Game Development Reference
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In addition, the RAC model requires that the angle of incidence between the
optical axis of the camera and the calibration plane should be at least
0
30
(Tsai,
1987). This ill-conditioned situation can be avoided by setting cos
α
= 1 and sin
α
0 (Zhuang & Wu, 1996).
The above modifications improved the capabilities of the original Tsai's algo-
rithm. However, Tsai's algorithm can still only take the radial distortion into
consideration. And, the strategy of recovering several subsets of the whole
camera parameter space in separate steps may suffer from stability and
convergence problems due to the tight correlation between camera parameters
(Slama, 1980). It is desirable, therefore, to estimate all parameters simulta-
neously. Methods based on this idea are discussed below.
α
=
α
when
Iterative Two-Phase Strategy
During the 1980s, camera calibration techniques were mainly full-scale nonlinear
optimization incorporating distortion (Slama, 1980) or techniques that only take
into account the linear projection relation as depicted by equation 5 (Abdel-Aziz
& Karara, 1971). The
iterative two-phase strategy
was proposed at the
beginning of the 1990s to achieve a better performance by combining the above
two approaches (Weng et al., 1992). With this iterative strategy, a linear
estimation technique such as DLT is applied in phase 1 to approximate the
imaging process by
p
l
, and then in phase 2, starting with the linearly recovered
p
l
and
p
d
=
0
, an optimization process is performed iteratively until a best fitting
parameter point
p
c
is reached.
Because for most cameras, the linear model (ref. equation 5) is quite adequate,
and the distortion coefficients are very close to 0, it can be argued that this
iterative two-phase strategy would produce better results than pure linear
techniques or pure full-scale nonlinear search methods. Camera calibration
methods employing the iterative two-phase strategy differ mainly in the following
three aspects: 1) The adopted distortion model and distortion coefficients; 2) The
linear estimation technique; and 3) The objective function to be optimized. In Sid-
Ahmed & Boraie (1990), for example, the reconstruction-distortion model is
utilized and
k
1
Re
,
k
2
Re
,
k
3
Re
,
P
1
Re
, and
P
2
Re
are considered. The DLT method
introduced is directly employed in phase 1. Then, in phase 2, assuming that
[
]
T
x
0
is already known, the Marquardt method is used to solve a least-
squares problem with respect to
y
[
]
T
T
Re
1
Re
2
Re
3
Re
Re
2
(ref.
p
=
p
k
k
k
P
P
1
equation 21). All camera parameters are made
implicit
.
To further guarantee the geometric validity of the estimated
p
, one extra phase
can be introduced between phase 1 and phase 2. In this extra phase, elements
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