360° Panorama Coordinate Systems

Unwrapped pictures from the 360° panorama lens, treated with b-splines, looked pretty. But they weren't right.

How do we know? We checked:

And for that a 360° panoramic calibration checker board was created.

Confused yet? Pay attention to the height of the squares. Still confused?

Unwrapping the picture with Polar to Cartesian transformation, we can see that the squares aren't square. In fact they get less and less square.

It turns out that the correct transformation would be from Log-Polar to Cartesian coordinate system. And even then with a calibration parameter for the lens, since the real world is not perfect and the log base != e.

So we get, what the camera sees.

What we want to see.

What math sees.