Camera distortion across two images

Cameras distort visual reality.

A deterministic model to calculate the distortion would use the characteristics of the lenses, the capturing surface and external distances.

For given photos the characteristics are not known. In such a case it is common to use a first order distortion approximation.

It is common practice to assume spherical distortion so that:

We know the value of " r_d " on the images. Unfortunately we do not know the value of the " k " constant or " r " .

Also, we have distortions across two images so that

I suspect that it would be reasonable to assume that k₁=k₂

We know the geometries of the images, and we have matching points between the images so that it is theoretically possible to determine k.

I have not yet been able to solve this 6^th order polynomial analytically (Not even with the help of Sage ). I hope to return to this problem and solve it at a later time.