使用Marr算子提取图像边缘的matlab代码，要求： （1）标注出算子的大小 （2）改变 σ 的值，观察图像的变化

以下是使用Marr算子提取图像边缘的MATLAB代码，其中标注了算子的大小为5x5：

img = imread('lena.jpg');
img = rgb2gray(img);
sigma1 = 1;
sigma2 = 2;
[m,n] = size(img);
L = zeros(m,n);
for i = 1:m
    for j = 1:n
        L(i,j) = img(i,j);
    end
end
filter_size = 5; % Marr算子大小为5x5
Marr = zeros(filter_size,filter_size);
for i = 1:filter_size
    for j = 1:filter_size
        x = i - ceil(filter_size/2);
        y = j - ceil(filter_size/2);
        Marr(i,j) = -(x^2+y^2)/(2*pi*sigma1^4)*exp(-(x^2+y^2)/(2*sigma1^2));
    end
end
for i = 1:m-filter_size+1
    for j = 1:n-filter_size+1
        patch = L(i:i+filter_size-1,j:j+filter_size-1);
        response = sum(sum(patch.*Marr));
        L(i+ceil(filter_size/2)-1,j+ceil(filter_size/2)-1) = response;
    end
end

figure,imshow(L);

sigma1 = 2;
Marr = zeros(filter_size,filter_size);
for i = 1:filter_size
    for j = 1:filter_size
        x = i - ceil(filter_size/2);
        y = j - ceil(filter_size/2);
        Marr(i,j) = -(x^2+y^2)/(2*pi*sigma1^4)*exp(-(x^2+y^2)/(2*sigma1^2));
    end
end
for i = 1:m-filter_size+1
    for j = 1:n-filter_size+1
        patch = L(i:i+filter_size-1,j:j+filter_size-1);
        response = sum(sum(patch.*Marr));
        L(i+ceil(filter_size/2)-1,j+ceil(filter_size/2)-1) = response;
    end
end

figure,imshow(L);

运行该代码，将会得到两张提取边缘后的图像，其中第一张使用的是sigma1=1，第二张使用的是sigma1=2。可以发现，当sigma值增大时，边缘提取变得更加模糊。