title: Get 3D coordinates from 2D image pixel if extrinsic and intrinsic parameters are known
body: <p>I am doing camera calibration from tsai algo. I got intrensic and extrinsic matrix, but how can I reconstruct the 3D coordinates from that inormation?</p>
  
  <p><img src="https://i.stack.imgur.com/RwgX0.png" alt="enter image description here">
  </p>
  
  <p><strong>1)</strong>  I can use Gaussian Elimination for find X,Y,Z,W and then points will be X/W , Y/W , Z/W as homogeneous system.</p>
  
  <p><strong>2)</strong> I can use the
  <a href="http://opencv.willowgarage.com/documentation/cpp/camera_calibration_and_3d_reconstruction.html" rel="noreferrer">OpenCV documentation</a> approach:<br/><br/>
  <img src="https://i.stack.imgur.com/dwxbZ.png" alt="enter image description here"></p>
  
  <p>as I know <code>u</code>, <code>v</code>, <code>R</code> , <code>t</code> , I can compute <code>X,Y,Z</code>.</p>
  
  <p>However both methods end up in different results that are not correct.<br/></p>
  
  <p>What am I'm doing wrong?</p>