Image Processing Reference
In-Depth Information
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7
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10
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100
0
12
8
O
c
Z
c
3
13
100
X
c
1000
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Y
c
800
600
100
0
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Fig. 13.6. The various placements of the calibration pattern relative to the camera as computed
from the extrinsic parameters,
M
E
tion pattern, which is the world frame, at different positions but relative to the fixed
camera frame. Equivalently, each
M
E
expresses the position and the rotation of the
camera frame with respect to the world frame, which can be assumed fixed.
Example 13.1. The correspondences can be established by letting the camera ob-
serveaknownpattern,thecalibration pattern.Figure13.4illustratesadigitalcamera
calibrationset-up.Twodigitalcamerasofdifferentbrandswillbecalibrated,i.e.,the
intrinsic and extrinsic parameters of each of the cameras w.r.t. a (world) coordinate
frame will be determined. Each camera images calibration pattern whose geometry
isfullyknown,e.g,inthecaseofthefigurethismeansthatthecheckerboardconsists
of black and white squares with side length of 28 mm.
The world coordinate frame is assumed to be attached to the pattern (Fig. 13.5).
Because the sizes of the squares are known and the world coordinate frame is at-
tached to the calibration pattern, the world point coordinates,
X
j
,Y
j
,Z
j
,ofthe
corners of the squares are therefore known. Their corresponding image points
c
j
,r
j
can be identified in the camera image either automatically, e.g., by the lack of linear
symmetry technique discussed in Sect. 10.9 or manually. Together, this knowledge
allows us to determine
c
j
,
r
j
corresponding to the rows of the matrix
B
. For each
view imaged by the camera one can thus compute the data matrix
B
and thereby the
matrix
B
T
B
, least eigenvector corresponds to the TLS estimate of
m
.
Figure 13.6 depicts the 3D placements of the calibration pattern from the cam-
era viewpoint. The graphics were drawn by using 13 estimated matrices
M
E
cor-
responding to 13 different placements of the calibration pattern and using the left
camera in Fig. 13.4.
