Differential coding of images

Given an original image $l(x,y),$ using a

simple difference operator we can define a

difference image $d(x,y)$ as follows:

$d(x,y)=I(x,y)-I(x-1,y)$

Another approach is to use the discrete

version of the $2$D Laplacian operator to

define a difference image $d(x,y)$ as:

$d(x,y)=4I(x,y)-I(x,y-1)-I(x,y+1)$

$-I(x+1,y)-I(x-1,y)$

$($b$)$

$($b$)$

Fig. $7\mathrm{.}16$ Distributions for original versus derivative images, a$.$ b original gray$-$level image and

its partial derivative image; $c,d$ histograms for arigimal and derivative imges. This figure uses a

commonly employed image callod Bart