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.

this is a question about mathematics and transformations; not about programming... — Chris Maes
@Chris Maes, computer-vision is about programming mathematic transformations — berak
ok you have a point, my comment was maybe not clear enough. but this question is clearly a "how to do my math" question and not a programmatic question, no? — Chris Maes
@ChrisMaes , Thanks for your comment, I really don't know, how to do it that is why I am asking. I don't think anything is wrong in asking people who knows about it. — MMH
@MMH I didn't want to be rude. I understand your question but you'd better paste 5 lines of code on how you wrap your image and where exactly you are stuck; that is a lots easier to answer... my opinion maybe — Chris Maes

BConic BConic · Accepted Answer · 2014-03-18T07:52:48

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).

Calculating new positions of keypoints

1 Answers