We started with measured positions for the positions of the intersections of the grid lines. Using an assumed intersection point for the origin made it easier to fit the curves through it. But the intersection of the two axes also has an error associated with it which a search of the neighborhood of the origin showed. This gave us an improved estimate of the position for the origin. One could repeat the process for all pairs of lines for the grid to get improved estimates of these pixel points in the image. Chosing a pair of axes for the grid was an arbitrary decision. We could have used any of the intersections for the origin.
It's likely that the improved estimates of the grid points will result in a lower variance for the fitted transformation function. We can use this improved fit as our equivalent of Ptolemy's Governing Faculty. There seems to be a number of converging approaches in the sciences. The psychologists study evoked potentials. The engineering approach is fuzzy logic. For the mystic there is Zen. We might consider this to be the rational version.
We can't rule out that it is possible to go beyond the actual measurements. Just what our limit in precision is remains to be seen. Redundant data gives better results.
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