Extension To Other Dimensions
The Sobel operator consist of two separable operations :
- Smoothing perpendicular to the derivative direction with a triangle filter :
- Simple central difference in the derivative direction :
Sobel filters for image derivatives in different dimensions with :
1D:
2D:
3D:
4D:
Thus as an example the 3D Sobel kernel in z-direction:
Read more about this topic: Sobel Operator
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