Inverse depth parametrization

<p>In <a href="/facts/Computer_vision/Tl2Yyk66">computer vision</a>, the inverse depth parametrization is a <a href="/facts/Parametrization_(geometry)/SQK3P4sc">parametrization</a> used in methods for <a href="/facts/3D_reconstruction_from_multiple_images/fyYQxnrH">3D reconstruction from multiple images</a> such as <a href="/facts/Simultaneous_localization_and_mapping/sUFsNFG9">simultaneous localization and mapping</a> (SLAM). Given a point 
  
    
      
        
          p
        
      
    
    {\displaystyle \mathbf {p} }
  
 in 3D space observed by a <a href="/facts/Monocular/DglqwGdb">monocular</a> <a href="/facts/Pinhole_camera/8JmYNdeL">pinhole camera</a> from multiple views, the inverse depth parametrization of the point's position is a 6D vector that encodes the <a href="/facts/Optical_centre/7vqmsXJy">optical centre</a> of the camera 
  
    
      
        
          
            c
          
          
            0
          
        
      
    
    {\displaystyle \mathbf {c} _{0}}
  
 when in first observed the point, and the position of the point along the ray passing through 
  
    
      
        
          p
        
      
    
    {\displaystyle \mathbf {p} }
  
 and 
  
    
      
        
          
            c
          
          
            0
          
        
      
    
    {\displaystyle \mathbf {c} _{0}}
  
.
</p><p>Inverse depth parametrization generally improves <a href="/facts/Numerical_stability/jRDdo8zV">numerical stability</a> and allows to represent points with zero <a href="/facts/Parallax/Gu8W21LP">parallax</a>. Moreover, the error associated to the observation of the point's position can be modelled with a <a href="/facts/Gaussian_distribution/UapjjPyQ">Gaussian distribution</a> when expressed in inverse depth. This is an important property required to apply methods, such as <a href="/facts/Kalman_filter/wNK7rnbk">Kalman filters</a>, that assume normality of the measurement error distribution. The major drawback is the larger memory consumption, since the dimensionality of the point's representation is doubled.
</p>

Inverse depth parametrization open-in-new

Inverse depth parametrization