cameraMatrix.at<double>(0, 2);
double  fy = cameraMatrix.at<double>(1, 1);
double  cy = cameraMatrix.at<double>(1, 2);
double z = 1.;

for (int i = 0; i < img.cols; i++)
{
    for (int j = 0; j < img.rows; j++)
    {
        /* Solved by removing this...
        double x = (double)i*fx + cx*z;
        double y = (double)j*fy + cy*z;
        double r2 = x*x + y*y;

        double dx = 2 * p1*i*j + p2*(r2 + 2 * i*i);
        double dy = p1*(r2 + 2 * j*j) + 2 * p2*i*j;
        double scale = 1. + k1*r2 + k2*r2*r2 + k3*r2*r2*r2;

        double xCorr = x*scale + dx;
        double yCorr = y*scale + dy;*/

        // ...and adding this:
        double x = (i - cx) / fx;
        double y = (j - cy) / fy;
        double r2 = x*x + y*y;

        double dx = 2 * p1*x*y + p2*(r2 + 2 * x*x);
        double dy = p1*(r2 + 2 * y*y) + 2 * p2*x*y;
        double scale = (1 + k1*r2 + k2*r2*r2 + k3*r2*r2*r2);

        double xBis = x*scale + dx;
        double yBis = y*scale + dy;

        double xCorr = xBis*fx + cx;
        double yCorr = yBis*fy + cy;

        if (xCorr >= 0 && xCorr < uPhoto.cols && yCorr >= 0 && yCorr < uPhoto.rows)
        {
            uPhoto.at<uchar>(yCorr, xCorr) = img.at<uchar>(j, i);
        }
    }
}

cv::imwrite("uPhotoManual.jpg", uPhoto);

cv::Mat uPhotoAuto;
cv::undistort(img, uPhotoAuto, cameraMatrix, distortMat);
cv::imwrite("uPhotoAuto.jpg", uPhotoAuto);

return 0;
}

int main（无效）
{
cv:：Mat扭曲Mat=（cv:：Mat_（1,5）=0&&yCorr