如何在MATLAB中创建梯度幅度图像

Question

我给出了灰度图像，我想从中创建梯度幅度图像。 我知道有一个叫imgradient功能，但我不知道该怎样修改幅度的想法，以便它的计算方式如下：

∇f ≈ abs(z7+ 2z8+ z9- z1- 2z2- z3) + abs(z3+ 2z6+ z9- z1- 2z4- z7) 

Answer 1

你必须实现自己的梯度功能，并将其应用到图像I中的每个像素：

//example of a 4x5 image I 
I = [1 3 2 6 5; 6 1 0 18 21; 13 12 13 14 11; 16 15 28 9 20] 

G = I; //set your gradient matrix to be equal to I so that the sides have a value 

//get the height and width of image I 
[h, w] = size(I); 

//loop through each pixel that is not on the side 
for x=2:w-1 
    for y=2:h-1 
     //for each pixel: 
     z1 = I(y-1, x-1); //e.g z1 is the pixel on the upper left 
     z2 = I(y, x-1); 
     z3 = I(y+1, x-1); 
     z4 = I(y-1, x); 
     z6 = I(y+1, x); 
     z7 = I(y-1, x+1); 
     z8 = I(y, x+1); 
     z9 = I(y+1, x+1); 
     G(y,x) = abs(z7+ 2*z8+ z9- z1- 2*z2- z3) + abs(z3+ 2*z6+ z9- z1- 2*z4- z7); 
    end  
end 

Answer 2

我得到你想要使用sobel mask（按照你的等式）进行空间滤波。所以，我建议你使用下面的命令：BW = edge（I，'Sobel'）;

，或者如果你想精确的输出按你所给出那就试试这个公式：

I = imread('cameraman.tif'); 
I = padarray(I,[1 1],'symmetric'); 
sobel_mask_x = [-1 -2 -1; 0 0 0; 1 2 1]; 
sobel_x = filter2(sobel_mask_x ,I); 
sobel_mask_y = sobel_mask_x'; 
sobel_y = filter2(sobel_mask_y ,I); 
sobel_responce = abs(sobel_x)+abs(sobel_y); 
figure,imshow(sobel_responce,[]); title('Sobel gradient'); 

这是更快，而不是使用循环。