%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% Affine Parameter Calculation 
% ---------------------------- 
%  AUTHOR: Maher Khoury 
%    DATE: March 1, 1999 
% PURPOSE: 
%         Calculates affine motion parameters 
% 
% Notes on called subroutines: 
%   -warp.m warps frame2 back onto frame1 using the calculated parameters 
%   -grad.m calculates the image spatio-temporal gradients 
%   -Parametric.m calculates the values of the parameters 
% 
% Variables: 
%   -pyrIter        = level of the pyramid 
%   -step           = sampling step 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
function k = affine(image1,image2); 
%% Initialize values of k to be zero %% 
k(1:4) = 0; 

%%%%% Hierarchical loop %%%%% 
for pyrIter=2:-1:0, 
  step=2.^pyrIter; 

  %% Double the value of the transitional parameters %% 
  k = [k(1) k(2) 2.*k(3) 2.*k(4)]; 

  im1 = corrDn(image1, step); 
  im2 = corrDn(image2, step); 

  for l=1:3 
    %%% Motion compensate frame 2 %%% 
    warped = warp(im2,k); 

    %%% Get image gradients %%% 
    [Ix Iy It] = grad(im1,warped); 

    %%% Find residual k's %%% 
    resid_k = Parametric(Ix,Iy,It); 

    %%% Update the k values %%% 
    k = k + resid_k; 
  end 
end