What is the difference between gradient and imgradient?

Question

I would like to compute gradient of image I. I have two options that are

[Gx, Gy] = gradient(I);
g = sqrt(Gx.^2+Gy.^2);

and

[g,~] = imgradient(I, 'sobel');

My question are

1. What is gradient method using in first option?

2. What is befinet of finding gradient using sobel method ?

Thank all

This is what I tried

I=zeros([128 128]);
I(50:100,50:100)=100;
[Gx, Gy] = gradient(I);
g1 = sqrt(Gx.^2+Gy.^2);
[g2,~] = imgradient(I, 'sobel');
subplot(121);imshow(g1,[]);title('First option')
subplot(122);imshow(g2,[]);title('Second option')

When noisy is added to image, the different will be more clear

I=zeros([128 128]);
I(50:100,50:100)=100;
%% Add noise image;
noiseStd=5;
I_noise = I + (noiseStd * randn([128, 128]));
[Gx, Gy] = gradient(I_noise);
g1 = sqrt(Gx.^2+Gy.^2);
[g2,~] = imgradient(I_noise, 'sobel');
subplot(121);imshow(g1,[]);title('First option')
subplot(122);imshow(g2,[]);title('Second option')

As visualization, the second option provided more brightness value

Answer 1

The difference is the 'Sobel' operator indeed. The sobel operator is a matrix that is convoluted with the image to compute its directional gradients.

The sobel operator is defined as (from wikipedia):

while what gradient does is just directional differences. You can interpret this as gradient doing

Gx=[ 0 0 0;                Gx=[ 0 -1 0;
    -1 0 1;         and         0  0 0;
     0 0 0]                     0  1 0];

This difference is because when one has an image, it is know that it is a discretization of a continuous domain. The Sobel operator helps to take into account things that happen "around" the given pixel.