Image Processing Reference
In-Depth Information
to use display on a 2D image plane (or mapping onto a 2D plane), because
the human vision cannot observe the whole of the 3D image directly. This is
the major premise in considering visualization discussed in this chapter.
We will add the following minor premises:
(i) The input to visualization procedure or the object data used to be visu-
alized are voxel data representing a 3D gray-tone image.
(ii) Input data (an input 3D image) are given beforehand. They are usually
obtained experimentally or as a result of observation or measurement.
Mathematical descriptions and definitions of an explicit form are rarely
available.
These facts stand in remarkable contrast to computer graphics in which
most of the visualized objects are described by mathematical expressions or
algorithms. More exactly, objects defined mathematically or by way of an
algorithmic procedure will also be contained in a target of visualization. We
need to treat the above types of data in visualization as well as well-formed
data.
Remark 7.1.
There are exceptional cases in which a 3D input image can be
visualized on a 2D plane without losing any information:
(1) All 2D cross sections are presented as 2D images. This is a popular method
in the medical diagnosis of X-ray CT images. It often takes a lot of work
for human observers to do this due to large numbers of images that need
examining. The 3D form of an object, in particular one featuring the
spatial distribution of density values, is dicult to interpret.
(2) A 3D object consisting of a limited number of curved surfaces and polygons
is drawn exactly by various methods of descriptive geometry such as a set
of orthogonal projections in three directions which are perpendicular to
each other. It is not easy for those unfamiliar with these drawing methods
to intuitively understand 3D shapes.
(3) A polyhedron is specified by a net on a plane without any ambiguity.
(4) An “origami” is drawn on a 2D plane in the form of a net with folding
lines. This is used mainly to explain the procedure generating individual
work, and helps to visualize the procedure rather than the form. In fact
we hardly can imagine a 3D shape of an “origami” work from its net.
Thus a result drawn using the above methods of Remark 7.1 is not al-
ways comprehensible. Sometimes a stereoscopic display can be useful in some
kinds of applications, although these are not discussed here. In some computer
graphics applications, we may be able to design a 3D image (or the structure
of the 3D space) so that display results on a 2D plane are more effective for
observers. In the visualization, however, the given 3D data cannot be changed
in principle.
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