conv2d_by_partial_sum_grid.m

function result = conv2d_by_partial_sum_grid(image, filter)
    [is1, is2] = size(image);
    [fs1, fs2] = size(filter);
    r1 = is1-(fs1-1);
    r2 = is2-(fs2-1);
    result = zeros(r1, r2); 
    psum_result = cell(is1, fs1);
    for ir = 1:is1
        for fr = 1:fs1
            irow = image(ir,:);
            frow = filter(fr,:);
            psum_row = zeros(1, r2);
            for pr = 1:r2
                psum_row(pr) = dot_1d(irow(pr:pr+fs2-1), frow);
            end   
            psum_result{ir, fr} = psum_row;            
        end
    end    
    for i = 1:r1
        for fj = 1:fs1
            result(i,:) = result(i,:) + psum_result{i+fj-1, fj};
        end
    end        
    function r = dot_1d(x1, x2)
        r = sum(x1.*x2);
    end
end