The International Archives of the Photogrammetrv. Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
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4.4 Modeling Algorithm 
The integrated approach, as shown in Fig. 2, enhances Facets 
Stereo Vision (chapter 3.1) with photoclinometry (4.1) and in 
tegrates the derivation of surface reflectance (2 and 4.2) and 
atmospheric properties (4.3). Depending on the actual investi 
gation area, desired quality, and resolution, it might become 
useful or even necessary to constrain or omit individual parame 
ters. In general, surface reflectance and atmospheric models are 
interchangeable and can be replaced. E.g., Lambert’s Model 
may be used for very simple surface parameterization. 
In practice, the complexity of the algorithm should be increased 
along with the increase of resolution. Photoclinometry is not ne 
cessary to obtain a coarse DTM, and meaningful photometric 
parameters can only be obtained if geometric details of the sur 
face are modeled. In this context, it may still be useful to regu 
larize the least squares adjustment as described in 3.2. 
The integrated algorithm can be regarded as a complete surface 
modeling approach for Mars that makes use of all radiometric 
and geometric information contained in HRSC data. Because it 
is based on the entire image content - literally every pixel that 
is obtained in the investigation area it can be applied to small 
regions only, typically below 100x100 DTM facets. 
5. APPLICATION 
The integrated surface modeling algorithm has been implemen 
ted in MATLAB. It has been applied to several regions of Mars 
using HRSC imagery of different resolution obtained under va 
rious illumination and viewing geometries. In the following, 
two representative examples are discussed: a 25x25 km area of 
hills and mesas, which is located in southern Gusev, as well as a 
2.8x2.8 km area containing two small impact craters. 
5.1 Investigation Areas and HRSC Data 
The described surface modeling approach can make use of pan 
chromatic HRSC bands: stereo (S1/S2), photometry (P1/P2), 
and nadir (ND). (See chapter 6 for remarks on color.) 
The Gusev area has been imaged multiple times (cp. Jehl et al., 
2008), e.g., during orbit 648 from very high altitudes (Fig. 3; 
Table 1). Although this inevitably leads to rather low ground re 
solutions, the major advantage is large stereo angles due to orbit 
curvature - up to 31.2° in comparison to nominal HRSC angles 
of 18.9°. Local viewing angles range from 0° to 60°. The illu 
mination is generally low; it varies locally between 51° and 90°, 
casting some shadows. Such geometry potentially allows for the 
derivation of reliable atmospheric optical depth and surface re 
flectance. Therefore, radiometric results are discussed in-depth. 
Table 1: Overview of HRSC bands and viewing geometries 
Area: 
Gusev Southern Hills 
Two Craters 
Orbit: 
648 
894 
Band 
Ground 
Viewing 
Ground 
Viewing 
Resolution 
Angle 
Resolution 
Angle 
SI 
281 m/pixel 
31.2° 
36 m/pixel 
21.6° 
PI 
289 m/pixel 
21.4° 
- 
- 
ND 
165 m/pixel 
2.1° 
16 m/pixel 
o 
o 
P2 
448 m/pixel 
29.5° 
- 
- 
S2 
n/a 
n/a 
32 m/pixel 
21.7° 
Fig. 3: Investigation area (red rectangle) within Gusev crater. 
The second investigation area - two small craters in the Nanedi 
Valles region, imaged during orbit 894 (Fig. 6) - has been cho 
sen to demonstrate the approach’s strength in modeling fine 
surface details. With special emphasis on high resolution geo 
metry, HRSC photometry bands with ground resolutions around 
65 m/pixel (due to pixel binning) have not been used (Table 1). 
5.2 Gusev Southern Highlands 
For the Gusev area, surface radiometry and geometry as well as 
atmospheric properties have been successfully derived. The re 
sulting DTM features a post spacing of 500 m (Fig. 4). 
17S.J 
Fig. 4: Gusev hills DTM as color-coded perspective view. 
The optical depth has been determined with x = 1.55 ± 0.06, 
meaning that only 21% of the reflected light directly reached 
the nadir-looking detector. This number appears low but, how 
ever, it is well within the range that Hoekzema et al. (2006) 
derived for regions in and around Gusev crater. 
Based on the integrated adjustment results, one Hapke Model 
has been calculated for the entire investigation area, excluding 
shadows. The initial approach involved all four parameters of 
equation (1); it lead to a large c value that was also highly cor 
related with the other phase function parameter, b (Table 2).