大多数情况是您所拥有的，只是缺少一个初步步骤.这是我的版本(它是C#，但应该相同):public PointF Distort(PointF point){ // To relative coordinates <- this is the step you are missing. double x = (point.X - cx) / fx; double y = (point.Y - cy) / fy; double r2 = x*x + y*y; // Radial distorsion double xDistort = x * (1 + k1 * r2 + k2 * r2 * r2 + k3 * r2 * r2 * r2); double yDistort = y * (1 + k1 * r2 + k2 * r2 * r2 + k3 * r2 * r2 * r2); // Tangential distorsion xDistort = xDistort + (2 * p1 * x * y + p2 * (r2 + 2 * x * x)); yDistort = yDistort + (p1 * (r2 + 2 * y * y) + 2 * p2 * x * y); // Back to absolute coordinates. xDistort = xDistort * fx + cx; yDistort = yDistort * fy + cy; return new PointF((float)xDistort, (float)yDistort);}I have the cameraMatrix and the distCoeff needed to undistort an image or a vector of points. Now I'd like to distort them back.EDIT: I found the way to do it in this answer. It is also in the opencv developer zone (in this issue)But my results are not properly correct. There is some error of 2-4 pixel more or less. Probably there is something wrong in my code because in the answer I linked everything seems good in the unit test. Maybe type casting from float to double, or something else that I cannot see.here is my test case:#include <opencv2/core/core.hpp>#include <opencv2/imgproc/imgproc.hpp>#include <iostream>using namespace cv;using namespace std;void distortPoints(const std::vector<cv::Point2d> & src, std::vector<cv::Point2d> & dst, const cv::Mat & cameraMatrix, const cv::Mat & distorsionMatrix){ dst.clear(); double fx = cameraMatrix.at<double>(0,0); double fy = cameraMatrix.at<double>(1,1); double ux = cameraMatrix.at<double>(0,2); double uy = cameraMatrix.at<double>(1,2); double k1 = distorsionMatrix.at<double>(0, 0); double k2 = distorsionMatrix.at<double>(0, 1); double p1 = distorsionMatrix.at<double>(0, 2); double p2 = distorsionMatrix.at<double>(0, 3); double k3 = distorsionMatrix.at<double>(0, 4); for (unsigned int i = 0; i < src.size(); i++) { const cv::Point2d & p = src[i]; double x = p.x; double y = p.y; double xCorrected, yCorrected; //Step 1 : correct distorsion { double r2 = x*x + y*y; //radial distorsion xCorrected = x * (1. + k1 * r2 + k2 * r2 * r2 + k3 * r2 * r2); yCorrected = y * (1. + k1 * r2 + k2 * r2 * r2 + k3 * r2 * r2); //tangential distorsion //The "Learning OpenCV" book is wrong here !!! //False equations from the "Learning OpenCv" book below : //xCorrected = xCorrected + (2. * p1 * y + p2 * (r2 + 2. * x * x)); //yCorrected = yCorrected + (p1 * (r2 + 2. * y * y) + 2. * p2 * x); //Correct formulae found at : http://www.vision.caltech.edu/bouguetj/calib_doc/htmls/parameters.html xCorrected = xCorrected + (2. * p1 * x * y + p2 * (r2 + 2. * x * x)); yCorrected = yCorrected + (p1 * (r2 + 2. * y * y) + 2. * p2 * x * y); } //Step 2 : ideal coordinates => actual coordinates { xCorrected = xCorrected * fx + ux; yCorrected = yCorrected * fy + uy; } dst.push_back(cv::Point2d(xCorrected, yCorrected)); }}int main(int /*argc*/, char** /*argv*/) { cout << "OpenCV version: " << CV_MAJOR_VERSION << " " << CV_MINOR_VERSION << endl; // 2 4 Mat cameraMatrix = (Mat_<double>(3,3) << 1600, 0, 789, 0, 1600, 650, 0, 0, 1); Mat distorsion = (Mat_<double>(5,1) << -0.48, 0, 0, 0, 0); cout << "camera matrix: " << cameraMatrix << endl; cout << "distorsion coefficent: " << distorsion << endl; // the starting points std::vector<Point2f> original_pts; original_pts.push_back( Point2f(23, 358) ); original_pts.push_back( Point2f(8, 357) ); original_pts.push_back( Point2f(12, 342) ); original_pts.push_back( Point2f(27, 343) ); original_pts.push_back( Point2f(7, 350) ); original_pts.push_back( Point2f(-8, 349) ); original_pts.push_back( Point2f(-4, 333) ); original_pts.push_back( Point2f(12, 334) ); Mat original_m = Mat(original_pts); // undistort Mat undistorted_m; undistortPoints(original_m, undistorted_m, cameraMatrix, distorsion); cout << "undistort points" << undistorted_m << endl; // back to array vector< cv::Point2d > undistorted_points; for(int i=0; i<original_pts.size(); ++i) { Point2d p; p.x = undistorted_m.at<float>(i, 0); p.y = undistorted_m.at<float>(i, 1); undistorted_points.push_back( p ); // NOTE THAT HERE THERE IS AN APPROXIMATION // WHAT IS IT? STD::COUT? CASTING TO FLOAT? cout << undistorted_points[i] << endl; } vector< cv::Point2d > redistorted_points; distortPoints(undistorted_points, redistorted_points, cameraMatrix, distorsion); cout << redistorted_points << endl; for(int i=0; i<original_pts.size(); ++i) { cout << original_pts[i] << endl; cout << redistorted_points[i] << endl; Point2d o; o.x = original_pts[i].x; o.y = original_pts[i].y; Point2d dist = redistorted_points[i] - o; double norm = sqrt(dist.dot(dist)); std::cout << "distance = " << norm << std::endl; cout << endl; } return 0;}And here is my output: OpenCV version: 2 4camera matrix: [1600, 0, 789; 0, 1600, 650; 0, 0, 1]distorsion coefficent: [-0.48; 0; 0; 0; 0]undistort points[-0.59175861, -0.22557901; -0.61276215, -0.22988389; -0.61078846, -0.24211435; -0.58972651, -0.23759322; -0.61597037, -0.23630577; -0.63910204, -0.24136727; -0.63765121, -0.25489968; -0.61291695, -0.24926868][-0.591759, -0.225579][-0.612762, -0.229884][-0.610788, -0.242114][-0.589727, -0.237593][-0.61597, -0.236306][-0.639102, -0.241367][-0.637651, -0.2549][-0.612917, -0.249269][24.45809095301274, 358.5558144841519; 10.15042938413364, 357.806737955385; 14.23419751024494, 342.8856229036298; 28.51642501095819, 343.610956960508; 9.353743900129871, 350.9029663678638; -4.488033489615646, 350.326357275197; -0.3050714463695385, 334.477016554487; 14.41516474594289, 334.9822130217053][23, 358][24.4581, 358.556]distance = 1.56044[8, 357][10.1504, 357.807]distance = 2.29677[12, 342][14.2342, 342.886]distance = 2.40332[27, 343][28.5164, 343.611]distance = 1.63487[7, 350][9.35374, 350.903]distance = 2.521[-8, 349][-4.48803, 350.326]distance = 3.75408[-4, 333][-0.305071, 334.477]distance = 3.97921[12, 334][14.4152, 334.982]distance = 2.60725 解决方案 The initUndistortRectifyMap linked in one of the answers of the question you mention does indeed what you want. Since it is used in Remap to build the full undistorted image, it gives, for each location in the destination image (undistorted), where to find the corresponding pixel in the distorted image so they can use its color. So it's really an f(undistorted) = distorted map.However, using this map will only allow for input positions that are integer and within the image rectangle.Thankfully, the documentation gives the full equations.It is mostly what you have, except that there is a preliminary step that you are missing.Here is my version (it is C# but should be the same):public PointF Distort(PointF point){ // To relative coordinates <- this is the step you are missing. double x = (point.X - cx) / fx; double y = (point.Y - cy) / fy; double r2 = x*x + y*y; // Radial distorsion double xDistort = x * (1 + k1 * r2 + k2 * r2 * r2 + k3 * r2 * r2 * r2); double yDistort = y * (1 + k1 * r2 + k2 * r2 * r2 + k3 * r2 * r2 * r2); // Tangential distorsion xDistort = xDistort + (2 * p1 * x * y + p2 * (r2 + 2 * x * x)); yDistort = yDistort + (p1 * (r2 + 2 * y * y) + 2 * p2 * x * y); // Back to absolute coordinates. xDistort = xDistort * fx + cx; yDistort = yDistort * fy + cy; return new PointF((float)xDistort, (float)yDistort);} 这篇关于OpenCV:扭曲回的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持！ 上岸，阿里云！
