CPU-times per additional image point [sec]
Number of frames
LI ] ] ] ] ] ] ] ]
460 2726 5178 7246 9437 12056 14198 16604 18580 20860
Number of observations
LI | I ] ] ] | ] I 1
282 510 570 624 693 792 852 906 966 1026
Number of unknowns
Figure 7: CPU-times for the inclusion of one additional image point into the sequence.
(Sequential estimation in OLTRIS on a SPARCstation 1+, Sun Microsystems)
between 0.01 seconds per additional image point meas-
urement at the start phase of the triangulation and 1.54
seconds at the stage of the last frame of the sequence. In
comparison with these results this speed could not be
achieved with simultaneous adjustment. Here, the normal
equation system is relinearized, if the updating of the so-
lution vector is requested after adding an image point
measurement into the normals. For that, forming and solv-
ing the normal equations during the triangulation takes 3
seconds per iteration at the stage of 10 introduced image
frames including 2726 observations and approximately 20
seconds at the stage of 40 frames (9437 observations).
This is approximately by a factor 70 worse than the se-
quential mode and is far away from video real-time.
4, CONCLUSIONS
Our investigations have shown that sequential estimation
in a general point positioning and camera orientation
module (bundle adjustment) using Givens transformations
can result in very short response times for system updat-
ing. In our example the insertion of one additional image
point required 0.01 seconds at the stage of the first CCD-
frame and 1.54 seconds at 88 frames on a Sun SPARCsta-
tion 1+. The simultaneous solution required by a factor 70
higher computing times. Thus within this computer envi-
ronment, an image point insertion (and deletion) at video
rate (0.02 sec) can be achieved at a system size of 10
frames. This excellent computational performance makes
the procedure of sequential updating of bundle systems by
Givens transformations particularly useful in time-con-
strained machine vision and robot vision applications.
From a system point of view, however, object space fea-
ture positioning may be only a minor portion of the over-
all computing time budget. Since image analysis and
image understanding operations can easily chew up a
large amount of computing time, it should be worthwhile
to investigate also into possible sequential formulations of
related algorithms.
As a by-product of our investigations we could show that
even with an “amateur” TV video camera with integrated
analog storage device a fairly good accuracy (1/10^^ of a
pixel from 3-D check points) can be achieved. We believe
that even better accuracies are possible if emphasis is put
on a more sophisticated procedure for systematic error
compensation. This opens interesting perspectives for the
use of TV video cameras in a great variety of measure-
ment applications.
5. ACKNOWLEDGEMENTS
The software package OLTRIS was developed in the
project “On-line point positioning with single frame cam-
era data”, which was sponsored by the U.S. Government,
Department of Defense, represented through its European
Research Office of the U.S. Army in London. This sup-
port is gratefully acknowledged.
6. REFERENCES
Baltsavias, E., Gruen, A., Meister, M., 1991: DOW - A
System for Generation of Digital Orthophotos from Aerial
and SPOT Images. Presented Paper ACSM/ASPRS An-
nual Convention, March 25-29, Baltimore, Maryland.
Beyer, H.A., 1987. Einige grundlegende Designfragen für
die Entwicklungsumgebung für Digitale Photogram-
metrie auf den Sun Workstations (DEDIP, Development
