International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
parameter direct sol. | constrained
principal dist. c | 1157.8 pel pel | 1160.5 pel
pitch angle a :*29.99 deg 30.01 deg
roll angle ^ -2.52 deg +0.08 deg
camera height Z 2.49 m 2.49 m
Table 3: shows the results of the direct solution and its
constrained add-on.
height of the chairs H = 0.77 m, on = 0.02 m has
been introduced. Table 4 summarizes the results of the
initial calibration with a redundancy of 38. The pro-
cess converged after four iterations. The estimated factor
89 — 3.75 lies in the expected magnitude for the precisions
of the image points. Figure 3 shows the results qualitative.
Drawn in the image is the estimated horizon line with its
hyperbolic error band. The position and orientation of the
horizon line can be easily checked by visual inspection of
the vanishing lines.
parameter |. estim. | est. std. dev.
principal dist. c 1196.8 pel 32.3 pel
pitch angle a *29.37 deg 0.48 deg
roll angle y -1.96 deg 0.37 deg
camera height Z 2.3m 0.05 m
Table 4: shows the results of the initial calibration.
4.3 Object Measurement
The observed and measured chair legs are illustrated in
fig. 4 in an upright projection, together with the projection
center, the footprint of the principal point and the projec-
tion of an image raster. The positions and heights of new,
unknown objects can be determined by (8) and (9).
[ul x
0
e
deque
Figure 4: shows the footprints of a image raster and the
positions (x) of the chair legs on the ground plane.
5 CONCLUSIONS AND OUTLOOK
Conclusions. An easy camera calibration procedure has
been presented for the observation of objects of equal
heights on a ground plane. The procedure uses a minimal
parametrization for the camera itself and its exterior orien-
tation. Few efforts are associated with the installation; the
foot and head points of the objects serve as observations.
After an initialization phase with a first scene the approach
1072
allows within the continuous operation a parameter check
and update if necessary. For the calibration results the sin-
gle parameter values are less important than the specific
parameter combination; the change of one parameter can
to some degree be compensated by the others. Due to the
sequential build-up of the normal equations, the demand
of storage space is minimal. For the set-up of the camera
system a pitch angle > 20° and a large aperture angle (or
small principal distance) are advisable. Otherwise prior
information has be be introduced to cope with the weak
geometric configuration. The prior information guarantees
but also dominates the solution. The height of the camera
should be measured wherever possible in order to impose
more geometric constraints onto the solution.
Outlook. In order to eliminate the influence of gross ob-
servational errors, a robust estimation is desirable. Fur-
thermore, the integration of other easily available measure-
ments — such as distances in the object space — is advan-
tageous, depending on the precise location to be recorded.
REFERENCES
Criminisi, A., 2001. Accurate Visual Metrology from Sin-
gle and Multiple Uncalibrated Images. Distinguished Dis-
sertations, Springer, London, Berlin, Heidelberg.
Faugeras, O. and Lustman, F., 1988. Motion and Structure
from Motion in a piecewise planar Environment. Interna-
tional Journal of Pattern Recognition in Artificial Intelli-
gence 2, pp. 485—508.
Hartley, R. and Zisserman, A., 2000. Multiple View Ge-
ometry in Computer Vision. Cambridge University Press,
Cambridge.
Jones, G. A., Renno, J. and Remagnino, P, 2002.
Auto-Calibration in Multiple-Camera Surveillance Envi-
ronments. In: 3rd IEEE Workshop on Performance Evalua-
tion of Tracking and Surveillance (PETS 02), Copenhagen,
pp. 40-47.
Mikhail, E. M., 1976. Observations and Least Squares.
With Contributions by F. Ackerman. University Press of
America, Lanham.
Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flan-
nery, B. P., 1992. Numerical Recipies in C. Cambridge
University Press.
Renno, J, Orwell, J. and Jones, G., 2002. Learn-
ing Surveillance Tracking Models for the Self-Calibrated
Ground Plane. In: British Machine Vision Conference.
Poster Session.
Semple, J. G. and Kneebone, G. T., 1952. Algebraic Pro-
jective Geometry. Oxford Univ. Press, New York.
Welch, G. and Bishop, G., 2002. An Introduction to the
Kalman Filter. Technical Report TR 95-041, Department
of Computer Science, Univ. of North Carolina at Chapel
Hill.
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