Re-distort points with camera intrinsics/extrinsics

Question

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.

morotspaj · Accepted Answer

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);

Zock77 · Answer

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)

ChronoTrigger · Answer

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

xu bin · Answer

undistortPoint is a simple reverse version of project points

In my case I would like to do the following:

Undistort points:

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.