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 x )
(11.14)
y = y t ·
tan 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
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