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Version 1
1
Table 2: Results of the bundle adjustment with self-calibration for the video camera calibration
Precision from adjustment
Accuracy from check points
Ver| In |AP|Co|Ch| r So
Object space [mm]
[pm] ?
Image space [um] Object space [mm] Image space [um]
Ox Oy 07
Ox Oy Mx My Hz Hx Hy
11419131721605|] 0.96 | 045 ] 0.50 | 0.35
13 1.3 0.60 |. 0.53. .] 0.37 1.6 1.4
2141918 671622| 1.021 0.28 | 0.27 | 0.62
0.8 0.7 0.41 | 0.30 | 0.76 11 0.8
Meuse een Version
Im. ees Number of images GG eornm Standard deviation of measured image coordinates a posteriori
AP ii Number of additional parameters Oxyz e Theoretical precision in object space
CQ, centres Number of control points Oy e Theoretical precision in image space
Ch retten Number of check points HX vertere Empirical accuracy in object space
Trsssressareeres Redundancy Bay enn Empirical accuracy in image space
summarizes the results of the calibration with a minimal
control datum (three control points on the wall). In ver-
sion 2, eight well-distributed control points on the wall
and testfield frame were used in the adjustment. The em-
pirical accuracy measures (Ux, Ly, Hz) shows that an ac-
curacy of better than one millimeter was obtained.
An accuracy in the order of 1/10*^ of the pixel spacing in
image space could be achieved. The camera constant was
determined as c = 10.337 mm, and the pixel spacing as
10.9 jum (H) x 10.0 um (V). The curve of radial distortion
of the JVC is illustrated in Figure 5. The 6.4 x 4.8 mm?
sensor of the JVC is affected by a maximum distortion of
-57 pm at the sensor border.
-60 T T T T
0 1 2 4
Radius [mm]
Figure 5: Radial distortion of the JVC video camera
3.3. On-line triangulation
In OLTRIS, the image sequence was triangulated to dem-
onstrate the performance and capability of sequential ad-
justment for point positioning purposes. As mentioned
earlier, the triangulation was processed without self-cali-
bration. The image coordinates for the object points in the
88 images were determined in a similar fashion as de-
scribed above for the camera calibration. Known data at
the start of the triangulation included the station orienta-
tion data of the first image (introduced as initial values)
and five distributed object points of the testfield which de-
fined the datum. After including a new frame into the tri-
angulation process, at least three points have to be
measured to compute the approximate values of the exte-
rior orientation of the “current” camera position. These
orientation values of each consecutive image in the se-
quence were computed by resection in space using the ori-
entation data of the preceding image as initial values. In
each image, between 79 and 146 points were measured. A
total of 166 different object points in the testfield were
used. In total, 20 860 observations (498 object and 20 362
image point coordinates) were processed with a maximum
number of 1026 unknowns to be determined in the bundle
adjustment. The path of the video camera for the test se-
quence is plotted in Figure 6. The lower line represents
Y [mm]
1650
er ——= End
1400
1200 Start
1100 —T T T T T TX
4000 4500 5000 5500 6000 6600
[mm]
Z [mm]
4400
4300 La
4200
4100
4000 —T T T T T T T T T T
1 10 20 30 40 50 60 70 80 90
Number of frames
Figure 6: Path of the video camera
the estimated path (i.e. exterior orientation of the 88 imag-
es) as determined by OLTRIS (with sequential estimation
and simultaneous adjustment inbetween). The upper line
indicates the "path" as estimated in a (simultaneous) bun-
dle adjustment with self calibration in DEDIP. The mean
of the differences between the two paths is 4.5 mm in x-,
and -11 mm in y-, and 12 mm in z-direction. This differ-
ence can be attributed to the absence of systematic error
compensation in the sequentially estimated version.
The important comparison to be made here between the
two adjustment techniques, simultaneous and sequential,
relates to their respective computation times (CPU) for
updating the normal equation system and calculating the
solution vector. In OLTRIS, it is possible to perform se-
quential update with Givens transformations and simul-
tancous adjustment with Cholesky factorization and back-
substitution. Computing times (CPU) for the updating of
the solution vector when including the observations of
one additional image point are illustrated in Figure 7. The
plotted line shows the increase of CPU-time consumption
depending on the number of frames, observations and un-
knowns respectively. The computation time measured was
