Graphics Reference
In-Depth Information
Fig. 4.8
C-space expansion in disparity space: original left view image (
a
), stereo disparity map
(
b
), C-space expanded disparity map (
c
), pixels with warmer colors are located closer to the observer
(a)
(b)
ZY view
XZ view
1.4
1.8
1.6
1.2
S
1.4
1
1.2
P
0.8
S
1
0.8
0.6
P
0.6
0.4
0.4
0.2
0.2
0
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
−1 −0.8 −0.6 −0.4 −0.2
0
0.2
0.4
0.6
0.8
1
z
x
Fig. 4.9
C-space expansion example: The expansion
square
covers the expansion
sphere
from the
camera view point (0, 0, 0) completely—its disparity is constant.
a
side view in ZY plane,
b
top
down view in XZ plane
Technically, this expansion operation increases the expansion volume around
a world point, since the correct projection of a sphere into the image is a circle,
but this method has the advantage that the operation now is separable into two 1D
operations—a horizontal expansion along image scan lines and a vertical expansion
along image columns—reducing computational cost significantly.
The horizontal and vertical expansion limits depend on the viewing angle of each
pixel and the expansion radius
r
v
. The horizontal viewing angle
ʱ
to a point
P
in
world coordinates is defined as
tan
−
1
ʱ
=
(
z
w
/
x
w
)
(4.6)
and the horizontal angular field of view
of the expansion sphere
S
around
P
is
defined by the distance of
P
from the camera origin and the expansion radius
r
v
ʳ
2sin
−
1
r
v
/
x
w
z
w
+
ʳ
=
2
ʱ
1
=
(4.7)
