A fast way to compute gradient information

Hello everybody,

I am doing image registration and for one of my metrics and I need to use gradient information beteween two images, but it is very slow to compute (I tried to resize my images but it is still very slow).

I don't know if it is because there is an error in my code or because it is not optimized (of course it is not since I use a for loop for my third step).

My problem: we have two images (I and J) to register (they are not the same size, I>J)

• 1st step: we crop a part of I to the size of J
• 2nd step: we compute the gradient information
• 3rd step: we translate I of 1 pixel(to the right or to the bottom, depends in where we are on the picture ) and we restart from the begining until J has "browsed" every part of I.

Here is my code for the second step:

function GI=GI_1(I,J)

%gradients' magnitude and direction
[Gmag_I, Gdir_I] = imgradient(I);
[Gmag_J, Gdir_J]=imgradient(J);

[a,b]=size(I);

%angle between the two gradients
theta_tab=Gdir_I-Gdir_J;

%making the gradients of same direction more visible
theta_tab=0.5*(cosd(2*theta_tab)+1)

%gradients
gradient_I=imgradient(I);
gradient_J=imgradient(J);

min_norm=min(norm(gradient_I), norm(gradient_J));
min_multi=theta_tab*min_norm;
GI=sum(min_multi(:));

end

The third step is basically a for loop such as this one (I know it is a little bit messy but I think we get the main idea):

im_crop=I;
for i=1:x+10
    im_trans=imtranslate(im_crop, [0 -1]);

      for j=1:z+10
          im_crop=im_trans;
          im_crop=imtranslate(im_crop, [-j 0]);
          rect3=[0 0 (rect2(3)+1)*scale (rect2(4)+1)*scale];
          im_crop2 = imcrop(im_crop, rect3);
          GI=GI_1(im_crop2,J);
          GI_tab(j,i)=GI;   

      end  
      im_crop=im_trans;
  end

There you go, don't hesitate to ask any question. I hope somebody will have a solution. Thanks in advance, have a nice day!