Image Processing Reference
In-Depth Information
Fig. 10.2. In
top, left
, the image generated by
g
(
t
)=sin(
ωt
) with the argument
t
=
k
T
r
is given. The
solid
and
dashed
vectors represent
k
and
−
k
respectively. The 3D graph in
top, right
represents
g
(
k
T
r
) as a surface. The FT magnitudes of
g
(
t
) and
g
(
k
T
r
) are shown
in
bottom, left
and
bottom, right
. The FT coordinates are in the angular frequencies
ω
and
(
ω
x
,ω
y
)
T
simplicity, we will therefore not make a distinction between an image and a local
neighborhood of it. Both variants will be referred to as an image here, unless an
ambiguity calls for further precision.
Below we detail the process of constructing linearly symmetric images from 1D
functions first by three examples of 1D functions
g
, that are continuous. The last one
of these will model an ideal line. Then we will study a discontinuous
g
which will
be a model of ideal edges. Both ideal lines and ideal edges have been used to model
and to detect discontinuities in image processing.
