Fusion of CT and MRI images, MI method

I've got theoretical question about fusing medical images. After Matlab calculate mutual information between CT and MRI images what should be the next step? I know that calculated value of mutual information should be parameter in certain function that should be minimized, but I don't know any details. Could you tell me what should I do after calculating MI?

Answer 1

[Jurgen]

Same as least squares, transform 1 of the images according to your criteria (e.g. rotate) then re-calculate MI. Try various transforms according to your algorithm, then choose the transform that had the hightest MI to get an optimal match.

The joint entropy should be minimized to maximize the MI.

Answer 2

[D C]

Thanks.

You suggest to execute it in loop which works until MI has its maximum, but i do not know this maximum, so I should use something like fminsearch for joint entropy first?

could you present it on any example?

Answer 3

[Jurgen]

Alright, for a rotation and xtranslation example:

stepsize1 = pi/180; %e.g. 1 degree
stepsize2 = 1;      %e.g. 1 pixel

rotations    = 0:stepsize1:pi;   %vector of angles
translationx = -10:stepsize2:10; %vec. of x-shifts

a = 0; %index row
b = 0; %index col
M = zeros(length(rotations),length(translationsx)); %stores MI scores 

IM1 = rand(300); %reference image
IM2 = rand(300); %floating image

%---
% Lets say mytransformfcn is a function taking inputs for 
% (rotation & xtranslation & image) and outputs a transformed image
%
% Lets also say MI is a function that calculates the mutual information
% (=scalar) between 2 images.
%---

for ii = rotations
    a = a+1;
    for jj = translationx
        b = b+1;
        newIM  = mytransformfcn(ii,jj,IM2);
        M(a,b) = MI(newIM,IM1);
    end
end

%------find max MI + corresponding parameters
[mx idx]            = max(M(:));
[angleidx transidx] = ind2sub(size(M),idx); clear idx;
max_angle           = rotations(angleidx); 
max_trans           = translationx(transidx);