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Fig. 8.8 ( a ) Perspective view of the DEM of the eastern half of Theaetetus, extracted from the
topographic data by Cook ( 2007 ). ( b ) Perspective view of the LOLA DEM and ( c ) the GLD100
of the eastern half of Theaetetus from southwestern direction. The vertical axis is three times
exaggerated
As an example of the combination of shape from shading with sparse depth data,
d'Angelo and Wöhler ( 2008 ) analyse a sequence of five images of the lunar crater
Kepler acquired by the SMART-1 spacecraft on January 13, 2006, from heights
above the lunar surface between 1613 and 1702 km (European Space Agency, 2006 )
using the method described in Sect. 5.3.3 . The crater diameter amounts to 32 km.
During image acquisition the spacecraft flew over the crater and at the same time ro-
tated around its axis, such that the crater remained in the field of view over a consid-
erable period of time (European Space Agency, 2006 ). The first and last images of
the sequence are shown in Fig. 8.9 a. The image size is 512
512 pixels. Figure 8.9 b
shows the reconstructed part of the surface, which is smaller than the complete field
of view, as the surface albedo becomes non-uniform at larger distances from the
crater. The image is rotated such that north is to the top and west to the left. Relying
on a structure from motion analysis based on bundle adjustment (cf. Sect. 1.3 ), a
three-dimensional point cloud is extracted from the image sequence, as shown in
Fig. 8.9 c after Delaunay triangulation. Since no lens calibration data are available,
it is assumed that the lens can be described by the pinhole model with the principal
point in the image centre. The image scale amounts to 146 m per pixel (European
Space Agency, 2006 ), such that the scaling constant can be readily determined for
the structure from motion result.
Since no polarisation information is available, d'Angelo and Wöhler ( 2008 )
combine the shape from shading method with the result of structure from motion
(cf. Sect. 5.3.3 ), making use of the lunar-Lambert reflectance function according
to ( 8.6 ). The viewing direction was determined according to the normal vector of a
plane fitted to the three-dimensional point cloud extracted by structure from motion
analysis. For this non-specular surface, the uniform albedo ρ was estimated based
on all image pixels in the course of the iteration process according to ( 5.24 )asex-
plained in Sect. 5.3.2 . Saturated (white) pixels were excluded from the shape from
shading analysis.
The three-dimensional reconstruction result shown in Fig. 8.10 a distinctly reveals
the uneven crater floor of Kepler as well as the material that has slumped down the
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