VISUALIZATION OF 3D GRAY-TONE IMAGES - Fundamentals of Three-Dimensional Digital Image Processing - page 228

the progress of this field [Nishita85, Cohen85, Cohen88]. For details, see topics
on technical computer graphics [Watt98].
However, a different kind of rendering has attracted much attention in
these years, and this rendering is called nonphotorealistic rendering . This tech-
nique aims at generating a freer style of images such as pictures that look like
classical European style paintings, those similar to India-ink paintings, and
those similar to other fine arts produced by human artists.
We stress that visualization is different from any of those. The most im-
portant feature of this is using rendering as a tool to understand the charac-
teristics of given data (a 3D gray-tone image). We must consider that a 3D
image that is to be visualized is put at the position of an object in Fig. 7.12,
and a viewpoint and an image plane are the same as in that figure. All other
factors such as a light source and the interaction of objects and light itself are
simply tools for perceiving the data structure with the human vision. There
do not always have to be meanings related to real optical and other physical
phenomena. The process of volume rendering described in the next section
is regarded as a method developed for visualization of a 3D gray-tone image
with a rough analogy of optical phenomena.

7.8 Displaying density values based on ray casting -
volume rendering

7.8.1 The algorithm of volume rendering

Consider a 3D image in which each point has a density value (3D gray-tone
image). Using the same scheme of ray casting as in the previous section, a
point P in 3D space (virtual space) is projected to a point P on an image
plane H P (Fig. 7.13). Then all points on a line segment connecting a view-
point V e and a point P (wecallthislinea ray , too) are projected to the
same point P . This means that all points on this ray in 3D space are seen,
overlapping each other at the position P . The problem to be solved here is
how to visualize information of density values at these points. One basic idea
employed here is to accumulate in some ways information stored at points
on the ray. A color or brightness value of a point P on an image plane is
determined by a result of this accumulation. This method is called volume
rendering [Levoy88, Drebin88]. Below we present a procedure to perform this
processing (Fig. 7.13).
First let us assume that a brightness value b i is stored at a point P i in
a 3D image, and that an intermediate result of accumulation I in ( i ) has been
sent to P i . Then a brightness value I out ( i ) given below is output to be sent to
the next point.

(7.11)
Here a letter i represents the sequential number given to a sample point (voxel)
selected along a current ray, which is smaller at a point further from a view-

I out ( i )= I in ( i ) · ( 1 − α i )+ b i · α i