Is there a way to "flatten" a Chessboard pattern apart from lense correction?

Question

I checked the tutorials here and here, and I'm looking for something similar.

So far, I managed to solve lense distortion using a Chessboard pattern, just as below (this is an average result example, i made it quickly just for this question, but you get the point):

Here

To this

The "barrel" distortion due to the cyllindrical surface from which the chessboard is in is partially fixed. But, more than the lense/distortion correction, I wanted the camera_matrix to "flatten" the chessboard pattern (i.e., to make all squares same size), similarly as the unwrap wine label similarly as used in Nepherhotep/unwrap_labels, but using the Chessboard rather than the markers instead.

Is there anything similar?