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I've found programs to turn fish eye pictures into flat ones.

I'd like to learn the process behind the scenes.

Can someone share their knowledge about the technique?

+1  A: 

My understanding is that fish eye effect is basically a projection on a semi-sphere, right? To reverse that you need to use equations for projecting a semi-sphere into a plane. A quick search revealed those Fisheye Projection equations, reversing them should be easy. I hope that puts you in the right direction.

Nadia Alramli