function [Hxy] = entropy(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 entropy for just one displacement and angular direction

  P     = co_occurrence(I, d,phi);
  indsP = find( P(:)>0 ); mv = min(P(indsP)); % fix any zero elements so we can take the log2 of them
  indsN = find( P(:)<=0 ); P(indsN) = 1.e-6 * mv; 
  LP   = log2(P);
  PnLP = -P .* LP;
  Hxy  = sum(PnLP(:));
  
else % compute the entropy for all angles and average 
  
  d = 1; % assume d=1

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