DTM REFINEMENT USING MULTI IMAGE SHAPE FROM SHADING 
C. Piechullek, C. Heipke 
Technical University Munich 
Chair for Photogrammetry and Remote Sensing 
Munich, Germany 
E-Mail: peik@photo.verm.tu-muenchen.de 
Working Group III/2: Geometric-Radiometric Models and Object Reconstruction 
KEY WORDS: Shape from Shading, radiometric surface model, DTM reconstruction, simulation 
ABSTRACT 
We present a new approach to Shape from Shading (SFS) to be used with imagery of the MARS96 
 HRSC/WAOSS mission. The work builds upon prior investigations of multi image SFS [Heipke 1992; Heipke, 
Piechullek 1994]. Our SFS approach simultaneously processes multiple images and incorporates an object space 
model for the terrain surface. In contrast to most SFS methods which rely on the often too simple Lambertian 
surface reflection we introduce the Lommel-Seeliger law widely used in planetary science [Lumme, Bowell 1981; 
Hapke 1993] for modeling light reflection at the object surface. We investigate both the Lambertian and the 
Lommel-Seeliger model using synthetic images in order to compare the characteristics of both approaches and 
to show the advantages over existing SFS methods. 
1. INTRODUCTION 
Shape from Shading (SFS) is a technique for surface 
reconstruction which exploits the fact that surface 
patches, having different orientation towards a light 
source, are imaged with different brightness in the 
images. The grey values of these patches are directly 
related to surface inclination. The surface is generally 
assumed to have uniform reflectance properties. 
Therefore, SFS only performs well in areas with poor 
image texture. 
Digital image matching is a widely used tool in digital 
photogrammetry to derive surface information from 
multiple images. In the absence of sufficient, non- 
periodic image texture, however, digital image 
matching techniques fail to produce correct and 
reliable results. Thus, SFS can be used as a means to 
complete and refine a digital terrain model (DTM) 
which has been generated by digital image matching. 
The basic assumption for all SFS algorithms states 
that since different parts of a surface have different 
orientations relative to the direction of illumination 
they are imaged with different brightness. This spatial 
variation in brightness, called shading, is used to 
locally reconstruct the surface slope. The surface is 
described by small planar surface elements; the size of 
a surface element approximately equals the size of a 
pixel multiplied with the average image scale factor. 
The inclinations of neighbouring surface elements are 
then integrated to produce a geometric model of the 
object surface; all other influences which take part in 
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
the image formation process, i.e. illumination, sensor 
or atmosphere are assumed to be known. 
The basic equation of SFS can be derived assuming a 
constant albedo A along with Lambertian reflectance 
for the whole surface. In this case, the grey value 
g(X,y) at the position x', y' in image space only 
depends on the angles between illumination direction, 
viewing direction and the local surface normal. Since 
the local normal vector n — [-ny;-ny;1]" contains two 
unknown components for surface inclination, namely 
ny and ny, but only one observation, namely g(x,y’), 
for each point in object space, there exists an infinite 
number of inclinations, which all result in the same 
grey value. To overcome this indeterminability, 
additional information must be brought to bear. For 
possible solutions and a detailed bibliography on SFS 
see [Horn, Brooks 1989]. 
2. IMAGE FORMATION 
In this chapter the image formation process is shortly 
reviewed, since the relation between surface 
reflectance properties and image irradiance is the basis 
for our SFS model. 
Trying to express the orientations of the surface 
patches as a function of the grey values makes it 
necessary to take into account all influences in object 
and image space which are part of the imaging 
process. The amount of radiance reflected towards a 
sensor is a function of 
    
  
   
  
  
  
    
   
  
   
  
  
  
  
  
  
  
  
   
  
  
  
  
  
  
   
   
  
  
  
  
  
  
   
   
  
  
  
  
   
  
   
  
  
   
  
   
   
   
   
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