Game Development Reference
In-Depth Information
c
im
x
c
xx
im
f
−
y
yy
f
−
x
'
y
'
=−
=
0
=−
=
0
,
, and
r
2
=+
xy
'
2
'
2
.
c
z
c
z
y
x
Im
3
Im
1
,
Im
2
,
k
(Radial),
Im
,
Im
(De-centering), and
Im
,
Im
2
(Thin Prim)
k
k
P
P
s
s
Im
y
∆
represent
distortions in the horizontal (x-axis) and vertical (y-axis) directions, respectively.
The radial distortion is caused by the fact that objects at different angular
distances from the lens axis undergo different magnifications. The de-centering
distortion is due to the fact that the optical centers of multiple lenses are not
correctly aligned with the center of the camera. The thin-prim distortion arises
from the imperfection in the lens design and manufacturing, as well as the
camera assembly.
This distortion model can be simplified by neglecting certain parameters.
Im
x
represent the imaging-distortion coefficients, while
∆
and
Im
1
k
usually accounts for about 90% of the total distortion (Slama, 1980). For
example, in some cases, only radial and tangential components were taken into
consideration. The effect of the thin prim coefficients (
2
s
) was
overlooked without affecting the final accuracy, because this component only
causes additional radial and tangential distortions (Weng et al., 1992).
Im
and
Im
s
Reconstruction-distortion model
Besides being modeled as imaging distortion, the distortion can also be modeled
as
“reconstruction distortion”
as follows:
Re
=
im
ˆ
ˆ
im
f
⋅∆
x
x
x
x
−
,
(12)
Re
im
im
f
⋅∆
y
y
y
y
where
Re
∆
ˆ
2
ˆ
4
ˆ
6
ˆ
2
2
ˆ ˆ
2
xr
xr
xr
2
x
+
r
2
xy
r
0
x
Re
=
⋅
p
,
(13)
Re
d
∆
ˆ
2
ˆ
4
ˆ
6
ˆ ˆ
ˆ
2
2
2
yr
yr
yr
2
xy
2
y
+
r
0
r
y
T
Re
Re
Re
Re
Re
Re
Re
Re
p
=
k
k
k
PPs
s
,
d
1
2
3
1
2
1
2
Search WWH ::
Custom Search