Variance and Deviation for the Transformation

I checked the neighborhood of the arbitrarily chosen zero point for the graph paper and found a minimum for the sum of the variances of the horizontal and vertical lines through the zero point.


As expected the accuracy of the fit is limited by the accuracy in the determination of the data points. The nonlinearity of the pixel function makes it difficult to find the inverse function. But the transformation is one-to-one so one can still search for the graph paper coordinates which correspond to a given pixel point.