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Royi
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Why are there two different common 3x3 kernelsAre There Two Different Common $ 3 \times 3 $ Kernels for the Laplacian?

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Why are there two different common 3x3 kernels for the Laplacian?

I find both of these 3x3 Laplacian kernels to be commonly used:

 0 -1  0
-1  4 -1
 0 -1  0

and:

-1 -1 -1
-1  8 -1
-1 -1 -1

Is there a reason to choose one or the other? What's the difference between them?

(My math is not good enough to understand the Wikipedia article, so I can't figure it out myself from reading that. Googling is failing me for this one.)