The Sobel operator applies two 3x3 convolution kernels to the input image. These kernels are designed to respond maximally to edges running horizontally and vertically relative to the pixel grid. The kernels are:
Gx (horizontal changes):
[[-1, 0, +1],
[-2, 0, +2],
[-1, 0, +1]]
Gy (vertical changes):
[[-1, -2, -1],
[ 0, 0, 0],
[+1, +2, +1]]
By convolving these kernels with the image, the algorithm produces two gradient images which are then combined to create an overall gradient magnitude image. This highlights the edges within the histological sample.
