The Mean Operation ($K_0$):
Acts as a low-pass filter. Each output pixel is the average of its $3 \times 3$ neighborhood:
$$ K_{0} = \frac{1}{9} \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix} $$
Instructions: Hover over any Output cell ($\mathbf{Y}$) to see the corresponding receptive field in the Input ($\mathbf{X}$).
The different kernels capture different spatial frequencies. $K_0$ smooths the signal, while $K_1$ and $K_2$ emphasize high-frequency changes.