Rotating back points from a rotated image in OpenCV

Question

I’m having troubles with rotation. What I want to do is this:

• Rotate an image
• Detect features on the rotated image (points)
• Rotate back the points so I can have the points coordinates corresponding to the initial image

I’m a bit stuck on the third step.

I manage to rotated the image with the following code:

cv::Mat M(2, 3, CV_32FC1);
cv::Point2f center((float)dst_img.rows / 2.0f, (float)dst_img.cols / 2.0f);
M = cv::getRotationMatrix2D(center, rotateAngle, 1.0);
cv::warpAffine(dst_img, rotated, M, cv::Size(rotated.cols, rotated.rows));

I try to rotate back the points with this code:

float xp = r.x * std::cos( PI * (-rotateAngle) / 180 ) - r.y * sin(PI * (rotateAngle) / 180);
float yp = r.x * sin(PI * (-rotateAngle) / 180) + r.y * cos(PI * (rotateAngle) / 180);

It is not to fare to be working but the points don’t go back well on the image. There is an offset.

Thank you for your help

Answer 1

I had the same problem.

For a transform M and point pp in the rotated image, we wish to find the point pp_org in the coordanates of the original image. Use the following lines:

cv::Mat_<double> iM;
cv::invertAffineTransform(M, iM);
cv::Point2f pp_org = iM*pp;

Where the operator * in the above line is defined as:

cv::Point2f operator*(cv::Mat_<double> M, const cv::Point2f& p)
{ 
    cv::Mat_<double> src(3/*rows*/,1 /* cols */); 

    src(0,0)=p.x; 
    src(1,0)=p.y; 
    src(2,0)=1.0; 

    cv::Mat_<double> dst = M*src; //USE MATRIX ALGEBRA 
    return cv::Point2f(dst(0,0),dst(1,0)); 
} 

Note: M is the rotation matrix you used to go from the original to the rotated image

Answer 2

If M is the rotation matrix you get from cv::getRotationMatrix2D, to rotate a cv::Point p with this matrix you can do this:

cv::Point result;
result.x = M.at<double>(0,0)*p.x + M.at<double>(0,1)*p.y + M.at<double>(0,2);
result.y = M.at<double>(1,0)*p.x + M.at<double>(1,1)*p.y + M.at<double>(1,2);

If you want to rotate a point back, generate the inverse matrix of M or use cv::getRotationMatrix2D(center, -rotateAngle, scale) to generate a matrix for reverse rotation.