Rotating back points from a rotated image in OpenCV - c++

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

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.

Answer 2

For a rotation matrix, its transpose is its inverse. So you can just do M.t() * r to move it back to your original frame, where r is a cv::Mat (you might have to convert it to a cv::Mat from a cv::Point2f or whatever, or just write out the matrix multiplication explicitly).
Here's the code to do it explicitly (should be correct, but warning, it's entirely untested):
cv::Point2f p;
p.x = M.at<float>(0, 0) * r.x + M.at<float>(1, 0) * r.y;
p.y = M.at<float>(0, 1) * r.x + M.at<float>(1, 1) * r.y;
// p contains r rotated back to the original frame.

Answer 3

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 4

You need to rotate your points accorning to center point of your image.
Here x and y are your points which you want to rotate, imageCenter_x aand _y is center point of your image.
Below is my code.
angle = angle * (M_PI / 180);
float axis_x = x - imageCenter_x;
float axis_y = y - imageCenter_y;
x = axis_x * cos(angle) + axis_y * sin(angle);
y = (-axis_x) * sin(angle) + axis_y * cos(angle);
x = x + imageCenter_x;
y = y + imageCenter_y;