Given a set of 2D points, how can I apply the opposite of undistortPoints?
I have the camera intrinsics and distCoeffs and would like to (for example) create a square, and distort it as if the camera had viewed it through the lens.
I have found a 'distort' patch here : http://code.opencv.org/issues/1387 but it would seem this is only good for images, I want to work on sparse points.
This question is rather old but since I ended up here from a google search without seeing a neat answer I decided to answer it anyway.
There is a function called projectPoints that does exactly this. The C version is used internally by OpenCV when estimating camera parameters with functions like calibrateCamera and stereoCalibrate
EDIT:
To use 2D points as input, we can set all z-coordinates to 1 with convertPointsToHomogeneous and use projectPoints with no rotation and no translation.
cv::Mat points2d = ...;
cv::Mat points3d;
cv::Mat distorted_points2d;
convertPointsToHomogeneous(points2d, points3d);
projectPoints(points3d, cv::Vec3f(0,0,0), cv::Vec3f(0,0,0), camera_matrix, dist_coeffs, distorted_points2d);
A simple solution is to use initUndistortRectifyMap to obtain a map from undistorted coordinates to distorted ones:
cv::Mat K = ...; // 3x3 intrinsic parameters
cv::Mat D = ...; // 4x1 or similar distortion parameters
int W = 640; // image width
int H = 480; // image height
cv::Mat mapx, mapy;
cv::initUndistortRectifyMap(K, D, cv::Mat(), K, cv::Size(W, H),
CV_32F, mapx, mapy);
float distorted_x = mapx.at<float>(y, x);
float distorted_y = mapy.at<float>(y, x);
I edit to clarify the code is correct:
I cite the documentation of initUndistortRectifyMap:
for each pixel (u, v) in the destination (corrected and rectified) image, the function computes the corresponding coordinates in the source image (that is, in the original image from camera.
map_x(u,v) = x''f_x + c_x
map_y(u,v) = y''f_y + c_y
initUndistortRectifyMap function is usually used together with remap to undistort full images. According to the documentation of remap, the code should be right (I also use it like this). –
Principate I have had exactly the same need. Here is a possible solution :
void MyDistortPoints(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);
//BOOST_FOREACH(const cv::Point2d &p, src)
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 * r2);
yCorrected = y * (1. + k1 * r2 + k2 * r2 * r2 + k3 * r2 * r2 * r2);
//tangential distorsion
//The "Learning OpenCV" book is wrong here !!!
//False equations from the "Learning OpenCv" book
//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));
}
}
void MyDistortPoints(const std::vector<cv::Point2d> & src, std::vector<cv::Point2d> & dst,
const cv::Matx33d & cameraMatrix, const cv::Matx<double, 1, 5> & distorsionMatrix)
{
cv::Mat cameraMatrix2(cameraMatrix);
cv::Mat distorsionMatrix2(distorsionMatrix);
return MyDistortPoints(src, dst, cameraMatrix2, distorsionMatrix2);
}
void TestDistort()
{
cv::Matx33d cameraMatrix = 0.;
{
//cameraMatrix Init
double fx = 1000., fy = 950.;
double ux = 324., uy = 249.;
cameraMatrix(0, 0) = fx;
cameraMatrix(1, 1) = fy;
cameraMatrix(0, 2) = ux;
cameraMatrix(1, 2) = uy;
cameraMatrix(2, 2) = 1.;
}
cv::Matx<double, 1, 5> distorsionMatrix;
{
//distorsion Init
const double k1 = 0.5, k2 = -0.5, k3 = 0.000005, p1 = 0.07, p2 = -0.05;
distorsionMatrix(0, 0) = k1;
distorsionMatrix(0, 1) = k2;
distorsionMatrix(0, 2) = p1;
distorsionMatrix(0, 3) = p2;
distorsionMatrix(0, 4) = k3;
}
std::vector<cv::Point2d> distortedPoints;
std::vector<cv::Point2d> undistortedPoints;
std::vector<cv::Point2d> redistortedPoints;
distortedPoints.push_back(cv::Point2d(324., 249.));// equals to optical center
distortedPoints.push_back(cv::Point2d(340., 200));
distortedPoints.push_back(cv::Point2d(785., 345.));
distortedPoints.push_back(cv::Point2d(0., 0.));
cv::undistortPoints(distortedPoints, undistortedPoints, cameraMatrix, distorsionMatrix);
MyDistortPoints(undistortedPoints, redistortedPoints, cameraMatrix, distorsionMatrix);
cv::undistortPoints(redistortedPoints, undistortedPoints, cameraMatrix, distorsionMatrix);
//Poor man's unit test ensuring we have an accuracy that is better than 0.001 pixel
for (unsigned int i = 0; i < undistortedPoints.size(); i++)
{
cv::Point2d dist = redistortedPoints[i] - distortedPoints[i];
double norm = sqrt(dist.dot(dist));
std::cout << "norm = " << norm << std::endl;
assert(norm < 1E-3);
}
}
undistortPoint is a simple reverse version of project points
In my case I would like to do the following:
int undisortPoints(const vector<cv::Point2f> &uv, vector<cv::Point2f> &xy, const cv::Mat &M, const cv::Mat &d)
{
cv::undistortPoints(uv, xy, M, d, cv::Mat(), M);
return 0;
}
This will undistort the points to the very similar coordinate to the origin of the image, but without distortion. This is the default behavior for the cv::undistort() function.
int distortPoints(const vector<cv::Point2f> &xy, vector<cv::Point2f> &uv, const cv::Mat &M, const cv::Mat &d)
{
vector<cv::Point2f> xy2;
vector<cv::Point3f> xyz;
cv::undistortPoints(xy, xy2, M, cv::Mat());
for (cv::Point2f p : xy2)xyz.push_back(cv::Point3f(p.x, p.y, 1));
cv::Mat rvec = cv::Mat::zeros(3, 1, CV_64FC1);
cv::Mat tvec = cv::Mat::zeros(3, 1, CV_64FC1);
cv::projectPoints(xyz, rvec, tvec, M, d, uv);
return 0;
}
The little tricky thing here is to first project the points to the z=1 plane with a linear camera model. After that, you must project them with the original camera model.
I found these useful, I hope it also works for you.
undistortPoints used in the distortPoints function? –
Triboluminescent This question and it's related questions on SO have been around for nearly a decade, but there still isn't an answer that satisfies the criteria below so I'm proposing a new answer that
It is important to distinquish between ideal coordinates (also called 'normalized' or 'sensor' coordinates) which are the input variables to the distortion model or 'x' and 'y' in the OpenCV docs vs. observed coordinates (also called 'image' coordinates) or 'u' and 'v' in OpenCV docs. Ideal coordinates have been normalized by the intrinsic parameters so that they have been scaled by the focal length and are relative to the image centroid at (cx,cy). This is important to point out because the undistortPoints() method can return either ideal or observed coordinates depending on the input arguments.
undistortPoints() can essentially do any combination of two things: remove distortions and apply a rotational transformation with the output either being in ideal or observed coordinates, depending on if a projection mat (InputArray P) is provided in the input. The input coordinates (InputArray src) for undistortPoints() is always in observed or image coordinates.
At a high level undistortPoints() converts the input coordinates from observed to ideal coordinates and uses an iterative process to remove distortions from the ideal or normalized points. The reason the process is iterative is because the OpenCV distortion model is not easy to invert analytically.
In the example below, we use undistortPoints() twice. First, we apply a reverse rotational transformation to undo image rectification. This step can be skipped if you are not working with rectified images. The output of this first step is in observed coordinates so we use undistortPoints() again to convert these to ideal coordinates. The conversion to ideal coordinates makes setting up the input for projectPoints() easier (which we use to apply the distortions). With the ideal coordinates, we can simply convert them to homogeneous by appending a 1 to each point. This is equivalent to projecting the points to a plane in 3D world coordinates with a linear camera model.
As of currently, there isn't a method in OpenCV to apply distortions to a set of ideal coordinates (with the exception of fisheye distortions using distort()) so we employ the projectPoints() method which can apply distortions as well as transformations as part of its projection algorithm. The tricky part about using projectPoints() is that the input is in terms of world or model coordinates in 3D, which is why we homogenized the output of the second use of undistortPoints(). By using projectPoints() with a dummy, zero-valued rotation vector (InputArray rvec) and translation vector (Input Array tvec) the result is simply a distorted set of coordinates which is conveniently output in observed or image coordinates.
Some helpful links
Before providing the solution to recovering the original image coordinates with distortions we provide a short snippet to convert from the original distorted image coordinates to the corresponding rectified, undistorted coordinates that can be used for testing the reverse solution below.
The rotation matrix R1 and the projection matrix P1 come from stereoRectify(). The intrinsic parameters M1 and distortion parameters D1 come from stereoCalibrate().
const size_t img_w = 2448;
const size_t img_h = 2048;
const size_t num_rand_pts = 100;
// observed coordinates of the points in the original
// distorted image (used as a benchmark for testing)
std::vector<cv::Point2f> benchmark_obs_dist_points;
// undistorted and rectified obnserved coordinates
std::vector<cv::Point2f> obs_rect_undist_points;
// initialize with uniform random numbers
cv::RNG rng( 0xFFFFFFFF );
for(size_t i =0;i<num_rand_pts;++i)
benchmark_obs_dist_points.push_back(
cv::Point2f(rng.uniform(0.0,(double)img_w),
rng.uniform(0.0,(double)img_h))
);
// undistort and rectify
cv::undistortPoints(benchmark_obs_dist_points,obs_rect_undist_points,
M1,D1,R1,P1);
We will need three mats to reverse the rectification: the inverse of the rectification rotation matrix from stereoRectify R1, and two others to 'swap' the P1 and M1 projections that happen in undistortPoints(). P1_prime is the rotation matrix sub-portion of the projection matrix and M1_prime converts the rectification rotation matrix into a projection matrix with no translation. Note this only works if the output of stereoRectify has no translation, i.e. the last column of P1 is zeros which can be easily verified.
assert(cv::norm(P1(cv::Rect(3,0,1,3))==0.0));
// create a 3x3 shallow copy of the rotation matrix portion of the projection P1
cv::Mat P1_prime = P1(cv::Rect(0,0,3,3));
// create a 3x4 projection matrix with the rotation portion of
// the rectification rotation matrix R1
cv::Mat M1_prime = cv::Mat::zeros(3,4,CV_64F);
M1.copyTo(M1_prime(cv::Rect(0,0,3,3)));
With these mats, the reversal can proceed as follows
// reverse the image rectification transformation
// (result will still be undistorted)
std::vector<cv::Point2f> obs_undist_points;
cv::undistortPoints(obs_rect_undist_points,obs_undist_points,
P1_prime,cv::Mat(),R1.inv(),M1_prime);
// convert the image coordinates into sensor or normalized or ideal coordinates
// (again, still undistorted)
std::vector<cv::Point2f> ideal_undist_points;
cv::undistortPoints(obs_undist_points,ideal_undist_points,M1,cv::Mat());
// artificially project the ideal 2d points to a plane in world coordinates
// using a linear camera model (z=1)
std::vector<cv::Point3f> world_undist_points;
for (cv::Point2f pt : ideal_undist_points)
world_undist_points.push_back(cv::Point3f(pt.x,pt.y,1));
// add the distortions back in to get the original coordinates
cv::Mat rvec = cv::Mat::zeros(3,1,CV_64FC1); // dummy zero rotation vec
cv::Mat tvec = cv::Mat::zeros(3,1,CV_64FC1); // dummy zero translation vec
std::vector<cv::Point2f> obs_dist_points;
cv::projectPoints(world_undist_points,rvec,tvec,M1,D1,obs_dist_points);
To test the results, we can compare them to the benchmark values
for(size_t i=0;i<num_rand_pts;++i)
std::cout << "benchmark_x: " << benchmark_obs_dist_points[i].x
<< " benchmark_y: " << benchmark_obs_dist_points[i].y
<< " computed_x: " << obs_dist_points[i].x
<< " computed_y: " << obs_dist_points[i].y
<< " diff_x: "
<< std::abs(benchmark_obs_dist_points[i].x-obs_dist_points[i].x)
<< " diff_y: "
<< std::abs(benchmark_obs_dist_points[i].y-obs_dist_points[i].y)
<< std::endl;
This is main.cpp. It is self-sufficient and does not need anything else but opencv. I don't remember where I found this, it works, I used it in my project. The program eats the set of standard chessboard images and generates json/xml files with all the distortions of the camera.
#include <iostream>
#include <sstream>
#include <time.h>
#include <stdio.h>
#include <opencv2/core/core.hpp>
#include <opencv2/imgproc/imgproc.hpp>
#include <opencv2/calib3d/calib3d.hpp>
#include <opencv2/highgui/highgui.hpp>
#ifndef _CRT_SECURE_NO_WARNINGS
# define _CRT_SECURE_NO_WARNINGS
#endif
using namespace cv;
using namespace std;
static void help()
{
cout << "This is a camera calibration sample." << endl
<< "Usage: calibration configurationFile" << endl
<< "Near the sample file you'll find the configuration file, which has detailed help of "
"how to edit it. It may be any OpenCV supported file format XML/YAML." << endl;
}
class Settings
{
public:
Settings() : goodInput(false) {}
enum Pattern { NOT_EXISTING, CHESSBOARD, CIRCLES_GRID, ASYMMETRIC_CIRCLES_GRID };
enum InputType {INVALID, CAMERA, VIDEO_FILE, IMAGE_LIST};
void write(FileStorage& fs) const //Write serialization for this class
{
fs << "{" << "BoardSize_Width" << boardSize.width
<< "BoardSize_Height" << boardSize.height
<< "Square_Size" << squareSize
<< "Calibrate_Pattern" << patternToUse
<< "Calibrate_NrOfFrameToUse" << nrFrames
<< "Calibrate_FixAspectRatio" << aspectRatio
<< "Calibrate_AssumeZeroTangentialDistortion" << calibZeroTangentDist
<< "Calibrate_FixPrincipalPointAtTheCenter" << calibFixPrincipalPoint
<< "Write_DetectedFeaturePoints" << bwritePoints
<< "Write_extrinsicParameters" << bwriteExtrinsics
<< "Write_outputFileName" << outputFileName
<< "Show_UndistortedImage" << showUndistorsed
<< "Input_FlipAroundHorizontalAxis" << flipVertical
<< "Input_Delay" << delay
<< "Input" << input
<< "}";
}
void read(const FileNode& node) //Read serialization for this class
{
node["BoardSize_Width" ] >> boardSize.width;
node["BoardSize_Height"] >> boardSize.height;
node["Calibrate_Pattern"] >> patternToUse;
node["Square_Size"] >> squareSize;
node["Calibrate_NrOfFrameToUse"] >> nrFrames;
node["Calibrate_FixAspectRatio"] >> aspectRatio;
node["Write_DetectedFeaturePoints"] >> bwritePoints;
node["Write_extrinsicParameters"] >> bwriteExtrinsics;
node["Write_outputFileName"] >> outputFileName;
node["Calibrate_AssumeZeroTangentialDistortion"] >> calibZeroTangentDist;
node["Calibrate_FixPrincipalPointAtTheCenter"] >> calibFixPrincipalPoint;
node["Input_FlipAroundHorizontalAxis"] >> flipVertical;
node["Show_UndistortedImage"] >> showUndistorsed;
node["Input"] >> input;
node["Input_Delay"] >> delay;
interprate();
}
void interprate()
{
goodInput = true;
if (boardSize.width <= 0 || boardSize.height <= 0)
{
cerr << "Invalid Board size: " << boardSize.width << " " << boardSize.height << endl;
goodInput = false;
}
if (squareSize <= 10e-6)
{
cerr << "Invalid square size " << squareSize << endl;
goodInput = false;
}
if (nrFrames <= 0)
{
cerr << "Invalid number of frames " << nrFrames << endl;
goodInput = false;
}
if (input.empty()) // Check for valid input
inputType = INVALID;
else
{
if (input[0] >= '0' && input[0] <= '9')
{
stringstream ss(input);
ss >> cameraID;
inputType = CAMERA;
}
else
{
if (readStringList(input, imageList))
{
inputType = IMAGE_LIST;
nrFrames = (nrFrames < (int)imageList.size()) ? nrFrames : (int)imageList.size();
}
else
inputType = VIDEO_FILE;
}
if (inputType == CAMERA)
inputCapture.open(cameraID);
if (inputType == VIDEO_FILE)
inputCapture.open(input);
if (inputType != IMAGE_LIST && !inputCapture.isOpened())
inputType = INVALID;
}
if (inputType == INVALID)
{
cerr << " Inexistent input: " << input << endl;
goodInput = false;
}
flag = 0;
if(calibFixPrincipalPoint) flag |= CV_CALIB_FIX_PRINCIPAL_POINT;
if(calibZeroTangentDist) flag |= CV_CALIB_ZERO_TANGENT_DIST;
if(aspectRatio) flag |= CV_CALIB_FIX_ASPECT_RATIO;
calibrationPattern = NOT_EXISTING;
if (!patternToUse.compare("CHESSBOARD")) calibrationPattern = CHESSBOARD;
if (!patternToUse.compare("CIRCLES_GRID")) calibrationPattern = CIRCLES_GRID;
if (!patternToUse.compare("ASYMMETRIC_CIRCLES_GRID")) calibrationPattern = ASYMMETRIC_CIRCLES_GRID;
if (calibrationPattern == NOT_EXISTING)
{
cerr << " Inexistent camera calibration mode: " << patternToUse << endl;
goodInput = false;
}
atImageList = 0;
}
Mat nextImage()
{
Mat result;
if( inputCapture.isOpened() )
{
Mat view0;
inputCapture >> view0;
view0.copyTo(result);
}
else if( atImageList < (int)imageList.size() )
result = imread(imageList[atImageList++], CV_LOAD_IMAGE_COLOR);
return result;
}
static bool readStringList( const string& filename, vector<string>& l )
{
l.clear();
FileStorage fs(filename, FileStorage::READ);
if( !fs.isOpened() )
return false;
FileNode n = fs.getFirstTopLevelNode();
if( n.type() != FileNode::SEQ )
return false;
FileNodeIterator it = n.begin(), it_end = n.end();
for( ; it != it_end; ++it )
l.push_back((string)*it);
return true;
}
public:
Size boardSize; // The size of the board -> Number of items by width and height
Pattern calibrationPattern;// One of the Chessboard, circles, or asymmetric circle pattern
float squareSize; // The size of a square in your defined unit (point, millimeter,etc).
int nrFrames; // The number of frames to use from the input for calibration
float aspectRatio; // The aspect ratio
int delay; // In case of a video input
bool bwritePoints; // Write detected feature points
bool bwriteExtrinsics; // Write extrinsic parameters
bool calibZeroTangentDist; // Assume zero tangential distortion
bool calibFixPrincipalPoint;// Fix the principal point at the center
bool flipVertical; // Flip the captured images around the horizontal axis
string outputFileName; // The name of the file where to write
bool showUndistorsed; // Show undistorted images after calibration
string input; // The input ->
int cameraID;
vector<string> imageList;
int atImageList;
VideoCapture inputCapture;
InputType inputType;
bool goodInput;
int flag;
private:
string patternToUse;
};
static void read(const FileNode& node, Settings& x, const Settings& default_value = Settings())
{
if(node.empty())
x = default_value;
else
x.read(node);
}
enum { DETECTION = 0, CAPTURING = 1, CALIBRATED = 2 };
bool runCalibrationAndSave(Settings& s, Size imageSize, Mat& cameraMatrix, Mat& distCoeffs,
vector<vector<Point2f> > imagePoints );
int main(int argc, char* argv[])
{
// help();
Settings s;
const string inputSettingsFile = argc > 1 ? argv[1] : "default.xml";
FileStorage fs(inputSettingsFile, FileStorage::READ); // Read the settings
if (!fs.isOpened())
{
cout << "Could not open the configuration file: \"" << inputSettingsFile << "\"" << endl;
return -1;
}
fs["Settings"] >> s;
fs.release(); // close Settings file
if (!s.goodInput)
{
cout << "Invalid input detected. Application stopping. " << endl;
return -1;
}
vector<vector<Point2f> > imagePoints;
Mat cameraMatrix, distCoeffs;
Size imageSize;
int mode = s.inputType == Settings::IMAGE_LIST ? CAPTURING : DETECTION;
clock_t prevTimestamp = 0;
const Scalar RED(0,0,255), GREEN(0,255,0);
const char ESC_KEY = 27;
for(int i = 0;;++i)
{
Mat view;
bool blinkOutput = false;
view = s.nextImage();
//----- If no more image, or got enough, then stop calibration and show result -------------
if( mode == CAPTURING && imagePoints.size() >= (unsigned)s.nrFrames )
{
if( runCalibrationAndSave(s, imageSize, cameraMatrix, distCoeffs, imagePoints))
mode = CALIBRATED;
else
mode = DETECTION;
}
if(view.empty()) // If no more images then run calibration, save and stop loop.
{
if( imagePoints.size() > 0 )
runCalibrationAndSave(s, imageSize, cameraMatrix, distCoeffs, imagePoints);
break;
}
imageSize = view.size(); // Format input image.
if( s.flipVertical ) flip( view, view, 0 );
vector<Point2f> pointBuf;
bool found;
switch( s.calibrationPattern ) // Find feature points on the input format
{
case Settings::CHESSBOARD:
found = findChessboardCorners( view, s.boardSize, pointBuf,
CV_CALIB_CB_ADAPTIVE_THRESH | CV_CALIB_CB_FAST_CHECK | CV_CALIB_CB_NORMALIZE_IMAGE);
break;
case Settings::CIRCLES_GRID:
found = findCirclesGrid( view, s.boardSize, pointBuf );
break;
case Settings::ASYMMETRIC_CIRCLES_GRID:
found = findCirclesGrid( view, s.boardSize, pointBuf, CALIB_CB_ASYMMETRIC_GRID );
break;
default:
found = false;
break;
}
if ( found) // If done with success,
{
// improve the found corners' coordinate accuracy for chessboard
if( s.calibrationPattern == Settings::CHESSBOARD)
{
Mat viewGray;
cvtColor(view, viewGray, COLOR_BGR2GRAY);
cornerSubPix( viewGray, pointBuf, Size(11,11),
Size(-1,-1), TermCriteria( CV_TERMCRIT_EPS+CV_TERMCRIT_ITER, 30, 0.1 ));
}
if( mode == CAPTURING && // For camera only take new samples after delay time
(!s.inputCapture.isOpened() || clock() - prevTimestamp > s.delay*1e-3*CLOCKS_PER_SEC) )
{
imagePoints.push_back(pointBuf);
prevTimestamp = clock();
blinkOutput = s.inputCapture.isOpened();
}
// Draw the corners.
drawChessboardCorners( view, s.boardSize, Mat(pointBuf), found );
}
//----------------------------- Output Text ------------------------------------------------
string msg = (mode == CAPTURING) ? "100/100" :
mode == CALIBRATED ? "Calibrated" : "Press 'g' to start";
int baseLine = 0;
Size textSize = getTextSize(msg, 1, 1, 1, &baseLine);
Point textOrigin(view.cols - 2*textSize.width - 10, view.rows - 2*baseLine - 10);
if( mode == CAPTURING )
{
if(s.showUndistorsed)
msg = format( "%d/%d Undist", (int)imagePoints.size(), s.nrFrames );
else
msg = format( "%d/%d", (int)imagePoints.size(), s.nrFrames );
}
putText( view, msg, textOrigin, 1, 1, mode == CALIBRATED ? GREEN : RED);
if( blinkOutput )
bitwise_not(view, view);
//------------------------- Video capture output undistorted ------------------------------
if( mode == CALIBRATED && s.showUndistorsed )
{
Mat temp = view.clone();
undistort(temp, view, cameraMatrix, distCoeffs);
}
//------------------------------ Show image and check for input commands -------------------
imshow("Image View", view);
char key = (char)waitKey(s.inputCapture.isOpened() ? 50 : s.delay);
if( key == ESC_KEY )
break;
if( key == 'u' && mode == CALIBRATED )
s.showUndistorsed = !s.showUndistorsed;
if( s.inputCapture.isOpened() && key == 'g' )
{
mode = CAPTURING;
imagePoints.clear();
}
}
// -----------------------Show the undistorted image for the image list ------------------------
if( s.inputType == Settings::IMAGE_LIST && s.showUndistorsed )
{
Mat view, rview, map1, map2;
initUndistortRectifyMap(cameraMatrix, distCoeffs, Mat(),
getOptimalNewCameraMatrix(cameraMatrix, distCoeffs, imageSize, 1, imageSize, 0),
imageSize, CV_16SC2, map1, map2);
for(int i = 0; i < (int)s.imageList.size(); i++ )
{
view = imread(s.imageList[i], 1);
if(view.empty())
continue;
remap(view, rview, map1, map2, INTER_LINEAR);
imshow("Image View", rview);
char c = (char)waitKey();
if( c == ESC_KEY || c == 'q' || c == 'Q' )
break;
}
}
return 0;
}
static double computeReprojectionErrors( const vector<vector<Point3f> >& objectPoints,
const vector<vector<Point2f> >& imagePoints,
const vector<Mat>& rvecs, const vector<Mat>& tvecs,
const Mat& cameraMatrix , const Mat& distCoeffs,
vector<float>& perViewErrors)
{
vector<Point2f> imagePoints2;
int i, totalPoints = 0;
double totalErr = 0, err;
perViewErrors.resize(objectPoints.size());
for( i = 0; i < (int)objectPoints.size(); ++i )
{
projectPoints( Mat(objectPoints[i]), rvecs[i], tvecs[i], cameraMatrix,
distCoeffs, imagePoints2);
err = norm(Mat(imagePoints[i]), Mat(imagePoints2), CV_L2);
int n = (int)objectPoints[i].size();
perViewErrors[i] = (float) std::sqrt(err*err/n);
totalErr += err*err;
totalPoints += n;
}
return std::sqrt(totalErr/totalPoints);
}
static void calcBoardCornerPositions(Size boardSize, float squareSize, vector<Point3f>& corners,
Settings::Pattern patternType /*= Settings::CHESSBOARD*/)
{
corners.clear();
switch(patternType)
{
case Settings::CHESSBOARD:
case Settings::CIRCLES_GRID:
for( int i = 0; i < boardSize.height; ++i )
for( int j = 0; j < boardSize.width; ++j )
corners.push_back(Point3f(float( j*squareSize ), float( i*squareSize ), 0));
break;
case Settings::ASYMMETRIC_CIRCLES_GRID:
for( int i = 0; i < boardSize.height; i++ )
for( int j = 0; j < boardSize.width; j++ )
corners.push_back(Point3f(float((2*j + i % 2)*squareSize), float(i*squareSize), 0));
break;
default:
break;
}
}
static bool runCalibration( Settings& s, Size& imageSize, Mat& cameraMatrix, Mat& distCoeffs,
vector<vector<Point2f> > imagePoints, vector<Mat>& rvecs, vector<Mat>& tvecs,
vector<float>& reprojErrs, double& totalAvgErr)
{
cameraMatrix = Mat::eye(3, 3, CV_64F);
if( s.flag & CV_CALIB_FIX_ASPECT_RATIO )
cameraMatrix.at<double>(0,0) = 1.0;
distCoeffs = Mat::zeros(8, 1, CV_64F);
vector<vector<Point3f> > objectPoints(1);
calcBoardCornerPositions(s.boardSize, s.squareSize, objectPoints[0], s.calibrationPattern);
objectPoints.resize(imagePoints.size(),objectPoints[0]);
//Find intrinsic and extrinsic camera parameters
double rms = calibrateCamera(objectPoints, imagePoints, imageSize, cameraMatrix,
distCoeffs, rvecs, tvecs, s.flag|CV_CALIB_FIX_K4|CV_CALIB_FIX_K5);
cout << "Re-projection error reported by calibrateCamera: "<< rms << endl;
bool ok = checkRange(cameraMatrix) && checkRange(distCoeffs);
totalAvgErr = computeReprojectionErrors(objectPoints, imagePoints,
rvecs, tvecs, cameraMatrix, distCoeffs, reprojErrs);
return ok;
}
// Print camera parameters to the output file
static void saveCameraParams( Settings& s, Size& imageSize, Mat& cameraMatrix, Mat& distCoeffs,
const vector<Mat>& rvecs, const vector<Mat>& tvecs,
const vector<float>& reprojErrs, const vector<vector<Point2f> >& imagePoints,
double totalAvgErr )
{
FileStorage fs( s.outputFileName, FileStorage::WRITE );
time_t tm;
time( &tm );
struct tm *t2 = localtime( &tm );
char buf[1024];
strftime( buf, sizeof(buf)-1, "%c", t2 );
fs << "calibration_Time" << buf;
if( !rvecs.empty() || !reprojErrs.empty() )
fs << "nrOfFrames" << (int)std::max(rvecs.size(), reprojErrs.size());
fs << "image_Width" << imageSize.width;
fs << "image_Height" << imageSize.height;
fs << "board_Width" << s.boardSize.width;
fs << "board_Height" << s.boardSize.height;
fs << "square_Size" << s.squareSize;
if( s.flag & CV_CALIB_FIX_ASPECT_RATIO )
fs << "FixAspectRatio" << s.aspectRatio;
if( s.flag )
{
sprintf( buf, "flags: %s%s%s%s",
s.flag & CV_CALIB_USE_INTRINSIC_GUESS ? " +use_intrinsic_guess" : "",
s.flag & CV_CALIB_FIX_ASPECT_RATIO ? " +fix_aspectRatio" : "",
s.flag & CV_CALIB_FIX_PRINCIPAL_POINT ? " +fix_principal_point" : "",
s.flag & CV_CALIB_ZERO_TANGENT_DIST ? " +zero_tangent_dist" : "" );
cvWriteComment( *fs, buf, 0 );
}
fs << "flagValue" << s.flag;
fs << "Camera_Matrix" << cameraMatrix;
fs << "Distortion_Coefficients" << distCoeffs;
fs << "Avg_Reprojection_Error" << totalAvgErr;
if( !reprojErrs.empty() )
fs << "Per_View_Reprojection_Errors" << Mat(reprojErrs);
if( !rvecs.empty() && !tvecs.empty() )
{
CV_Assert(rvecs[0].type() == tvecs[0].type());
Mat bigmat((int)rvecs.size(), 6, rvecs[0].type());
for( int i = 0; i < (int)rvecs.size(); i++ )
{
Mat r = bigmat(Range(i, i+1), Range(0,3));
Mat t = bigmat(Range(i, i+1), Range(3,6));
CV_Assert(rvecs[i].rows == 3 && rvecs[i].cols == 1);
CV_Assert(tvecs[i].rows == 3 && tvecs[i].cols == 1);
//*.t() is MatExpr (not Mat) so we can use assignment operator
r = rvecs[i].t();
t = tvecs[i].t();
}
cvWriteComment( *fs, "a set of 6-tuples (rotation vector + translation vector) for each view", 0 );
fs << "Extrinsic_Parameters" << bigmat;
}
if( !imagePoints.empty() )
{
Mat imagePtMat((int)imagePoints.size(), (int)imagePoints[0].size(), CV_32FC2);
for( int i = 0; i < (int)imagePoints.size(); i++ )
{
Mat r = imagePtMat.row(i).reshape(2, imagePtMat.cols);
Mat imgpti(imagePoints[i]);
imgpti.copyTo(r);
}
fs << "Image_points" << imagePtMat;
}
}
bool runCalibrationAndSave(Settings& s, Size imageSize, Mat& cameraMatrix, Mat& distCoeffs,vector<vector<Point2f> > imagePoints )
{
vector<Mat> rvecs, tvecs;
vector<float> reprojErrs;
double totalAvgErr = 0;
bool ok = runCalibration(s,imageSize, cameraMatrix, distCoeffs, imagePoints, rvecs, tvecs,
reprojErrs, totalAvgErr);
cout << (ok ? "Calibration succeeded" : "Calibration failed")
<< ". avg re projection error = " << totalAvgErr ;
if( ok )
saveCameraParams( s, imageSize, cameraMatrix, distCoeffs, rvecs ,tvecs, reprojErrs,
imagePoints, totalAvgErr);
return ok;
}
For those still searching, here is a simple python function that will distort points back:
def distortPoints(undistortedPoints, k, d):
undistorted = np.float32(undistortedPoints[:, np.newaxis, :])
kInv = np.linalg.inv(k)
for i in range(len(undistorted)):
srcv = np.array([undistorted[i][0][0], undistorted[i][0][1], 1])
dstv = kInv.dot(srcv)
undistorted[i][0][0] = dstv[0]
undistorted[i][0][1] = dstv[1]
distorted = cv2.fisheye.distortPoints(undistorted, k, d)
return distorted
Example:
undistorted = np.array([(639.64, 362.09), (234, 567)])
distorted = distortPoints(undistorted, camK, camD)
print(distorted)
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projectPointsactually projects 3D points onto 2D points by taking calibration into account, you don't get distorted points from undistorted 2D points. – Principate