function [idf] = IDF(I, d,phi)
% 
% Written by:
% -- 
% John L. Weatherwax                2005-08-04
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
% Epage 
% 
%-----

if( nargin>1 ) % compute the IDF for just one displacement and angular direction

  P   = co_occurrence(I, d,phi);
  N_g = size(P,1);
  
  iiArray = repmat( (0:(N_g-1))', [1,N_g] );
  jjArray = repmat( (0:(N_g-1)) , [N_g,1] );
  D       = ones(N_g) + (iiArray - jjArray).^2; % compute the denominator 
  PoD     = P ./ D;
  idf     = sum(PoD(:));
  
else % compute the IDF for all angles and average 
  
  d = 1; % assume d=1

  all_phis = [ 0, 45, 90, 135 ];
  all_idfs = zeros(1,length(all_phis));
  for ii=1:length(all_phis)
    
    c = IDF(I, d,all_phis(ii)); % recursively call the three argument case  
    all_idfs(ii) = c;
    
  end
  
  idf = mean(all_idfs);
  
end