Calculating new positions of keypoints

Question

can somebody help me, how we can calculate the new positions of keypoints in the transformed image,the keypoints were detected in original image. I am using opencv homography matrix and warpPerspective to make the transformed image.

Here is a code..

...
 std::vector< Point2f > points1,points2;
 for( int i = 0; i < matches1.size(); i++ )
    {
     points1.push_back( keypoints_input1[matches1[i].queryIdx ].pt );
     points2.push_back( keypoints_input2[matches1[i].trainIdx ].pt );
    }
 /* Find the Homography Matrix for current and next frame*/
 Mat H1 = findHomography( points2, points1, CV_RANSAC );
 /* Use the Homography Matrix to warp the images*/
cv::Mat result1;
warpPerspective(input2, result1, H1, Size(input2.cols+150, input2.rows+150),              
INTER_CUBIC);
...
}

Now I want to calculate the new positions of points2 in the result1 image.

For example in the below transformed image , we know the corner points. Now I want to calculate the new position of the keypoints say before transformation {(x1,y1),(x2,y2),(x3,y3)...}, How we can calculate it?

Update: opencv 'perspectiveTransform' does what I trying to do.

Answer 1

Let's call I' the image obtained by warping image I using homography H.

If you extracted keypoints m_i = (x_i, y_i, 1) in original image I, you can get the keypoints m'_i in the warped image I' using the homography transform: S * m'_i = H * m_i. Notice the scale factor S, if you want the keypoints coordinates in pixels, you have to scale m'_i so that the third element is 1.

If you want to understand where the scale factor comes from, have a look at Homogeneous Coordinates.

Also, there is an OpenCV function to apply this transformation to an array of points: perspectiveTransform(documentation).