Christian Piechullek 
  
SIMULATION STUDIES AND PRACTICAL TESTS USING MULTI IMAGE SHAPE FROM SHADING! 
| Christian Heipke'?, Christian Piechullek, Heinrich Ebner? 
© Institut für Photogrammetrie und Ingenieurvermessungen, Universitit Hannover, http://www.ipi.uni-hannover.de 
® Axel Springer Verlag, Ahrensburg 
©) Lehrstuhl fiir Photogrammetrie und Fernerkundung, Technische Universitit Miinchen, http://Www.verm.photo.tu- 
muenchen.de 
Commission III, Working Group III/2 
KEY WORDS: shape from shading, multiple images, surface reconstruction, real imagery 
ABSTRACT 
Multi image shape from shading (MI-SFS) is a surface reconstruction method which has been studied intensively by ou 
group over the last years. Our goal is to develop a method incorporating MI-SFS and image matching for use in plane. 
tary science. MI-SFS directly relates the grey values of one or more images to the heights of a digital terrain model 
(DTM) and the parameters of a radiometric surface 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 square 
adjustment. 
In this paper we shortly review the principles of MI-SFS, and analyse its characteristics using theoretical investigations 
and a practical example. Throughout the text a comparison of two widely used reflectance models in planetary science, 
the well-known Lambert and the Lommel-Seeliger reflectance model, is given together with an investigation into the 
pros and cons of using more than one image and thus of MI-SFS compared to classical SFS. Results from a practical 
test using digitised aerial images are described, which demonstrate the potential of MI-SFS and its advantages over 
single image SFS. 
1 INTRODUCTION 
Shape from Shading (SFS) is a method for surface reconstruction from digital images which exploits the fact that sur- 
face patches, having different inclination relative to a light source, are imaged with different brightness. The surface is 
generally assumed to have constant and known reflectance properties. Therefore, SFS only performs well in areas with 
poor image texture. Using a single digital image, the result is ambiguous because the inclination of a surface patch is 
determined by two components (e. g. the slopes in x and y direction) while only one observation, namely the grey val 
ues of the patch is available. In order to overcome this well known indeterminability of SFS, various constraints wer 
suggested. 
SFS has first been suggested by Rindfleisch (1966) and Horn (1970). In the field of astrogeology, where SFS is also 
referred to as 'photoclinometry' and only few or no stereoscopic images are available, the main research interest lies in 
the geometric reconstruction of planetary surfaces (e. g. Davis, Soderblom 1984; McEwen 1991; Giese et al. 1996). In 
computer vision, SFS has been developed for the reconstruction of surfaces in terrestrial and close-range surroundings 
(e. g. Oren, Nayar 1994; Fua 1997; Lee, Kuo 1997; Wei, Hirzinger 1997). A collection of papers on SFS and a detailed 
bibliography up to the late eighties is presented in Horn, Brooks (1989), a recent survey of the field is contained in 
Zhang et al. (1999). 
Multi image shape from shading (MI-SFS) is a surface reconstruction method first suggested some time ago (Heipke 
1992) and has been studied intensively by our group over the last years (see Piechullek 2000 for a comprehensive de- 
scription of the work carried out to date). In contrast to classical SFS, MI-SFS is based on perspective transformations 
between image and object space and directly relates the grey values of one or more images to the heights of a digital 
terrain model (DTM) and the parameters of a radiometric surface model, which describes the surface reflectance be 
haviour. The DTM heights as well as the parameters of the radiometric model are estimated from the image grey values 
in a least squares adjustment. Our goal is to develop a method incorporating MI-SFS and image matching for use In 
planetary science, e. g. for images from the Mars Express mission which is expected to derive high resolution DTM 
from the Martian Surface. Mars Express will be equipped with an updated version of the HRSC camera and is planed to 
be launched in 2003 (Neukum 1998). The integration of SFS and image matching for this task is advantageous, because 
the respective prerequisites of both methods are complementary: while SFS needs constant albedo resulting in poor 
image texture, image matching inherently relies on local grey value differences. In our long term strategy it is planned 
  
! Most of the work reported in this paper was carried out while all three authors were with the Lehrstuhl für Photogrammetrie und 
Fernerkundung, Technische Universität München 
  
724 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
to fi 
In tl 
and 
the 
and 
in cc 
wide 
of th 
In fi 
Fror 
tal s 
why 
with 
subs 
In oi 
mod 
The 
Xi Y