OpenCV:扭曲回 [英] Opencv: distort back
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问题描述
我具有使图像或点向量不失真所需的cameraMatrix和distCoeff.现在我想将它们扭曲回去.
Opencv是否可以?
我记得我在stackoverflow中读到了有关它的内容，但现在找不到.
我在此 answer 中找到了解决方法.它也在opencv开发人员专区(在此问题中)
但是我的结果不正确.或多或少有2-4像素的误差.我的代码中可能有问题，因为在答案中，我链接的所有内容在单元测试中似乎都很好.也许将类型从浮点型转换为双精度型，或者我看不到的其他类型.
这是我的测试用例:
#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;
}
这是我的输出:
OpenCV version: 2 4
camera 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
在您提到的问题的答案之一中链接的initUndistortRectifyMap确实可以满足您的需求.由于在Remap中使用它来构建完整的未失真图像，因此它为目标图像中的每个位置(未失真)提供了在失真图像中找到相应像素的位置，以便他们可以使用其颜色.所以它实际上是一个f(undistorted) = distorted地图.
但是，使用此映射将仅允许输入整数位置且在图像矩形内的位置. 幸运的是，该文档提供了完整方程.
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.
Is it possible with Opencv?
I remember I read something about it in stackoverflow but cannot find now.
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 4
camera 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);
}
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