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