It is used for image sharpening and image edge detection.

Different operators correspond to different methods to find the gradient:

Take Sobel operator (with good effect) as an example:

For digital images, first-order differential can be used instead of first-order differential;

△xf(x，y)=f(x，y)-f(x- 1，y)；

△yf(x，y)=f(x，y)-f(x，y- 1)

When calculating the gradient, the sum of squares and the root operation can be expressed by the sum of the absolute values of two components, namely:

G[f(x，y)]={[△xf(x，y)] +[△yf(x，y)] } |△xf(x，y)|+|△yf(x，y)|；

Sobel gradient operator is to do a weighted average first, then differentiate, and then find the gradient, that is:

△xf(x，y)= f(x- 1，y+ 1) + 2f(x，y+ 1) + f(x+ 1，y+ 1)- f(x- 1，y- 1) - 2f(x，y- 1) - f(x+ 1，y- 1)

△yf(x，y)= f(x- 1，y- 1) + 2f(x- 1，y) + f(x- 1，y+ 1)- f(x+ 1，y- 1) - 2f(x+ 1，y) - f(x+ 1，y)

G[f(x，y)]=|△xf(x，y)|+|△yf(x，y)|；