What is the 5×5 equivalent of the 3×3 emboss kernel?

-2  -1  0
-1   1  1
 0   1  2

This is 3×3 emboss kernel. How should I write this in 5×5?

Answer

As I understand, these filters take directional differences (see the wikipidea page).

We can decompose you filter into directions

0 -1  0        0  0  0       -2  0  0

0  0  0       -1  0  1        0  0  0

0  1  0        0  0  0        0  0  2

So, I think you can expand it over these 3 directions giving emphasis

0  0 -1  0  0        0  0  0  0  0       -2  0  0  0  0

0  0 -1  0  0        0  0  0  0  0        0 -2  0  0  0

0  0  0  0  0       -1 -1  0  1  1        0  0  0  0  0

0  0  1  0  0        0  0  0  0  0        0  0  0  2  0

0  0  1  0  0        0  0  0  0  0        0  0  0  0  2

So, the final kernel would be

-2  0 -1  0  0

 0 -2 -1  0  0

-1 -1  1  1  1

 0  0  1  2  0

 0  0  1  0  2

May be you can also try interpolating filter coefficients marked as x

-2  x -1  0  0

 x -2 -1  0  0

-1 -1  1  1  1

 0  0  1  2  x

 0  0  1  x  2