Vectoring a nested for loop containing matrix indexing

I'm trying to optimize this piece of a code a bit, and usually my first instict is to vectorize it. I cannot for the life of me figure out how to do this. Is it even possible? I am leaning towards no, but I have a gut feeling that it can be done.

 for i = 1:1:region_max_y-template_max_y
      for j = 1:1:region_max_x-template_max_x
          cc(i,j) = sum(abs(template_gradient(:)-...
              reshape(region_gradient(i:i+template_max_y-1,j:j+template_max_x-1,:),...
              templateArea,1)));
      end
  end

Answer 1

[Walter Roberson]

At various points, template_gradient(1) will have subtracted from it region_gradient(1,1), region_gradient(1,2), ... region_gradient(region_max_y-1,region_max_x-1) . You can arrange all of those in a row vector. You can do the same sort of thing for each template_gradient entry, construct the vector of values that will be subtracted from it in order. Then you can replicate each of the column vector region_gradient entries to a 2D array that is as wide as the array of coefficients. Now, subtract and abs() and sum along the columns. The result will be all of the values that correspond to c, simultaneously. Reshape that result.

[Phillip Miller]

The problem is, each value returned is dependent on the values around each pixel. (this is why two-dimensional indexing is present.)

A simpler way to present this problem is

for i = 1:1:alpha
    for j = 1:1:beta;
       A = sum(B(i:(i+5),j:(j+5)));
    end 
end

This would sum all values in a certain region of B, as defined by the for loop.