Image Processing Reference
In-Depth Information
Fig. 10.4. (
Top
) The gray image is generated by substituting
t
=
k
T
r
in Eq. (10.4). The 3D
graph shows
g
(
k
T
r
).(
Bottom
) The 1D and 2D FT magnitudes of
g
(
t
) and
g
(
k
T
r
), respec-
tively
pure lines and edges, without a provision for other types of patterns that have well-
defined directions. In the next example, we show that pure lines can be modeled as a
linearly symmetric function generated by means of an analytic function, a Gaussian.
Example 10.3. The 1D Gaussian
g
(
t
)=exp
,
t
2
2
σ
2
−
with
σ
=3
,
(10.5)
is plotted as the green curve in Fig. 10.5. The synthetic image represented by the
function
g
(
k
T
r
) is linearly symmetric and is illustrated by the gray image in Fig.
10.5. The function values are scaled and linearly mapped to 256 gray tones, with 0
correspondingtoblack,and1correspondingtowhite.Inthedirectionof
k
,anycross
section of the image is identical to the 1D Gaussian of Fig. 10.5.
