Game Development Reference
In-Depth Information
1992). Any more elaborate distortion model than a radial one could help in
increasing the accuracy, but may incur numerical instability (Tsai, 1987). Thus,
most calibration algorithms usually take into account only the radial distortion.
However, when wide-angle cameras are used, adding a non-radial distortion
component in the distortion model will improve accuracy significantly (Weng,
Cohen & Herniou, 1992).
Therefore, the complexity of the distortion model (i.e., the number of distortion
coefficients considered) should match the available computation resources and
the accuracy required by the application.
Distortion Models
Two different models have been constructed to describe the distortion phenom-
enon. They were developed for the purpose of projection and that of 3-D
reconstruction, respectively.
Imaging-distortion model
For the camera projection purpose, the distortion can be modeled as “imaging
distortion” as:
Im
ˆ
ˆ
im
im
f
⋅∆
=
x
x
x
x
+
,
(10)
Im
im
im
f
⋅∆
y
y
y
y
where
∆
Im
2
4
6
2
2
2
xr
'
xr
'
xr
'
2'
x
+
r
2' '
x y
r
0
x
=
⋅
p
Im
, (11)
d
∆
Im
yr
'
2
yr
'
4
yr
'
6
2
xy
'
'
2
y
'
2
+
r
2
0
r
2
y
T
Im
Im
Im
Im
Im
Im
Im
Im
p
=
k
k
k
PPs
s
,
d
1
2
3
1
2
1
2
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