Game Development Reference
In-Depth Information
By further requiring that
a
12
= 1 or (
a
9
)
2
+ (
a
10
)
2
+ (
a
11
)
2
= 1, we can carry out a
constrained non-linear search to obtain the 10 independent parameters (
x
0
,
y
0
,
a
3
,
a
4
,
a
6
, ...,
a
11
; in case
a
12
= 1) or (
x
0
,
y
0
,
a
3
,
a
4
,
a
6
, ...,
a
10
,
a
12
; in case (
a
9
)
2
+ (
a
10
)
2
+ (
a
11
)
2
= 1).
Up to this point, only linear relations in the imaging process were considered. This
already suffices if one aims more at efficiency than accuracy. However, for
highly accurate measurements, the distortion should also be taken into account.
A straightforward way to achieve this is to incorporate the distortion coefficients
directly into the DLT calculation by adding some nonlinear elements. This is the
topic of the next section.
DLT Considering Distortion
Both simple DLT and geometrically valid DLTs cannot take the distortion
component into account. In this section, an innovative way of incorporating the
distortion into the DLT is discussed. Its advantages and disadvantages are
addressed, as well.
Because of the existence of two distortion models, the 3-D reconstruction and
the projection have to be handled differently.
Two-plane approach using reconstruction-distortion model
This approach is used for 3-D reconstruction.
Rearranging equation 5, we obtain:
w
w
−
1
im
w
xRKxt
≅
+
,
(31)
c
c
where
−
1/
f
0
x
/
f
x
0
x
K
−
1
=
0
−
1/
f
yf
/
.
(32)
y
0
y
0
0
1
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