6. Conclusions
The theory of a stabilizing method for ill-posed problems
has been given, applied for object surface reconstruction
by FAST Vision and tested with some first experiments.
In comparison to the often used procedure of curvature
minimization, the following merits have evolved:
e Surface reconstruction is definitely better, especially the
reconstruction of edges or breaklines.
e The results do not depend as much on the regula-
rization parameters as they do with curvature mini-
mization. So, the time consuming determination of local
regularization parameters is not necessary.
e The standard errors of the results are still directly
affected by the regularization parameter. But with additional
computer work, refined and more reliable standard errors
may be computed.
e In general, statistically well defined accuracy measures
are at hand, since the approach is modeled as a Gauf-
Markov estimation.
Finally, the theory of adaptive regularization, section 4..
may be transfered to other problems with ill-posedness or
ill-conditioning, e.g. least squares image matching or
self-calibration of analytical photogrammetry.
T. References
Boult, T.E., What is Regular in Regularization. Proceedings
of the Ist International Conference on Compu-
ter Vision, p.p. 451-462, London, 1987
Huang, T.S. (ed), Image Enhancement and Restoration,
Picture Processing and Digital Filtering. Sprin-
ger Verlag, Berlin Heidelberg New York, 1975
Grimson, W.E.L. From images to Surfaces: À Computatio-
nal Study of the Human Early Visual System.
MIT Press, Cambridge, MA, 1981
Kaiser, B./ Wrobel, B./ Hausladen, J./ Tsay, J.-R., Applica-
tion of FAST Vision for Digital Terrain Model
Generation. Presented Paper, XVIIth Congress of
ISPRS, Comm. III/2, Washington 1992
Poggio, T/Torre, V/Koch, C. Computational Vision and
Regularization Theory. Nature Vol. 3lT, pp.
139-155, 1985
Rauhala, U.A/ Davis, D/ Baker, K., Automated DTM Va-
lidation and Progressive Sampling Algorithm
Of Finite Element Array Relaxation. Photo-
grammetric Engineering and Remote Sensing,
Vol. 55, No. 4, pp. 449-465, 1989
Terzopoulos, D., The Computation of Visible Surface
Representations. PAMI, Vol. PAMI-1O, No. 4,
p.p.41T-438, July 1988
Tikhonov, A.N./Arsenin, V.Y. Solutions of Ill-Posed Pro-
blems. V.H. Winston & Sons, Washington D.C.,
1977
Weidner, U., Informationserhaltende Filterung digitaler
Bilder und ihre Bewertung. Mustererkennung
1991, Springer Verlag, Berlin, 1991
Weisensee, M., Modelle und Algorithmen für das Facet-
ten-Stereosehen. Deutsche Geodätische Kom-
mission, Reihe C, Nr. 374, München, 1991
831
Wrobel, B., On refinements of least squares solutions by
improving the condition number using additi-
ve modifications. Intern. Symp. on Comp.
Methods in Geodesy, Oxford, 1913
Wrobel, B., Zur Steigerung der Auflósungsgenauigkeit von
Normalgleichungen durch Konditionsverbesse-
rung mittels additiver Modifikation. Deutsche
Geodätische Kommission, Reihe C, Nr 199,
München, 1974
Wrobel, B., Digital Image Matching by Facets Using Ob-
ject Space Models. 4th International Symposi-
um on Optical and Optoelectr. Appl. Science
and Engineering, March 3Oth-April 3rd 1987,
The Hague, Netherlands, SPIE 3804, pp.
325-333
Wrobel, B. The Evolution Of Digital Photogrammetry
From Analytical Photogrammetry. Photogram-
metric Record, 13(TD), p.p. T65-TT6, April
1991
Wrobel, B./ Kaiser, B./ Hausladen, J. Adaptive Regulari-
zation of Surface Reconstruction By Image
Inversion. In: Fórstner, W./ Ruwiedel, St. (eds) :
Robust Computer Vision. Wichmann Verlag.
Karlsruhe 1992
These investigations are supported by Deutsche
Forschungsgemeinschaît.
