OpenCV Q&A Forum - RSS feedhttp://answers.opencv.org/questions/OpenCV answersenCopyright <a href="http://www.opencv.org">OpenCV foundation</a>, 2012-2018.Mon, 26 Mar 2018 11:05:49 -0500derivation for perspective transformation matrix (Q)http://answers.opencv.org/question/187734/derivation-for-perspective-transformation-matrix-q/Hi,
Opencv uses a perpective transformation matrix `Q` to convert pixels with disparity value into the corresponding `[x, y, z]` using the [reprojectImageTo3D](https://docs.opencv.org/2.4/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html#reprojectimageto3d) function. After searching on this site for a bit I found out that the matrix Q is as follows:
Q = |1 0 0 -Cx
|0 1 0 -Cy
|0 0 0 f
|0 0 -1/Tx (Cx - Cx')/Tx
I looked for equations to derive this but couldn't find any. I know about these matrix equations:
![image description](/upfiles/15220802288666572.png)
Is there a way to work back/invert this to get the matrix form of `Q` or am I missing something?
edit:
projection matrices are the follows:
Pright = |F skew Cx F*Tx
|0 Fy Cy 0
|0 0 1 0
and a similar one for Pleft without the Tx factor. I guess what I'm looking for is a derivation from the projection matrix `Pright` to the reprojection matrix `Q`. I would assume there's an inversion or something to get from one to the other.
Thank you2ros0Mon, 26 Mar 2018 11:05:49 -0500http://answers.opencv.org/question/187734/