# Measuring Similarity of Affine Transformations

I am currently working on a problem where a calibration Algorithm provides me with an Affine Transformation that transforms a 2D Image to it's assumed Position in a 3D Volume. To evaluate the accuracy of the procedure, I have been looking to find a standardized way of measuring the similarity of Affine Transformations or, as a backup, of 2D Planes. The Planes are finite, by the way.

Rephrasing: I have several Affine Transformations that should ideally be identical but are not due to statistical measuring errors.

I can easily come up with a home brew solution for this, but if there is a proper way to do it, I'd be glad to do it right =). Straightforward numerical solution would be to transform a point grid with each transformation and to calculate mean distance values from the various transformations.

Thanks a lot for your input and have nice day!

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Keno, maybe if you provided a couple of numerical examples to clarify. I'm not even sure what you mean by the Planes are finite - you mean bounded due to truncation or some exotic geometry? –  alancalvitti Nov 23 '12 at 15:17