I'm working on creating a homography 3x3 matrix to do a perspective correction of a photograph 2D piece of paper. The paper contains 3 markers (like the 3 corner markers of a QR code) in its corners, which already have been detected in photograph coordinates.
With the detection I also have the area of each marker, which basically is a measure for how far the marker is from the camera.
My challenge is to construct the matrix from the positions and the areas of the three markers in the photograph and the known positions and areas of the markers on the paper.
I know that is just working with points, you'd need 4 pairs of points to reconstruct the matrix, as outlined here, but i'd like to do it from the given information. My intuition tells me it should be possible, however, my linear algebra is a bit too rusty to provide the proof and the means.
