Graphics Reference
In-Depth Information
Fig. 6.14
Detail of the cumulative histogram with discrete values.
˄
is calculated by determining
x
˃
m
and
x
˃
m
+
1, such that
H
(
x
˃
m
)
≤
˃
m
and
H
(
x
˃
m
+
)>˃
m
,where
˃
m
represents a depth
1
plane number
cross section represents a depth plane
m
. The actual depth fraction
˄
m
for each cross
section
˃
m
, i.e., a depth plane, is calculated by first determining the depth value
x
˃
m
where
H
)>˃
m
. This is demonstrated in Fig.
6.14
.
Because the depth values
x
in the cumulative histogram are discrete, finding a value
x
˃
m
where
H
(
x
˃
m
)
≤
˃
m
and
H
(
x
˃
m
+
1
x
˃
m
)
=
˃
m
is unlikely, and not desirable when generating planes
that are dense, i.e., closer together, than the depth values provided in the cumulative
histogram.
Once
x
˃
m
is determined,
(
˄
m
is calculated as follows:
m
ʻ
−
H
(
x
)
˃
m
ʾ
=
(6.13)
H
(
x
+
1
)
−
H
(
x
)
˃
m
˃
m
˄
m
=
ʾ(
x
+
1
)
+
(
1
−
ʾ)(
x
)
(6.14)
˃
m
˃
m
Figure
6.13
b shows the transformation from a uniform depth plane distribution to
a nonuniform distribution based on the cumulative histogram. In region (1), where
the cumulative histogram is steep, there is a dense plane distribution, as can be seen
at (1*). When the cumulative histogram is flat, a sparse plane distribution is acquired,
as can be seen at (2*).
Using
˄
m
, an actual depth for every plane
m
(0
≤
m
<
M
) is determined and
used in the plane sweeping step:
D
m
=
D
min
+
˄
m
(
D
max
−
D
min
)
(6.15)
This is depicted in Fig.
6.15
. Here, the planes are redistributed using the cumulative
histogram of Fig.
6.13
b. More planes are available for determining the depth of the
objects, and less planes are available in empty space. It is desirable to include some
planes in the empty spaces between objects to allow the appearance of objects in
dynamic scenes. To allow this, all the values in the histogram are increased with a
fixed number, based on the number of pixels. This way, the cumulative histogram is
less flat in less interesting regions, allowing some planes here.
