
164 Image Enhancement and Correction
the gradient magnitude is maximum. Like the gradient operator, the Lapla-
cian operator can also be approximated by a spatial filter, for example,
h =
0 1 0
1 −4 1
0 1 0
. (5.6)
Its power spectrum is depicted in Figure 5.3. This filter ha s the desired
property of retur ning zero in regions of constant intensity and in regions of
constantly varying intensity (e.g., ramps), but nonzero at their onset or ter-
mination. Laplacian filters tend to be very sensitive to image noise. Often a
low-pass Gauss ian filter is fir st used to smooth the image before the Lapla-
cian filter is applied. This is eq uivalent to calculating ...