Game Development Reference
In-Depth Information
After that, some other approaches that utilize special calibration objects or
specific phenomena in the 3-D scene are summarized. Finally, the calibration is
evaluated and feature extraction issues are discussed.
Direct Linear Transformation (DLT)
Direct linear transformation
(
DLT
) (Abdel-Aziz & Karara, 1971) is the
simplest version of camera calibration and still plays a relatively important role
in computer vision. It can be applied if the distortion can be neglected or has been
removed in advance.
Without considering the distortion, from equation 4 the transfer function from a
3-D point
x
w
to the corresponding 2-D image pixel
x
im
can be described as:
x
w
1
1
1
1
1
t
p
p
p
p
1
2
3
4
w
y
2
2
2
2
2
t
≅
pppp
z
1
2
3
4
w
,
(17)
3
3
3
3
3
t
pppp
1
2
3
4
1
where
p
i
j
is the element of the matrix
~
at the
i
th
row and
j
th
column, and
, and
y
im
2
/
t
3
.
(18)
x
im
1
/
t
3
=
t
=
t
Substituting equation 18 into equation 17 and expanding the matrix product yields
the following two equations with 12 unknowns:
px
1
w
+
p y
1
w
+
pz
1
w
+
p
1
−
px x
3
w
im
−
p y x
3
w
im
−
pz x
3
w
im
−
px
3
im
=
0
,
(19)
1
2
3
4
1
2
3
4
2
w
2
w
2
w
2
3
w
im
3
w
im
3
w
im
3
im
px
+
py
+
pz
+
p
−
px y
−
py y
−
pz y
−
py
=
0
,
(20)
1
2
3
4
1
2
3
4
The 12 unknowns can be solved using
N
≥
6 points at
general positions
T
(Faugeras, 1993), with 3-D world coordinates
x
w
=
xyz
w
w
w
and corre-
i
i
i
i
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