Conversion from OpenGL to OpenCV

Question

What I have

I'm generating images using the standard perspective camera in unity. The camera is aiming to the ground plane (in unity it's the xz-plane), see image. From this I need to remove the perspective so all crop rows are parallel to each other.

Methode

The warpPerspective() function from openCV can be used to remove perspective from an image. All information is known such as, field of view, rotation, position, ... and thus I know how a 3D point maps on the 2D plane and visa versa. The problem is OpenCV uses an other system. In openCV should be a 3X3 matrix and the transformation matrix from unit is a 4X4 matrix. Is there a conversion between the two? Or should I think of another strategy?

EDIT

I can not use the orthographic camera in unity.

Fixed

Solved the issue by constructing a ray from the camera origin through each pixel and looking for an intersection with the ground plane. After this I discretised the ground plane in a grid with the same resolution of the original image. Points that map to the same cell are accumulated

Answer 1

I you cannot use the unity's orthographic camera, what I would try to imitate the c++ code from the examples from your link in open CV documentation. Another approach can be to try to obtain the projection matrix of the points you want the projection to be removed by multiplying by the inverse matrix (the inverse of the transformation matrix of that point). A matrix multiplied by its inverse is the identitiy so the projection transformation would be removed. I think that should be possible, you can dig on that you can obtain/change the projection matrix checking this. The point would be to undo the projection transformation. Then you would need to obtain the according othographic projection matrix and apply it to obtain the positions you're after. That should be the same thing that the unity's orthographic camera does.

To understand the projection matrix to the lowest level this source is awesome.