function fd=box_frac_dem(X);
% 差分盒維數
% Example:
%    X=double(imread('rice.tif'));
%    fd=box_frac_dem(X);
% Author email of the program:% zjliu2001@163.com
% 
% Reference:
% Sarkar N,Chaudhuri B B. An efficient approach to estimate fractal dimension
% of textural images [J].Pattern Recognition,1992,25(9):1035-1041

if size(X,1)~=size(X,2);
    error('The size of X must NxN.');
end
B=size(X,1);
if mod(log2(B),1)>0;
    error('The size of X must 2^n');
end
t=log2(B);
s=2.^(1:t);
Nr=zeros(1,t);
for k=1:t;
    d=s(k);
    h=256/d;
    for m=1:h;
        for n=1:h;
            A=X(d*(m-1)+[1:d],d*(n-1)+[1:d]);
            mn=min(A(:));
            mx=max(A(:));
            nr=fix(mx/d)-fix(mn/d)+1;
            Nr(k)=Nr(k)+nr;
        end
    end
end
r=B./s;
p=polyfit(log10(r),log10(Nr),1);
fd=p(1);