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There are a number of approaches to calibrate cameras. In this process you estimate the intrinsic parameters using a checkerboard of known size.

I'm confused on how the focal lengths are found. The issue is even with a known size, the location of the board remains indeterminate. Thus unless I am missing something everything is still unknown by a scale factor. Could someone explain this?

Further looking at the paper which is referenced by Matlab it doesn't appear that the question of uniqueness of focal length was addressed.

My issue is that intuitively moving the camera location and moving the focal length have the same effect and basically homography reproduction shows this.

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    $\begingroup$ wrong intuition. the focal length is nothing but a scale factor for the "sensor resolution". varying it is not equivalent to moving the camera. if it happens to be, you don't have any perspective component, hence the homography isn't a full homography but a lesser transform, something that isn't a perspective transform. $\endgroup$
    – Christoph Rackwitz
    Commented Feb 23, 2023 at 16:39
  • $\begingroup$ The dolly zoom effect demonstrates that moving the camera and changing the focal length are not equivalent. $\endgroup$
    – Cris Luengo
    Commented Sep 23, 2023 at 14:58

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