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While reading the Wikipedia article on Bundle adjustment, I came across the following objective function used to represent the bundle adjustment problem.

Bundle Adjustment Objective Function

I have two questions regarding this objective function

  1. Can the $\mathbf{b}_i$ be fixed if I already know the 3D points being projected onto the camera in its local coordinate system (like that of a calibration plane, for example)? I mainly wanted to use bundle adjustment for improving multi-camera extrinsic estimation accuracy.

  2. I understand that the inner summation is looping through all the $m$ cameras. But, this objective function doesn’t seem to capture the fact that each of the $m$ cameras can collect some $l$ images each.

In other words, I believe that the objective function can be re-written like this, to account for a data set of $l$ images for each camera.

$$\min_{a_i, b_i} \sum_{i=1}^n \sum_{j=1}^m \sum_{k=1}^l v_{ijk} d(Q(a_{jk}, b_i), x_{ijk})^2$$

Do I “break” something by doing this?

Thanks!

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