The (first order) derivatives can be approximated better than using the finite difference. The Sobel operators shown in the following diagram are used quite frequently:
The 1/8 term is not included in the standard definition of the Sobel operator as for edge detection purposes, it does not make a difference, although the normalization term is needed to get the gradient value correctly. The next Python code snippet shows how to use the sobel_h(), sobel_y(), and sobel() functions of the filters module of scikit-image to find the horizontal/vertical edges and compute the gradient magnitude using the Sobel ...
