Bundle Adjustment——光束平差法

1. Reprojection Error——重投影误差

     Reproject error is a geometric error corresponding to the image distance between a projected point and a measured one. It is used to quantify how closely an estimate of a 3D point X recreates the point's true projection x.

     

     In compute vision domain, reprojection/reconstruction error includes two errors:

• feature matching errors;
• camera-related errors.

 [ https://en.wikipedia.org/wiki/Reprojection_error ]

2. Bundle Adjustment

本质： minimizing reprojection error.

     

解决两类问题：

      adjusting the bundle of rays between:

• each camera center(angle of view) and the set of 3D points.
• each 3D point and the set of camera centers.

计算基于两个前提：

• it requires a good initialization to be provided
• it can become an extremely large minimization problem, because of a number of parameters involved.

何时计算此量？

      it should generally be used as a final step of any reconstruction algorithm.

 [  https://en.wikipedia.org/wiki/Bundle_adjustment ]

 [  http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/ZISSERMAN/bundle/bundle.html ]

3. Bundle adjustment ——ray divergence 射线分歧

ray divergence——the shortest distance between those rays.

     

计算前提：

    Assuming accurate feature matching, ray divergence reveals mainly camera parameters estimation inaccuracies.

 

 

      

    

      [Mauricio Hess-Flores, Kenneth I. Joy, et al.   Ray Divergence-Based Bundle Adjustment Conditioning for Multi-View Stereo]

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（***）补充内容：

• 摄像机内外参数（11个--5内6外）：

     

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       5个内参（alpha, beta, x0, y0, theta）和6个外参（R--r1, r2, r3，T--t1, t2, t3）

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• 常用的相机模型

【David A. Forsyth and Jean Ponce.  Computer Vision: A Modern Approach （计算机视觉——一种现代方法）】