The Robert cross operator performs a simple, quick to compute, 2-D spatial gradient measurement on image. The output pixels values at each point represent the absolute magnitude of the spatial gradient of the input at that point.
The operator consists of a pair of 2×2 convolution masks kernels as shown. One kernel is simply rotated by the other by 90 degree. It is very similiar to the Sobel operator
Gx=
Gy
These masks are designed to respond maximally to edges running at 45° o the pixel grid
Then these are applied to the input image to produce separate measurements of gradient component in each orientation. Gx and Gy
The gradient magnitude is given by
The angle of orientation of the edge giving rise to the spatial gradient
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