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What is a gradient? Please give an example. Tangible expression is the best ~
The gradient value is the place where the gray value of the image changes significantly.

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)|;