Image Processing Reference
In-Depth Information
Fig. 11.12
The spherical transformation
Fig. 11.13
The ripple transformation
11.2.4 Ripple Transformation
Another interesting non-linear geometric mapping is the ripple transformation. It
distorts the image locally using a sinus function. The effect is that an overall wave
pattern is introduced to the image. The backward mapping for the ripple transfor-
mation is defined as
sin
y
·
2
π
ω
x
x
+
x
=
a
x
·
(11.17)
sin
x
·
2
π
ω
y
y
+
y
=
a
y
·
(11.18)
where
a
x
and
a
y
are the amplitudes of the wave pattern in the x- and y-directions,
respectively and
ω
x
and
ω
y
control the frequencies of the waves in the x- and y-
directions, respectively. In Fig.
11.13
the ripple transformation is illustrated.
