Sobel Operator - Extension To Other Dimensions

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:

h_z'(:,:,-1) = \begin{bmatrix} +1 & +2 & +1 \\ +2 & +4 & +2 \\ +1 & +2 & +1 \end{bmatrix} \quad h_z'(:,:,0) = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix} \quad h_z'(:,:,1) = \begin{bmatrix} -1 & -2 & -1 \\ -2 & -4 & -2 \\ -1 & -2 & -1 \end{bmatrix}

Read more about this topic:  Sobel Operator

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