GEOMETRIC AND RADIOMETRIC MODELING OF THE MARTIAN SURFACE 
BASED ON OBJECT SPACE MATCHING AND PHOTOCLINOMETRY 
S. Gehrke a,b 
a TU Berlin, Geodesy and Geoinformation Science, Straße des 17. Juni 135, D-10623 Berlin, Germany 
b North West Geomatics, Pixelgrammetry Group, 212-5438 11 th Street NE, Calgary, AB T2E 7E9, Canada 
stephan.gehrke@pixelgrammetry.com 
Commission IV, WG IV/7 
KEY WORDS: Planetary Cartography, Radiometry, Matching, Visualization, DEM/DTM, Orthoimage, Atmosphere 
ABSTRACT: 
The unique image data of the High Resolution Stereo Camera (HRSC) on Mars Express enable for systematic derivation of Digital 
Terrain Models (DTMs) and orthoimages. Consequently, several photogrammetric processing algorithms have been investigated 
with HRSC imagery. The results form the basis for further research including photometric analysis. Within this paper, an integrated 
approach for photogrammetric and photometric modeling is presented: the combination of matching in object space and photoclino- 
metry. Using both geometric and radiometric image properties, geometry (DTM) and radiometry (Hapke reflectance parameters) of 
the Martian surface as well as atmospheric properties are jointly derived. Results will be shown for the Gusev crater southern hills 
and for an area with two small impact craters. 
KURZFASSUNG: 
Die einzigartigen Bilddaten der High Resolution Stereo Camera (HRSC) auf Mars Express ermöglichen die systematische Ableitung 
Digitaler Geländemodelle (DGMs) und Orthobilder. Folglich sind verschiedene photogrammetrische Verfahren zur HRSC-Daten- 
prozessierung untersucht worden. Die Ergebnisse bilden die Basis für weitere Forschungen wie die photometrische Analyse. In die 
sem Paper wird ein integrierter Ansatz zur photogrammetrischen und photometrischen Modellierung präsentiert: die Kombination 
von Matching im Objektraum und Photoklinometrie. Unter Ausnutzung der geometrischen und radiometrischen Bildeigenschaften 
werden Geometrie (DGM) und Radiometrie (Hapke-Reflexionsparameter) der Mars-Oberfläche sowie Atmosphäreneigenschaften 
gemeinsam abgeleitet. Ergebnisse werden für das Gusev-Bergland und für ein Gebiet mit zwei kleinen Einschlagkratem gezeigt. 
1. INTRODUCTION 
The High Resolution Stereo Camera (HRSC) on board of the 
European Mars Express mission is imaging Mars since January 
2004. After four years, HRSC is still unique regarding its ability 
to provide multiple stereo and full color within each imaging 
sequence. Altogether, this line scanner features nine bands in 
stereo angles between ±18.9° (Fig. 1), five of them panchroma 
tic and four colors: red, green, blue, and infrared. The entire 
data set is converted into Digital Terrain Models (DTMs) and 
orthoimages, which form the basis for map products and various 
scientific researches (Jaumann et al., 2007). Besides this sys 
tematic processing, several photogrammetric approaches have 
been investigated with HRSC imagery and recently compared 
in the HRSC DTM Test (Albertz et al., 2005; Heipke et al., 
2007); almost all of them involve either image matching or pho- 
toclinometry, which is also known as shape-from-shading. 
An entirely different approach for HRSC data processing is in 
vestigated by the author: Facets Stereo Vision, an algorithm for 
matching in object space (Wrobel, 1987; Weisensee 1992). It 
integrates traditionally consecutive steps of (image) matching, 
point determination, surface reconstruction, and orthoimage ge 
neration and implicitly allows for regarding the connections 
between geometric (DTM) and radiometric surface properties 
(basically, an orthoimage). First results for Mars have been pub 
lished by Gehrke & Haase (2006) and Gehrke (2007). 
In the context of this paper, significant enhancements of this 
approach - which are especially necessary but also very promi 
sing when applied on planetary surfaces like Mars - are sugges 
ted. Most important is the integration of object space matching, 
i.e., absolute height determination from image geometry, and 
photoclinometry, i.e., relative height (inclination) determination 
from image radiometry. Similar approaches have been presen 
ted in computer vision by Fua & Leclerc (1995) and in plane 
tary science by Lohse et al. (2006). 
As photoclinometry has to be based on an appropriate reflec 
tance model - in the context of this investigation: Hapke (1993) 
-, the new approach allows not only for geometric surface mo 
deling but for the integrated determination of material (reflec 
tance) parameters. Moreover, atmospheric properties - optical 
depth and the influence of ambient light - can be derived toge 
ther with surface models and, therefore, also corrected for. 
In the following, geometric and radiometric models suited to 
describe the Martian surface as well as the integrated approach 
that allows for determining these models are described. Results 
are presented for a sub-area of Gusev crater, in which the Mars 
Exploration Rover (MER) Spirit operates, and for two small im 
pact craters at the resolution limit of HRSC DTMs. 
2. SURFACE MODELS AND IMAGE FORMATION 
Any natural surface can be described by its shape and compo 
sition, i.e., in terms of a DTM and material parameters. These 
continuous properties are modeled in facets with appropriate in 
terpolation functions, within this investigation by bilinear inter