MULTI-IMAGE SHAPE-FROM-SHADING: DERIVATION OF PLANETARY DIGITAL 
TERRAIN MODELS USING CLEMENTINE IMAGES 
Volker Lohse, Christian Heipke 
University of Hannover, Institute of Photogrammetry and GeoInformation, Nienburger Strafe 1, 
30167 Hannover, Germany - (lohse, heipke)@ipi.uni-hannover.de 
Commission IV, WG 9 
KEY WORDS: High-resolution DTM, extraterrestrial surfaces, reconstruction method. 
ABSTRACT: 
In many cases, the derivation of high-resolution digital terrain models (DTMs) from planetary surfaces using only conventional 
digital image matching is a problem. The matching methods need at least a stereo pair of images covering an area with sufficient 
texture. Often though, space missions provide only a few stereo images and planetary surfaces often possess insufficient texture. 
This paper describes a method for the generation of high-resolution DTMs from planetary surfaces using digital optical images 
developed by the authors over a number of years. The suggested method, termed “multi-image shape-from-shading” (MI-SFS), is 
able to generate a planetary DTM with an arbitrary number of images of low texture. Therefore, MI-SFS is a suitable method in 
areas, in which image matching fails to yield a DTM. 
The paper contains a short review of the theory of MI-SFS, followed by a presentation of results, which were obtained with images 
from NASA's lunar mission Clementine. These results constitute the first practical application of MI-SFS using extraterrestrial 
imagery. The reconstruction of the lunar surface is made with the assumption of different kinds of reflectance models (Lommel- 
Seeliger and Lambert model). The represented work shows that the derivation of a high-resolution DTM of real digital planetary 
images by means of MI-SFS is feasible. 
1. INTRODUCTION 
Digital terrain models (DTMs) are an important information 
source for many applications in planetary sciences, such as for 
the description of local and regional topographic features, 
slopes, discontinuities of the surface and thus possible flow 
direction of liquid material and isostatic considerations to name 
only a few. On Earth, such DTMs can normally be generated by 
means of conventional photogrammetry including digital image 
matching. But planetary missions in general are not topographic 
missions, and therefore usually only a few stereoscopic images 
are available. Additionally, some planetary stereo pairs have a 
disadvantageous camera configuration (e.g. a poor base-to- 
height ratio or different images resolutions) and in many cases 
planetary images have poor image texture, which is an obstacle 
to automatic matching methods. For this reason, in many 
regions no complete high-resolution DTM of planetary bodies 
can be made available by means of conventional 
photogrammetric methods. 
Besides photogrammetry, there are other methods to generate a 
DTM of a planetary body. One example is laser scanning as 
employed by the “Mars Orbiter Laser Altimeter" (MOLA) 
flown on the Mars Global Surveyor mission (Smith et al., 
2001). MOLA acquired high-precision height information along 
one dimensional tracks, but despite simultaneous processing of 
multiple orbits, the horizontal resolution of the resulting data set 
is rather limited. 
For these reasons, it is of great interest to many planetary 
scientists to have at their disposal reconstruction methods, 
which are able to work with a single image and/or with images 
including low texture, such as "multi-image shape-from- 
shading" (MI-SFS). 
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MI-SFS has been developed by our group over the last years. A 
detailed description including results with simulated and aerial 
images from a desert area on Earth are given in (Heipke, 1992; 
Heipke,  Piechullek, 1994;  Piechullek, 2000). First 
investigations with real digital planetary images from NASA's 
lunar mission Clementine of 1994 are presented in (Lohse, 
Heipke, 2003). This paper deals with advanced results using 
Clementine images. Similar investigations, however with the 
goal to produce orthophoto mosaics from images taken at 
different illumination directions, are described in (Dorrer, 
2002). Other approaches worth mentioning are the iterative 
multi-image DTM reconstruction by (Gaskell, 2003) and the 
integration of image matching and  shape-from-shading 
suggested by (Fua, Leclerc., 1995). 
2. MULTI-IMAGE SHAPE-FROM-SHADING 
For solving the DTM reconstruction problem by SFS, the image 
formation process has to be modelled and inverted with respect 
to the parameters describing the object space (Horn et al., 
1989). Like other SFS methods, MI-SFS is based on the fact 
that surface patches, having different inclination relative to the 
light source, are imaged with different brightness. MI-SFS uses 
these variations in the grey values for the reconstruction of the 
surface. In contrast to classical SFS methods, MI-SFS can deal 
with an arbitrary number of images and spectral bands, is based 
on a perspective transformation between image and object 
space and relates directly the grey values to the heights of a 
DTM and the parameters of a radiometric model, which 
describes the surface reflectance behaviour. The DTM heights 
as well as the parameters of the radiometric model are estimated 
from the image grey values in a least-squares adjustment. 
For MI-SFS it is assumed that the albedo in the observed area i$ 
constant everywhere, because the method does not differ 
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