[Bf-committers] Movie distortion algorithm

[Jeroen Bakker]

Hi all!

last week Sergey and I had a discussion about the Movie (un)distortion 
algorithm in tracking/libmv.
The undistortion algorithm is a the same as described in 
http://en.wikipedia.org/wiki/Distortion_%28optics%29
but when distorting a video-clip a solver is used to determine the 
inverse of this algorithm what is slow.

Is there any mathemagician who can help out to find the inverse of this 
algorithm.

in code the algorithm is located in libmv/camera_intrinsics.cc
void CameraIntrinsics::ApplyIntrinsics(double normalized_x,
                                        double normalized_y,
                                        double *image_x,
                                        double *image_y) const {
   double x = normalized_x;
   double y = normalized_y;

   // Apply distortion to the normalized points to get (xd, yd).
   double r2 = x*x + y*y;
   double r4 = r2 * r2;
   double r6 = r4 * r2;
   double r_coeff = (1 + k1_*r2 + k2_*r4 + k3_*r6);
   double xd = x * r_coeff + 2*p1_*x*y + p2_*(r2 + 2*x*x);
   double yd = y * r_coeff + 2*p2_*x*y + p1_*(r2 + 2*y*y);

   // Apply focal length and principal point to get the final image 
coordinates.
   *image_x = focal_length_x() * xd + principal_point_x();
   *image_y = focal_length_y() * yd + principal_point_y();
}

Regards,
Jeroen Bakker