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.