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I am doing a project in opencv to detect obstacle in the path of a blind person using stereo calibration. I have calculated the disparity map correctly. Now to find the distance of obstacle from the camera, I want its 3D coordinates [X,Y,Z] , which I am guessing can be found by reprojectImageTo3D(), but I dont have the Q matrix to use in this function because the Q matrix I am getting from stereoRectify() is coming null probably because I used pre calibrated images. Although I do have the inrinsic and extrinsic parameters of my camera. So my question is that how can I manually create the Q matrix to directly use in the function reprojectImageTo3D(), if I know the focal length, baseline and everything else about my camera? What is the basic format of the Q matrix?

g.alisha12
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    A brief discription of the 3D reconstruction for stereo vision is given below in the following picture. You can get the **Q matrix** and have a better understanding of it from the process. [![enter image description here](https://i.stack.imgur.com/LrDRD.jpg)](https://i.stack.imgur.com/LrDRD.jpg) – Gavin Gao Jan 21 '19 at 14:39
  • @GavinGao what about going from rectified to unrectified coordinate system ? – Pedro77 Jul 27 '22 at 04:41
  • @Pedro77 It is the inverse process. – Gavin Gao Jul 30 '22 at 05:36

2 Answers2

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The form of the Q matrix is given as follows:

Q Matrix Image

In that image, cx and cy are the coordinates of the principal point in the left camera (if you did stereo matching with the left camera dominant), c'x is the x-coordinate of the principal point in the right camera (cx and c'x will be the same if you specified the CV_CALIB_ZERO_DISPARITY flag for stereoRectify()), f is the focal length and Tx is the baseline length (possibly the negative of the baseline length, it's the translation from one optical centre to the other I think).

I would suggest having a look at the book Learning OpenCV for more information. It's still based on the older C interface, but does a good job of explaining the underlying theory, and is where I sourced the form of the Q matrix from.

ssice
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Andrew W
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if you want to create directly Q matrix:

cv::Mat Q;
Q.at<double>(0,0)=1.0;
Q.at<double>(0,1)=0.0;
Q.at<double>(0,2)=0.0;
Q.at<double>(0,3)=-160; //cx
Q.at<double>(1,0)=0.0;
Q.at<double>(1,1)=1.0;
Q.at<double>(1,2)=0.0;
Q.at<double>(1,3)=-120;  //cy
Q.at<double>(2,0)=0.0;
Q.at<double>(2,1)=0.0;
Q.at<double>(2,2)=0.0;
Q.at<double>(2,3)=348.087;  //Focal
Q.at<double>(3,0)=0.0;
Q.at<double>(3,1)=0.0;
Q.at<double>(3,2)=1.0/95;    //1.0/BaseLine
Q.at<double>(3,3)=0.0;    //cx - cx'

But you should calibrate both cameras and then get Q matrix from cv::stereoRectify. Be carefull, read Q matrix as double values.

Javier Abellán Ferrer
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