# Bundle adjustment optimization parameters

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

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!