Image Processing Reference
In-Depth Information
(
a
)
(
b
)
(
c
)
(
d
)
(
e
)
(
f
)
Fig. 2.4.
Lattice in 3D space and a neighborhood: (
a
) Cubic lattice 7 (6-
neighborhood); (
b
) cubic lattice 8; (
c
) face-centered cubic lattice 13 (12-
neighborhood); (
d
) face-centered cubic lattice 19 (18-neighborhood); (
e
) cubic lat-
tice 19 (18-neighborhood); (
f
) cubic lattice 27 (26-neighborhood).
(
a
)
(
b
)
(
c
)
Fig. 2.5.
Digitization of a 2D and a 3D line figure: (
a
) Digitization by pixel (2D);
(
b
) digitization by grid (2D); (
c
) digitization by voxel (3D).
2.2.4 3D line figures and digitization
Digitization of a line figure in the 3D space must be discussed in full, because
a line figure has no width. Let us consider first the case of a 2D line figure.
The following two methods are used in the digitization of a 2D line figure
(Fig. 2.5).
(1)
Digitization by pixel
: Divide the continuous plane into pixels. A pixel
which a line figure passes is assigned the value
1
, and otherwise the value
0
.
Since the probability that a line figure exactly passes through the border
of a pixel is regarded as zero, a resulting digital line figure always becomes
4-connected.
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