I need some algorithm for distortion processing

My problem is: I have a set of 4 points O, A, B, C locating on a surface. Due to distortion of that surface, the points A, B, C are moved to new positions which are A', B', C'. Now I want to find new position of O that satisfies root mean square error (RMSE) of two sets of distances (O'A', O'B', O'C', O'O) and (OA, OB, OC, OO) is minimal. Dose anyone know which algorithm can solve my problem? Thank you!

Answer 1

[Image Analyst]

That's not distortion in the true optical sense. Distortion is where the distance the point moves is proportional to the cube of the distance from the optic axis, and it's radial, which is quite unlike what you have. You have some arbitrary warping of the image. Try imwarp() or related functions.

Answer 2

[Dan Do]

Thank you for your answer, but it is not exactly what I need. I mean O, A, B, C are points on a plane specified by their coordinates (they are not pixels). Being effected by something, A, B, C are moved to new positions with different movements, I want to find new position O' of O, so that the change in struct of the set of 4 points is the least. It means RMSE of the two set (O'A', O'B', O'C', OO') and (OA, OB, OC, OO) is minimal. So could you suggest me some ALGORITHM for doing that, thank you!

[Image Analyst]

Well obviously if the new position O' is the same as O, that would give the least possible RMSE you could get.