introduced,
final values;
only four lines are sufficient to obtain a good
convergence;
parameters K and Xc converge before the others;
a high accuracy estimation is reached with this
approach; rotational and translational errors are
smaller than 1' and 0.2 mm respectively.
the filter had already converged to the
6.3 Multi-frame Calibration
It was supposed we had a single camera, static in
space, observing a 70 mm cube moving on a conveyor belt
in X direction with a speed of 100 mm/s. A sequence of
nine images is taken by the camera. In the first image
the cube frame and base frame are coincident. Table
6.3.1 summarizes the camera vector state for this
instant.
Table 6.3.1 True Camera State and Predicted Values
Camera Predicted State| Predicted
State State Error| Variance
2
K 0.0 0.01 0.01 (0.01)
9 rad| 0.0 0.01 0.01 (0.01),
w 0.959931 0.949931 |-0.01 (0.01)
Xc 300 304 4. (4.),
Yc mm| -400 -396 4. (4.)
2
Zc 400 404 4. (4.)
Knowing the conveyor belt speed and the sampling
time, the object position can be computed and, then,
the object-to-base frame transformations for each image
can be stated. In order to simulate real environments,
randomic perturbations were introduced in object
position (Imm and 1° standard deviation in translation
and rotation parameters, respectively).
For the same set of data, results obtained for a
sequence of single frame calibration (a priori
estimates for each image are not related to the former
calibration) and a multi-frame calibration (a priori
estimates are obtained from the filtered estimates of
the former calibration) are presented in Figures 6.3.1
and 6.3.2, respectively.
ROTATIONS
True Errors (rad) Franes
0.048 |
0.04 |
on
(0. Ts
ü e P uium. Lc b ins PECs
ame? Ne per?
-- e^ eft X
=0.01 |-
70.048 |[-
Estinated Standard Deviations
0.015 >
0.01 >
ES rt NN
0 À. I -— e T
TRANSLATIONS
Trua Errors Cee) Franes
4.0 +
2.0 TE Sri =
0 E pa SE
Jm Nr NM NI en
-2.0
-4.0 |
Estinated Standard Deviations
4.0
Figure 6.3.1 Results of a sequence of single frame
calibrations
ROTATIOMS
True Errors (rad) vt
0.013 +
0.04 +
a PILLE Me
see TE
-0.01 }-
70,013 |-
Estinated Standard Deviations
9.015 |
0.0 |
; UU AED VIE
TRANSLATIONS
Trua Ervors Gwe) Frames
4.0 F
4
10 P.
0
-8.0 +
-4.0
Estimated Standerd Deviations
4.0
Figure 6.3.2 Results of a Multi-frame Calibration.
The improvements of the multi-frame calibration
process can be seen comparing Figures 6.3.1 and 6.3.2.
The final camera state estimation for the multi-frame
calibration is within an accuracy of 2’ for the
rotations and 0.5 mm for the translations.
6.4 Reduction of the search window in feature extraction
In order to illustrate the reduction of the search
space in the feature extraction level, the results
related to the single frame calibration discussed on
Section 6.2 are shown in Table 6.4.1.
Using the predicted estimates to define the first
search space results in a rectangle of 56,072 pixels
(1.16 x 3.6 mm), to be analysed, For the extraction of
the 12 feature using the ot estimate, the window
is reduced to a rectangle of 0.031x 3.53 mm (a window
of 3 pixels width), equivalent to 1,132 pixels.
Table 6.4.1 Reduction of the s earch window.
Areca Window width |Feature
2 Num. of pixels
mm mm Lenght
1 5.60 56,072 1.167 3.68
2 3.12 31,051 1.013 2.25
3 2.47 24,773 0.637 3.06
4 1.60 16,068 0.425 3.10
5 0.54 5,414 0.233 2.24
6 0.42 4,279 0.132 3.10
7 0.32 3,221 0.101 2.84
8 0.31 3,168 0.099 2.84
9 0.54 5,431 0.120 4.37
10 0.07 747 0.039 1.99
11 0.07 703 0.037 1.96
12 0.11 1,132 0.031 3.54
As can be seen from Table 6.4.1, the availability
of better estimates for the camera state vector along
the filter operation reduces the search window area. If
only a priori estimates were used to search for the
lines, 672,000 pixels (12 windows with 56,000 each one)
should be analyzed, whereas using the recursive
OM OO = = 0 EEO
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