在OpenCV中旋转旋转图像的后点

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 Mt() * 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;