title: How to compute the true depth given a disparity map of rectified images?
body: <p>I have calculated a disparity map for a given rectified stereopair! I can calculate my depth using the formula </p>
  
  <pre><code>z = (baseline * focal) / (disparity * p)
  </code></pre>
  
  <p>Let's assume that the baseline, focal length and pixel constant p are known and I used the same camera for both images.
  Now it is possible that my disparity is in the range of -32..128[pixel]. When I use the above formula I will get infinity/divided by zero for my values of 0 disparity. When i move my disparity values to lets say 1..161 I have chosen the range of my disparity values arbitrary and that's a problem because the function 1/disparity will give a completly different value spacing at 1..161 or 100..260 that isn't even linear. So I wouldn't even get a reconstruction up to (linear)scale because the scale change is non-linear. </p>
  
  <p>How can i determine in what area my disparity has to lie to get a metric reconstruction with the above formula?
  Or is it simply not possible to reconstruct something metrically with the above formula and rectified images? And if that's the case, why?</p>
  
  <p>(I know I can reproject to my non-rectified images and do a triangulation but I want to know especially WHY or IF it is not possible with the above formula. Thanks to anyone who can help me!)</p>