Image Processing Reference
In-Depth Information
Fig. 11.11
The twirl transformation
So, for each pixel
(x
,y
)
in the output image, we calculate a pixel position in the
input image
(x, y)
using Eqs.
11.12
and
11.13
. If the calculated pixel position is not
within the input image, we set
(x
,y
)
to black. In Fig.
11.11
the twirl transformation
is illustrated.
11.2.3 Spherical Transformation
This transform zooms in on the center of the image. The size of the zoomed area is
defined by
S
. The actual zoom effect is similar to how a lens would bend the light.
This is normally referred to as the refractive index,
n
. The backward mapping is
defined as
x
=
x
−
t
·
tan
(α
x
)
(11.14)
y
=
y
−
t
·
tan
(α
y
)
(11.15)
√
S
2
=
−
r
2
where
t
and
1
sin
−
1
,
1
n
x
√
x
2
α
x
=
−
·
t
2
+
1
sin
−
1
(11.16)
1
n
x
y
2
α
y
=
−
·
+
t
2
where
S
and
n
are defined by the user, and
x
and
y
are defined as above. Equa-
tions
11.14
and
11.15
are only defined for
r<S
. When this is not the case the
transformation is reduced to
x
y
. As for the transformation above,
we will insert a black pixel if the transformation results in a pixel outside the input
image. In Fig.
11.12
the spherical transformation is illustrated.
x
=
=
and
y
