title: 3D Reconstruction and SfM Camera Intrinsic Parameters
body: <p>I am trying to understand the basic principles of 3D reconstruction, and have chosen to play around with <a href="https://github.com/openMVG/openMVG" rel="nofollow noreferrer">OpenMVG</a>. <strong>However</strong>, I have seen evidence that the following concepts I'm asking about apply to <em>all/most</em> SfM/MVS tools, not just OpenMVG. As such, I suspect any Computer Vision engineer should be able to answer these questions, even if they have no direct OpenMVG experience.</p>
  
  <hr>
  
  <p>I'm trying to fully understand <strong>intrinsic camera parameters</strong>, or as they seem to be called, "<em>camera instrinsics</em>", or "<em>intrinsic parameters</em>". According to OpenMVG's documentation, camera intrinsics depend on the type of camera that is used to take the pictures (e.g., the <em>camera model</em>), of which, OpenMVG supports five models:</p>
  
  <ul>
  <li>Pinhole: 3 intrinsic parameters (focal, principal point x, principal point y)</li>
  <li>Pinhole Radial 1: 4 intrinsic params (focal, principal point x, principal point y, one radial distortion factor)</li>
  <li>Pinhole Radial 3: 6 params (focal, principal point x, principal point y, 3 radial distortion factors)</li>
  <li>Pinhole Brown: 8 params (focal, principal point x, principal point y, 5 distortion factors (3radial+2 tangential))</li>
  <li>Pinhole w/ Fish-Eye Distortion: 7 params (focal, principal point x, principal point y, 4 distortion factors)</li>
  </ul>
  
  <p>This is all explained on their <a href="http://openmvg.readthedocs.io/en/latest/openMVG/cameras/cameras/" rel="nofollow noreferrer">wiki page that explains their camera model</a>, which is the subject of my question.</p>
  
  <p>On that page there are several core concepts that I need clarification on:</p>
  
  <ul>
  <li><em>focal plane</em>: What it is and how does it differ from the <em>image</em> plane (as shown in the diagram at the top of that page)?</li>
  <li><em>focal distance/length</em>: What is it?</li>
  <li><em>principal point</em>: What is it, and why should it ideally be the center of the image?</li>
  <li><em>scale factor</em>: Is this just an estimate of how far the camera is from the image plane?</li>
  <li><em>distortion</em>: What is it and what's the difference between its various subtypes:
  
  <ul>
  <li>radial</li>
  <li>tangential</li>
  <li>fish-eye</li>
  </ul></li>
  </ul>
  
  <p>Thanks in advance for any clarification/correction here!</p>