Image Processing Reference
In-Depth Information
logical properties as an original solid (this is the same for the polygon model
mentioned previously).
Remark 7.3.
Thresholding operations may be performed simultaneously to
render the segmentation of a figure. This algorithm is also used for rendering
an equidensity surface. The connectivity index (Chapter 4) may be used for
testing the topology preservation.
7.3 Cross section, surface, and projection
7.3.1 Cross section
A cross section is a 2D gray-tone image presenting the surface plane of an
object that appears when an object is cut by a plane. Most currently available
CT systems generate many axial sections of the human body cut by parallel
planes. The most basic way of visualization is to present these 2D sections
directly. In fact, a clinical diagnosis in medicine is usually performed in this
way, examining the set of cross-sectional images of the studied organs carefully.
It is not dicult to generate a section in another direction if enough numbers
of original sections are given with a small enough interval. A suitable 2D or
3D interpolation may become necessary to obtain a good quality of images if
the direction of sections is different from the direction of rows and columns of
initial voxels.
In many CT images, the spatial resolution on each cross-section image
(or a
slice
) and the interval between section planes (or between slices) are
different from each other. Usually the first is higher than the last. In recent
CT machines the size of a voxel in each slice and the interval between slices
(called
reconstruction pitch
) is chosen individually. These facts should be taken
into consideration when obtaining good quality 3D images. Slices are often
interpolated in order to create a given image more similar to a 3D image of
cubic voxels when the slice interval is significantly larger than the voxel size
in each slice.
A well-known simple method of interpolation is linear interpolation, as
follows: Denote an arbitrary point on a cross section by P and assume that
we need to determine the density of a point P (Fig. 7.3). Let us consider eight
sample points
a, b,
,h
on original slices shown in Fig. 7.3. Then denoting
the density values of those eight points by
f
a
,f
b
,
···
···
,f
h
the density value
f
P
of a point P is calculated as
f
P
=
w
a
f
a
+
w
b
f
b
+
···
+
w
h
f
h
,
(7.1)
where
w
a
,w
b
,
,w
h
are suitable weight coecients.
More complicated interpolation (using splines and sampling functions, for
example) also may be available. Significance, necessity, and effectiveness of
such complicated methods still strongly depend on individual applications.
···
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