Applications to Lunar Remote Sensing - 3D Computer Vision: Efficient Methods and Applications - page 318

large-scale eastward slope of the profile, which can only be derived from the shadow
image. Effectively, the shadow allows one to adjust the albedo ρ such that the shape
from shading algorithm yields a surface profile consistent with both the small-scale
depth variations evident in the shading image and the large-scale slope derived from
the shadow image. Figure 8.6 b shows the inner eastern rim of the lunar crater Coper-
nicus. The surface profile reveals terraces and small craters in the crater wall. The
performance of the reconstruction algorithm is slightly decreased by small shadows
in the shading image cast by the central peaks. The correspondence of the simu-
lated shadow contour with its real counterpart is reasonable. In Fig. 8.6 c, the outer
eastern rim of the lunar crater Wolf is shown along with the depth differences at the
corresponding inner rim obtained by shadow analysis alone. A comparison reveals
that the crater floor is lying on the same level as the surrounding mare surface. The
simulated shadow shows all features displayed by the real shadow image.
Figure 8.7 shows the reconstructed surface profile of the floor of the lunar crater
Theaetetus, which has a diameter of 25 km. It was generated by the technique de-
scribed in Sect. 5.2.3 that relies on an initialisation of the shape from shading al-
gorithm by surface gradients obtained by the analysis of several shadows observed
under different illumination conditions. Both the simulated shading image and the
contours of the simulated shadows correspond well with their real counterparts.
Even the ridge crossing the crater floor, which is visible in the upper left corner
of the region of interest in Fig. 8.7 a and in the Lunar Orbiter photograph shown in
Fig. 8.7 c for comparison, is apparent in the reconstructed surface profile (arrow).
Hence, the reconstruction technique reliably indicates even small-scale structures
on the surface that cover only a few pixels. Furthermore, it turns out that the crater
floor is inclined from the north to the south, and a low central elevation (rising to
about 250 m above the floor level) becomes apparent in the reconstructed surface
profile. Such features are important for a geological interpretation of the crater, as
they essentially mark the difference between simple bowl-shaped craters and more
complex craters such as Theaetetus (Spudis, 1993 ). This central elevation does not
appear in the images in Fig. 8.7 a used for reconstruction but is clearly visible in
the telescopic image of Theaetetus acquired at a solar elevation angle of μ 28 . 7 ◦

shown in Fig. 8.7 e (lower arrow). The corresponding simulated image (lower part
of Fig. 8.7 e) is very similar to the real image, although that image has not been
used for reconstruction. This kind of comparison is suggested by Horn ( 1989 )asan
independent test of reconstruction quality. For comparison, traditional shape from
shading as outlined in Sect. 3.2.2.2 yields an essentially flat crater floor and no ridge
(Fig. 8.7 f). This shows that the traditional approach is obviously not able to extract
reliable information about surface gradients perpendicular to the azimuthal direction
of illumination under the given illumination conditions.
As an independent comparison, Fig. 8.8 a shows a three-dimensional reconstruc-
tion of the eastern half of Theaetetus extracted from the topographic maps pro-
vided by Cook ( 2007 ). These topographic data have a lateral resolution of 1 km and
were computed with the stereophotogrammetric approach described by Cook et al.
( 1999 ), relying on Clementine orbital imagery. The DEM in Fig. 8.8 a is fairly noisy
and contains some spike artefacts on the crater rim. Furthermore, for some points

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