Image Processing Reference
In-Depth Information
A brightness value
I
out
(
i
) to be output at a point P
i
along a ray is given
by the following equation.
I
out
(
i
)=
I
out
(
i
−
1
)+
β
i
·
b
i
,
i−
1
β
i
=
α
i
·
(
1
−
α
k
)
,
(7.15)
k
=1
where
α
i
= opacity value at a point P
i
,
b
i
= brightness value at a point P
i
.
The number
i
is given in the increasing order starting at a sample point
nearest to a viewpoint on a ray. The
β
i
in Eq. 7.15 is called
accumulated
opacity
. The calculation is iterated on each ray until a point is reached that
is regarded as having no significant effect on density values of a rendered
image. A resulting value of
I
out
(
i
) (accumulated brightness value) is given to
a corresponding pixel on a 2D image on an image plane.
This procedure is intuitively interpreted as follows. Let us assume first
that the
i
-th point P
i
has the brightness value
b
i
and opacity
α
i
.Thenwe
consider that there is a light source of the power
α
i
b
i
. The light reaches a
viewpoint (or an image plane) after passing through points P
i−
1
,
P
i−
2
,...,
P
i
.
The fraction (
1
·
b
i
incident to P
i−
1
passes through point P
i−
1
and
comes to the next point. Total sum of contribution from all of
K
sample points
on a ray to a viewpoint is given to a corresponding pixel on an image plane
as its density value (color value). In fact,
I
out
(
i
) of Eq. 7.15 is expressed as
follows considering all contributions from the
K
-th sample point to the first
sample point.
−
α
i
)
·
α
i
·
b
k
α
k
α
n
)
.
K
k−
1
I
out
(
K
)=
I
out
(
0
)+
b
1
α
1
+
(
1
−
(7.16)
k
=2
n
=1
Each term in the summation
in the right-hand side of this equation corre-
sponds to the term interpreted as was explained above.
7.8.4 Properties of volume rendering and surface rendering
Let us summarize properties of volume rendering compared with surface ren-
dering.
(a) Volume rendering
(1) Volume rendering can be applied without extracting surfaces to be visual-
ized beforehand. In this sense, volume rendering is a tool to visualize or to
observe the structure of a 3D gray-tone image that has not been structur-
ized yet. It does not require any preprocessing such as segmentation and
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