Code covered by the BSD License

# Fast mutual information, joint entropy, and joint histogram calculation for N-D images

by

### ja (view profile)

13 May 2013 (Updated )

Built for 'highest possible' speed. Can handle any number of dimensions, given sufficient memory.

ent(J,K)
```function [jhist jent MI] = ent(J,K)
%takes two images of equal size and pixel value ranges and returns the
%joint histogram, joint entropy, and mutual information. No error checking
%used, as this function is built for speed. For additional speed,
%instructions on how to remove what you do not need are in the comments
%below

%%assumes 256x256 (pixel values range from 0-255)
%%this assumption can be changed here if desired
dimen = 256;

x = numel(J);
t = 1:x;
xx = J(:)+1;
yy = dimen*K(:);

xx = xx + yy;
xx = sort(xx);

yy(1:x-1) = xx(2:x);

zz = yy - xx;
zz(x) = 1;
zz = t(zz ~=0);

yy = xx(zz);

t = numel(zz);

zz(2:t) = zz(2:t)-zz(1:t-1);
xx = zz/x;

%if you do not need the joint histogram but do need the mutual information,
%remove jhist from the returned variables, but do NOT comment this out.
%if you need neither the joint histogram nor the mutual information,
%comment out the following two lines
jhist = zeros(dimen);
jhist(yy) = xx;

%if you do not need joint entropy, comment out the following line and
%remove jent from the list of returned variables
jent = -sum(xx.*log2(xx));

%if you do not need mutual information, comment out all of the below and
%remove MI from the list of returned variables
xx = sum(jhist);
yy = sum(jhist,2);
xx(xx>1e-12) = (xx(xx>1e-12)).^-1;
yy(yy>1e-12) = (yy(yy>1e-12)).^-1;

xx = ones(dimen,1)*xx;
yy = yy*ones(1,dimen);

MI = xx.*yy.*jhist;
MI = sum(jhist(:).*log2(MI(:)+(MI(:)<=1e-12)));

%additional speed is possible by allocating some of these variables outside
%the function. Some things to consider are x(=numel(J)), t(=1:x),
%dimen(=256), and zz(=meshgrid(1:dimen)). Note that allocating these
%variables outside the function will require you to change the names of
%some of these variables within the function..
end```