Image Processing Reference
In-Depth Information
1
0.8
0.6
0.4
0.2
0
−40
−30
−20
−10
0
10
20
30
40
1
0.8
0.6
0.4
0.2
0
−1.5
−1
−0.5
0
0.5
1
1.5
Fig. 10.5. (
Top
) The graph represents the 1D Gaussian
g
(
t
) in Eq. (10.5) 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
When we study the 2D Fourier transform magnitudes of this linearly symmetric
image, Fig. 10.5 bottom, right, we note that it too equals to zero (red) outside of the
same central line (bright yellow) as in the previous two examples. The line has a
profile matching the 1D version of the Fourier transform magnitude, shown in the
bottom, left graph.
Example 10.4. The 1D step function
g
(
t
)=
1
,
if
t ≥
0
,
(10.6)
0
,
otherwise
,
