undistort.m

function [x] = undistort(xd,k)
% This function was copied from Bouguet's camera calibration toolbox!
%
%comp_distortion_oulu.m
%
%[x] = comp_distortion_oulu(xd,k)
%
%Compensates for radial and tangential distortion. Model From Oulu university.
%For more informatino about the distortion model, check the forward projection mapping function:
%project_points.m
%
%INPUT: xd: distorted (normalized) point coordinates in the image plane (2xN matrix)
%       k: Distortion coefficients (radial and tangential) (4x1 vector)
%
%OUTPUT: x: undistorted (normalized) point coordinates in the image plane (2xN matrix)
%
%Method: Iterative method for compensation.
%
%NOTE: This compensation has to be done after the subtraction
%      of the principal point, and division by the focal length.


  k1 = k(1);
  k2 = k(2);
  k3 = k(5);
  p1 = k(3);
  p2 = k(4);

  x = xd; 				% initial guess

  for kk=1:20,

      r_2 = sum(x.^2);
      k_radial =  1 + k1 * r_2 + k2 * r_2.^2 + k3 * r_2.^3;
      delta_x = [2*p1*x(1,:).*x(2,:) + p2*(r_2 + 2*x(1,:).^2);
      p1 * (r_2 + 2*x(2,:).^2)+2*p2*x(1,:).*x(2,:)];
      x = (xd - delta_x)./(ones(2,1)*k_radial);

  end;