How do you handle negative pixel values after filtering?

Question

I have a 8-bit image and I want to filter it with a matrix for edge detection. My kernel matrix is

0  1  0
1 -4  1
0  1  0

For some indic

Answer 1

Out of range values are extremely common in JPEG. One handles them by clamping.

If X < 0 then X := 0 ;   
If X > 255 then X := 255 ;