Graphics Reference
In-Depth Information
1.4.5 The Camera Calibration Toolbox by Bouguet (
2007
)
Bouguet (
2007
) provides a toolbox for the calibration of multiple cameras imple-
mented in Matlab. The calibration images should display a chequerboard pattern,
where the reference points have to be selected manually. The toolbox then deter-
mines the intrinsic and extrinsic parameters of all cameras. It is also possible to
rectify pairs of stereo images into standard geometry. The toolbox employs the cam-
era model by Heikkilä and Silvén (
1997
), where the utilised intrinsic and extrinsic
parameters are similar to those described in Sect.
1.1
.
1.4.6 Self-calibration of Camera Systems from Multiple Views
of a Static Scene
The camera calibration approaches regarded so far (cf. Sects.
1.4.2
-
1.4.5
) all rely
on a set of images of a calibration rig of known geometry with well-defined control
points that can be extracted at high accuracy from the calibration images. Camera
calibration without a dedicated calibration rig, thus exclusively relying on feature
points extracted from a set of images of a scene of unknown geometry and the
established correspondences between them, is termed 'self-calibration'.
1.4.6.1 Projective Reconstruction: Determination of the Fundamental Matrix
This section follows the presentation by Hartley and Zisserman (
2003
). The first step
of self-calibration from multiple views of an unknown static scene is the determi-
nation of the fundamental matrix
F
between image pairs as defined in Sect.
1.2.2
.
This procedure immediately allows us to compute a projective reconstruction of
the scene based on the camera projection matrices
P
1
and
P
2
which can be com-
puted with (
1.21
) and (
1.22
). As soon as seven or more point correspondences
(
S
1
x
,
S
2
x
)
are available, the fundamental matrix
F
can be computed based on (
1.19
).
We express the image points
˜
˜
S
1
S
2
x
in normalised coordinates by the vectors
(u
1
,v
1
,
1
)
T
and
(u
2
,v
2
,
1
)
T
. Each point correspondence provides an equation for
the matrix elements of
F
according to
x
and
˜
˜
u
1
u
2
F
11
+
u
2
v
1
F
12
+
u
2
F
13
+
u
1
v
2
F
21
+
v
1
v
2
F
22
+
v
2
F
23
+
u
1
F
31
+
v
1
F
32
+
F
33
=
0
.
(1.50)
In (
1.50
), the coefficients of the matrix elements of
F
only depend on the measured
coordinates of
x
. Hartley and Zisserman (
2003
) define the vector
f
of
length 9 as being composed of the matrix elements taken row-wise from
F
. Equa-
tion (
1.50
) then becomes
S
1
x
S
2
˜
and
˜
(u
1
u
2
,u
2
v
1
,u
2
,u
1
v
2
,v
1
v
2
,v
2
,u
1
,v
1
,
1
)
f
=
0
.
(1.51)
Search WWH ::
Custom Search