Image Processing Reference
In-Depth Information
be taken into consideration. It is not an original image itself but the spatial
distribution of the opacity that is visualized. Therefore, improper settings of
opacity parameters
{
α
i
}
also may cause artifacts.
Remark 7.10.
A 3D image (which is a set of density values filling 3D space)
is compared to a 3D space filled with dirty water or is seen as a foggy world in
which the density varies from place to place. Volume rendering is compared
to looking though such a space. A borderline or a border surface that we can
perceive on a 2D image rendered on an image plane can be seen as a result of
looking through such a world in a certain direction. It cannot be recognized
in its vicinity like a border of clouds in the sky. An object that is seen vaguely
at a distant place could be a solid wall of a building. The suitable setting of
opacities makes it possible to visualize an example such as the latter one.
Remark 7.11.
If we project the simple sum of density values along a ray to a
point P without designating a particular value for
, the result is approxi-
mately equivalent to the projection mentioned in Section 7.3.3. If a viewpoint
is infinitely far, the projection method reduces to the orthogonal projection
in Section 7.4 and the result coincides with the projection mentioned in Sec-
tion 7.3. The density values on a projected image may be a little different
from each other due to different approximations employed in the projection
performed in the digitized space. This type of projection is regarded as a
type of simulation in an imaging process. For example, in the visualization
of a 3D image obtained by X-ray CT, the above projection for visualization
is regarded as the simulation of taking an X-ray image of the human body,
in which an X-ray source is at the position of a viewpoint and an X-ray film
is put on a projection plane. This is an ideal imaging situation in which an
X-ray source is a point source and no scattering occurs by an object. An X-ray
source can be put at an arbitrary place in the human body in this simulation.
From this viewpoint, it might be possible to generate interesting images.
{
α
i
}
Remark 7.12.
The volume rendering explained above is a tool of visualiza-
tion and does not always relate exactly to real physical phenomena. Some
other methods of rendering have been developed that intend to simulate opti-
cal phenomena occurring along a ray propagating through continuous media
such as air and water. Effects of optical phenomena such as reflection, refrac-
tion, scattering, and absorption are accumulated along a path of light and
utilized to render a scene irradiated by various light sources. Those methods
are sometimes named
volume rendering
, too. Examples of applications include
rendering of cloud, fog, flare, smoke, and gemstones including impurity. This
kind of method originated from [Kajiya82, Kajiya84] and has been studied
actively in the field of computer graphics [Yokoi86, Nishita85, Horiuchi87,
Kurashige86, SIGGRPH88], etc. The expression such as “rendering volume
densities” was used in their papers. The term of volume rendering seems to
be first used in [Levoy88] among journal papers and appeared in several con-
ference proceedings about the same time.
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