How do Perwitt and Sobel detect edges?

Question

I read up on the Perwitt operator and it detects two types of edges (vertical and horizontal). The Sobel operator on the other hand does the same as the Perwitt except that the masks are not constant and could be dynamically adjusted. Why do the Sobel and the Perwitt matrices compute horizontal and vertical gradients?

Answer 1

Both Sobel and Prewitt imitate the Derivative to some degree.
The concept is to imitate the derivative using filters as in Finite Difference Coefficients.

The difference between them is choosing the values of the coefficient to balance some spatial phenomenons.