image processing - Is the Sobel Filter meant to be normalized? -

the x-derivative sobel looks way:

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

lets there 2 samples of image (0=black, 1=white):

0 0 1            1 0 0 0 0 1      &     1 0 0 0 0 1            1 0 0 

if perform convolution i'll end 4 , -4 respectively.

so natural response normalize result 8 , translate 0.5 - correct? (i wondering can't find wikipedia etc. mentioning normalization)

edit: use sobel filter create 2d structure tensor (with derivatives dx , dy):

                   b  structure tensor = c d   = dx^2        b = dx*dy       c = dx*dy        d = dy^2 

ultimately want store result in [0,1], right i'm wondering if have normalize sobel result (by default, not in order store it) or not, i.e.:

a = dx*dx  //or = (dx/8.0)*(dx/8.0) //or = (dx/8.0+0.5)*(dx/8.0+0.5) 

a mathematically correct normalization sobel filter 1/8, because brings result natural units of 1 gray-level per pixel. in practical programming, isn't right thing do.