%=======================================================================
% Copyright 2008-2014, LEGI UMR 5519 / CNRS UJF G-INP, Grenoble, France
%   http://www.legi.grenoble-inp.fr
%   Joel.Sommeria - Joel.Sommeria (A) legi.cnrs.fr
%
%     This file is part of the toolbox UVMAT.
%
%     UVMAT is free software; you can redistribute it and/or modify
%     it under the terms of the GNU General Public License as published
%     by the Free Software Foundation; either version 2 of the license,
%     or (at your option) any later version.
%
%     UVMAT is distributed in the hope that it will be useful,
%     but WITHOUT ANY WARRANTY; without even the implied warranty of
%     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%     GNU General Public License (see LICENSE.txt) for more details.
%=======================================================================

function [x] = comp_distortion_oulu(xd,k);

%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.


if length(k) == 1,
    
    [x] = comp_distortion(xd,k);
    
else
    
    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;
    
end;