Christian Piechullek
- The results of processing the images individually were significantly worse. This result demonstrates convincingly the
advantages of MI-SFS over single image SFS. Both, the implicit stereoscopic correspondence of the DTM meshes ay;
the higher redundancy of the whole adjustment contribute to this finding (see also discussion at the end of chapter j
It must be mentioned, however, that the pre-processing step — more precisely the estimation of the albedo - wag à
signed for the simultaneous processing of all three images. Thus, the pre-processed images individually do not neces.
sarily represent the correct grey values of the object surface any more.
In an additional set of experiments the radius of convergence using the real images was found to be about 16 pixels
which is in line with the simulation results (see again chapter 3). In these experiments the analytically measured DTy
was changed in absolute height by an offset value and in form by introducing a scale factor. In most cases the surface
form was reconstructed within only a few iterations, and for the absolute heights to converge towards the correct reg
up to 30 iterations were needed.
5 CONCLUSIONS
The reported MI-SFS results obtained from the simultaneous evaluation of the radiometrically pre-processed images
clearly demonstrate the applicability of the method to real imagery. DTM heights were determined from aerial images
of poor texture with a standard deviation of 0.3% of the flying height. Also the advantages of MI-SFS over single im.
age SFS could be proven. They consist in (1) the possibility to directly compute absolute DTM heights as opposed t
inclinations and thus height differences, (2) more reliable results in situations in which single image SFS can become
numerically instable, e. g. in the presence of noise, for small incidence angles or for similar values for incidence and
emittance angle (the latter only for the Lommel-Seeliger law).
However, the results with real images were only achieved after pre-processing the images. In this pre-processing step
the DTM heights of the object surface to be computed were already needed. The reason for this pre-processing was the
presence of significant brightness and contrast differences, larger than those which can be explained with respect to
different viewpoints in conjunction with commonly used reflectance models in planetary science. It was therefore as
sumed that these brightness and contrast differences stem from the photographic handling of the analogue images
Given this assumption and the fact that the photographic handling cannot be modelled adequately, MI-SFS could not be
independently assessed with the used experimental data, rather only the potential of the method could be proven. Or
could have also attempted to simultaneously solve for the parameters of the pre-processing and the DTM heights. In this
case a brightness offset and a contrast factor would have had to be considered for each image individually, and the un-
known surface albedo would have had to be introduced as a constant value, since image contrast and surface albedo ac
linearly dependent. However, such an approach would have weakened the adjustment model and was not pursued.
In spite of the mentioned shortcomings of the used experimental data, the presented results demonstrate the general a
plicability of MI-SFS, and in particular its advantages when compared to single image SFS: absolute heights can be de
rived rather than surface slopes only, the stereoscopic correspondence adds significantly to obtaining stable results, and the
higher redundancy renders the result more robust with respect to noise and blunders. Possible extensions of the method
include the introduction of another viewing geometry, e. g. the 3-line geometry of HRSC employed on the planed Mars
Express mission, the use of a more refined reflectance model, e. g. the Lunar-Lambert model, the consideration of spatially
varying albedo, and the introduction of multispectral imagery. In the latter case each spectral band has to be modella
individually as far as the radiometric model is concerned, however, the geometric model remains the same for all spectral
bands. As a final note it must be mentioned that a conclusive evaluation of MI-SFS can only be on directly acquired dig-
tal imagery from a radiometrically calibrated sensor.
6 REFERENCES
Davis, P. A., Soderblom, L. A. (1984): Modeling Crater Topography and Albedo From Monoscopic Viking Orbiter
Images; 1. Methodology, Journal of Geophysical Research (89) B11, 9449— 9457.
Fua, P. (1997): From Multiple Stereo Views to Multiple 3-D Surfaces, International Journal of Computer Vision, (24) |,
19-35.
Giese, B., Oberst, J., Kirk, R. L., Zeitler, W. (1996): The Topography of Asteroid Ida: A Comparison Between Photo
grammetric and Two-Dimensional Photoclinometric Image Analysis, International Archives for Photogrammetry and
Remote Sensing (31) B3/III, 245—250.
Hapke, B. (1993): Theory of Reflectance and Emittance Spectroscopy. Topics in Remote Sensing III, Cambridge Un
versity Press, Cambridge, Massachusetts.
730 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
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