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image processing - Formulas for Barrel/Pincushion distortion

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image processing - Formulas for Barrel/Pincushion distortion

Can't understand how to get (x', y') of original (x, y) in image, for Barrel/Pincushion distortion.

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Section 2 of this paper explains the transformation. Basically:

enter image description here

Here I made an example in Mathematica:

enter image description here


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