Image Processing Reference
In-Depth Information
Fig. 5.23.
Digital knots of the length
4
.
Fig. 5.24.
Example of a link consisting of two digital knots of the length
12
.
in practical algorithms to calculate it. We will briefly introduce one idea to
treat the Voronoi tessellation on a 3D image.
Let us consider a set of figures
S
{
F
1
,F
2
,
···
,F
n
}
=
on a 3D binary
.Here
F
i
is an object (figure) in 3D space. Then, for an arbitrary
voxel Q in the background of
F
image
S
R
defined by the following
equation (5.30) is called a
dominance area
(or
Voronoi region
) of a figure
F
i
.
F
,asetofvoxels
S
R
=
{
Q; min
i
d
(Q
,F
i
)=
d
(Q
,F
R
)
,F
i
∈
S
}
(5.30)
S
is
F
R
= set of all background voxels such that the nearest figure in
The result of division of all background voxels into dominance areas of figures
F
i
s (Voronoi regions) is called
Voronoi tessellation
. In the case of a 2D image,
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