Camera auto-calibration

<h2 id="problem-statement">Problem statement</h2>
<p>Given set of cameras 
  
    
      
        
          P
          
            i
          
        
      
    
    {\displaystyle P^{i}}
  
 and 3D points 
  
    
      
        
          X
          
            j
          
        
      
    
    {\displaystyle X_{j}}
  
 reconstructed up to projective ambiguity (using, for example, <a href="/facts/Bundle_adjustment/t1Uvf9ED">bundle adjustment</a> method) we wish to define rectifying homography 
  
    
      
        H
      
    
    {\displaystyle H}
  
 such that 
  
    
      
        
          {
          
            
              P
              
                j
              
            
            H
            ,
            
              H
              
                −
                1
              
            
            
              X
              
                J
              
            
          
          }
        
      
    
    {\displaystyle \left\{P^{j}H,H^{-1}X_{J}\right\}}
  
 is a metric reconstruction. After that internal camera parameters 
  
    
      
        
          K
          
            i
          
        
      
    
    {\displaystyle K_{i}}
  
 can be easily calculated using <a href="/facts/Camera_matrix/fXos7y5s">camera matrix</a> factorization 
  
    
      
        
          P
          
            M
          
          
            i
          
        
        ≡
        
          P
          
            i
          
        
        H
        =
        
          K
          
            i
          
        
        
          (
          
            
              R
              
                i
              
            
            
              |
            
            
              t
              
                i
              
            
          
          )
        
      
    
    {\displaystyle P_{M}^{i}\equiv P^{i}H=K_{i}\left(R_{i}|t_{i}\right)}
  
.
</p>
<h2 id="solution-domains">Solution domains</h2>
<ul><li>Motions
<ul><li>General Motion</li>
<li>Purely Rotating Cameras</li>
<li>Planar Motion</li>
<li>Degenerate Motions</li></ul></li>
<li>Scene Geometry
<ul><li>General Scenes with Depth Relief</li>
<li>Planar Scenes</li>
<li><a href="/facts/3D_projection/FATfGH2W">Weak Perspective</a> and Orthographic Imagers</li>
<li>Calibration Priors for Real Sensors</li>
<li>Nonlinear optical distortion</li></ul></li></ul>
<h2 id="algorithms">Algorithms</h2>
<ul><li>Using the Kruppa equations. Historically the first auto-calibration algorithms. It is based on the correspondence of <a href="/facts/Epipolar_geometry/Gvop868C">epipolar lines</a> tangent to the absolute conic on the plane at infinity.</li>
<li>Using the absolute dual quadric and its projection, the dual image of the absolute conic</li>
<li>The modulus constraint</li></ul>

<ul><li>O.D. Faugeras; Q.T. Luong; S.J. Maybank (1992). <a href="https://doi.org/10.1007%2F3-540-55426-2_37">"Camera Self-Calibration: Theory and Experiments"</a>. <i>ECCV</i>. Lecture Notes in Computer Science. 588: 321–334. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F3-540-55426-2_37">10.1007/3-540-55426-2_37</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-3-540-55426-4.</li>
<li>Q.T. Luong (1992). <i>Matrice fondamentale et auto-calibration en vision par ordinateur</i>. PhD Thesis, University of Paris, Orsay.</li></ul>
<ul><li>Q.T. Luong and Olivier D. Faugeras (1997). "Self-calibration of a moving camera from point correspondences and fundamental matrices". <i>International Journal of Computer Vision</i>. 22 (3): 261–289. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1023%2FA%3A1007982716991">10.1023/A:1007982716991</a>.</li></ul>
<ul><li>Olivier Faugeras and Q.T. Luong (2001). <i>The Geometry of Multiple Images</i>. MIT Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-262-06220-8.</li></ul>
<ul><li>Richard Hartley; Andrew Zisserman (2003). <i>Multiple View Geometry in computer vision</i>. Cambridge University Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-521-54051-8.</li></ul>

Camera auto-calibration open-in-new

Camera auto-calibration