by the control points. Improved results were obtained
by photogrammetry, while invariance performed less
accurately due to the location of the check points
relative to the control points frame. It is clear that the
invariance method works better if the check points are
confined with in and closer to the control points frame.
4. CONCLUSIONS AND CONTINUING RESEARCH
1. Linear image features arc significant source of
information which when properly exploited facilitate
three-dimensional object reconstruction, since they are
abundant in human-made infrastructure, and are
amenable to automated feature extraction.
2. Geometric constraints between various linear
features provide substantial information in support of
photogrammetric restitution and object reconstruction,
both in absolute and partially absolute sensc.
3. Feature recovery by photogrammetric techniques
(triangulation or extended rclative orientation) is
accurate, even though the recovery of the interior
orientation parameters may not be accurate, due to
projective compensation.
4. Invariance provides a useful tool for object
reconstruction, particularly since it does not require
approximate values.
5. The point sequence used to construct the invariance
equations can have a significant influence on the results,
particularly for the redundant case where position
estimates and their quality vary. A refined least squares
approach, which requires linearization of the equations
appears to alleviate this non-uniqueness problem.
6. It is crucial that the fundamental matrix, F, be well
recovered for the success of invariance technique,
especially for the convergent geometry case.
Furthermore, the configuration of control and check
object points is rather critical to the quality of the
results. Points used for both the estimation of F and
as control points should not fall close to a planc.
Rescarch is continuing on the following:
a. Experimentation to study the effects of various
configuration of the ground points (both control and
check) and the different camera geometry on the
performance of the invariance technique.
b. Extension of the invariance technique to apply to
multiple overlapping photos.
c. Investigate the line-based and combined point/line-
based invariance techniques for object reconstruction.
d. Study the possibility of developing a hybrid approach
combining invariance and photogrammetry for object
reconstruction.
5. ACKNOWLEDGEMENTS
This rescarch is sponsored by the Office of Research
540
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
and Development; the support and encouragement of
Dr. Yeongji Kim, the COTR, are gratefully
acknowledged. ^ Thanks are due E. Barrett and P.
Payton for their free exchange of information on
invariance.
6. REFERENCES AND BIBLIOGRAPHY
Barakat, H., Weerawong, K., and Mikhail, E.M., 1995.
Comparison Between Invariance and Photogrammetry
for Image and Object Transfer. SPIE, Orlando, FL,
Vol. 2486.
Barakat, H., Doucette, P., and Mikhail, E.M., 1994,
Photogrammetric Analysis of Image invariance. ISPRS
Commission III, Munich, Germany, pp. 25-34.
Barrett, E., Gheen, G., and Payton, P. 1994.
Algorithms for Invariant Model Transfer and Object
Reconstruction. IU Workshop, Monterey, CA, Vol. II,
pp 1429-1440.
Hartley, R., and Mundy. J., 1993. The Relationship
Between Photogrammetry and Computer Vision. SPIE,
Vol. 1944, pp. 92-105.
Mikhail, E.M., and Weerawong, K., 1994. Feature-
Based Photogrammetric object construction. ASPRS,
Reno, Nevada.
Mikhail, E.M, 1993. Linear Features for
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SPIE, Vol. 1944, pp. 16-30.
Mikhail, E.M., 1976. Observations and Least Squares.
University Press of America, New York.
Mulawa, D.C. and Mikhail, E.M. 1988.
Photogrammetric Treatment of Linear Features.
ISPRS, Kyoto, Japan, Vol. 10, pp. 383-393.
Zisserman, A., 1995. Uncalibrated Vision. ISPRS, The
Role of Models in Automated Scene Analysis,
Stockholm, Sweden.
C,(X) = Cross Ratio of the 4 Planes:
XVX2X3, Xi X3 X4, Xy Xa X3, X XX
(From Basrett 1994)
Tal
Tw
Twc
