Image Processing Reference
In-Depth Information
1
0.8
0.6
0.4
0.2
0
−80
−60
−40
−20
0
20
40
60
80
1
0.8
0.6
0.4
0.2
0
−1.5
−1
−0.5
0
0.5
1
1.5
Fig. 10.6. (
Top
) The graph represents the 1D step function
g
(
t
) in Eq. (10.6) and the 2D
function generated by the substitution
t
=
k
T
r
. The
solid
and
dashed
vectors represent
k
and
−
k
, respectively. (
Bottom
) The 1D FT magnitude of
g
(
t
) and the 2D FT magnitude of
g
(
k
T
r
)
are illustrated by the (
left
) graphics and the (
right
) image, respectively
is discontinuous. It is shown as the green curve in Fig. 10.6 with its corresponding
linearly symmetric gray image, which is obtained by sampling
1
,
if
k
x
x
+
k
y
y
≥
0
,
g
(
k
T
r
)=
(10.7)
0
,
otherwise
.
The gray image models what came to be known as the ideal edge in image process-
ing. Despite the fact that it is discontinuous, it too is a linearly symmetric function,
with Fourier transform magnitudes concentrated to the same central line as in the
previous examples.
