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Can anyone tell me how the operation FindGeometricTransform[pts1, pts2] works (I mean inside logic of the transformation function), or where can I find such an explanation?

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    $\begingroup$ It’ll be in the Details section of the docs. You can specify a different algorithm via the Method option too so you can check on that as well. $\endgroup$ – b3m2a1 Jun 25 '18 at 18:10
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    $\begingroup$ I don't know how it works, but since the geometric transforms in question are linear, the problem is expressible in terms of LeastSquares. $\endgroup$ – Szabolcs Jun 25 '18 at 18:14
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From the "Details and Options" section of the documentation for FindGeometricTransform, the available fitting methods are:

"Linear"                    linear solver based on SVD
"RANSAC"                    random sample consensus method
"FindFit"                   uses FindFit
{"ImageAlign", method}      ImageAlign transformation using the given method

Note also that "By default, the most suitable alignment method and transformation class are used for calculating the transformation." so, if you want to be sure of which method your code uses (e.g. for publication or testing), the best approach in my opinion would be to request your preferred method explicitly.

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