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Manfred Weisensee 
Every laser point contributes an error equation of this type, leading to a parameter estimation which can be solved by 
standard methods. An iterative procedure which re-weights the observations depending on the resulting residuals e has 
been given by Pfeiffer et al., /Steinborn and Fritsch 1999/. By this, upper and lower surfaces can be separated in a few 
iterations. 
In order to combine laser scanning data with digital images in a common adjustment, in addition to equation (12) error 
equations have to be set up for the unknown parameters dZ;; 
1.4 
1l... 1 
em NN as Yo dZ)-[Z, — V S a 05 Y,)- 25] (16) 
i-0 j-0 
i-0 j-0 
For using equations (12) and (16) for parameter estimation, the weights of the observations have to be determined either 
beforehand or during the iterative procedure in a variance estimation. Estimates for the variances of digital gray values 
G'(x',y"), G"(x",y"), … of an image or of the pseudo measurements that are used to accelerate the procedure can be 
derived from the ortho images G'(X,Y), G"(X,Y), … resulting from the image functions and the mean values G(X,Y). 
Similarly variances for laser scanning data can be computed. 
While the filter strategies mentioned above only rely on laser scanning data, filtering by re-weighting in the combined 
adjustment is strongly supported by digital image data. When reducing the total number of laser scanning points by 
those which correspond to the upper surface with this method, even the elementary median filter, /Koch 2000/, may be 
applied for the elimination of the remaining erroneous points. 
5 CONCLUSIONS 
In combining laser scanning data with digital photogrammetric images in a common parameter estimation, a fast and 
reliable process of surface reconstruction and ortho image production is at hand. Separating the upper surface points 
from laser scanning data in addition gives advantages for filtering true ground points in wooded areas. Further research 
has to be done considering the weighting and re-weighting strategies of the process. 
ACKNOWLEDGEMENTS 
This research was supported by the Volkswagen Foundation. The author would also like to thank Dr. Peter FrieB and 
Dr. Joachim Lindenberger from TopScan for their support. 
REFERENCES 
Baltsavias, E., (Ed.), 1999. Journal of Photogrammetry & Remote Sensing, Theme Issue on Airborne Laser Scanning. 
Vol. 54, Elsevier Science B.V. 
Franek, M., Müller, J., 1990. Regularizing Visible Surface Reconstruction with Facets Stereo Vision (FAST Vision). In: 
International Archives of Photogrammetry and Remote Sensing, Wuhan, China, Vol. XXVIII, Part 3/2. 
Fritsch, D., Spiller, R., (Eds.), 1999. Photogrammetric Week '99. Wichmann Verlag, Heidelberg. 
Koch, K. R., 2000. Einführung in die Bayes-Statistk. Springer Verlag, Berlin. 
Korten, T., Wrobel, B., Franek, M., Weisensee, M., 1988. Experiments with Facets Stereo Vision (FAST Vision) for 
Object Surface Computation. In: International Archives of Photogrammetry and Remote Sensing, Kyoto, Japan, Vol. 
XXVII, Part B3, pp. 231-258. 
Lindenberger, J., 1993. Laser-Profilmessung zur topographischen Geländeaufnahme. Deutsche Geodätische 
Kommission, Reihe C, 400, München. 
Schlüter, M., 1999. Von der 2/4D zur 3D Flächenmodellierung für die photogrammetrische Rekonstruktion im 
Objektraum. Deutsche Geodätische Kommission, Reihe C, 506, München. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 969