Image Processing Reference
In-Depth Information
Fig. 2.3.
Examples of CT slice images.
the 2D case. Quantization of density values is identical to that of a 2D image
(Fig. 2.2).
Avoxelatthe
i
-th row and the
j
-thcolumnonthe
k
-th plane is denoted
by a voxel (
i, j, k
). The notation
is employed to represent a 3D
digitized image (or simply a 3D image) in which the density value at a voxel
(
i, j, k
)isgivenby
f
ijk
. We usually understand the contents of a 3D image
by observing the array of 2D successive slices
F
=
{
f
ijk
}
for different
k
s,
whereas a computer accesses the 3D array directly. An example of a 3D digital
image is a set of cross sections of the human body obtained by CT or com-
putered (computerized) tomography system and MRI (magnetic resonance
imaging) system used in medicine (Fig. 2.3).
The physical meaning of the value of the function
f
is quite different from
those of 2D images. In 3D images values of
f
xyz
represent values of character-
istic features of an object at a point (
x, y, z
) and at the small volume element
including it. The contents vary according to the measurement technology em-
ployed in the imaging device. A few examples are shown below.
F
k
=
{
f
ij
(
k
)
}
(1) X-ray CT image: Attenuation or absorption factor to the X-ray of an ob-
ject.
(2) PET (positron emission CT) image: Intensity of
γ
-ray emitted from the
volume element of an object.
(3) MRI (magnetic resonance imaging): Strength of magnetic resonance at
the volume element of an object.
(4) 3D ultrasound image: The intensity of the ultrasound wave reflected by
an object.
Remark 2.2 (3D lattice).
An advantage of using a sampling point lattice
is that results known in physics, crystallography, and other fields can be used
effectively. A few well-known examples of lattices in 3D space are shown in
Fig. 2.4. In 3D image processing, use of voxels corresponding to those lattices
is also required. From the viewpoint of ease of treating voxels, the cubic lattice
is used in most practical applications.
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