Game Development Reference
In-Depth Information
ˆ
im
xx
ˆ
im
f
−
yy
f
−
x
ˆ
y
ˆ
=
0
=
0
,
, and
r
2
=+
x
ˆ
2
y
ˆ
2
.
y
x
A similar discussion as that on the imaging-distortion coefficients in the previous
section also applies to the reconstruction-distortion coefficients
Re
d
p
.
Principal point vs. distortion center
T
xy
used in equations 10
and 12 could be different from the principal point employed in equation 3 (Wei
& Ma, 1994). On the other hand, under radial distortion with a dominant
coefficient
[
]
It has been realized that the
distortion center
0
0
Im
1
Re
1
k
), a small shift of the distortion center is equivalent to
adding two de-centering distortion terms (Ahmed & Farag, 2001). Therefore, if
the distortion is estimated independently of the calibration of other camera
parameters, the principal point for the linear perspective transformation should
be distinguished from the distortion center. However, if all camera parameters
(including distortion coefficients) are calibrated simultaneously, the distortion
center and the principal point should be treated as being the same. In this case,
it is better to take the de-centering distortion component into consideration.
k
(or
Discussions
Both imaging and reconstruction-distortion models have advantages and disad-
vantages (ref. Table 1). In general, the imaging-distortion model is more efficient
for distortion correction using the “backward mapping” strategy (Lei & Hendriks,
2002). The reconstruction-distortion model is preferable if the subsequent
processing is mainly concerned with the 3-D model recovering.
Both models have been adopted in the calibration literature (Heikkilä, 2000; Tsai,
1987). It was demonstrated by Heikkilä (2000) that they are equivalent with
proper compensation. A least-squares method was further proposed for the
conversion between the two sets of distortion coefficients. Which model should
be adopted for a real situation is application-dependent.
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