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7. Increase the iteration index:
m
1.
8. Repeat steps 2-7 until topography-related artifacts begin to appear in the albedo
map
ρ
(m)
m
uv
.
At this point it is important to take into account the smoothing effect of the update
rule for
z
uv
in (
5.38
), which is due to the use of the local average
z
uv
in the discrete
approximation of the Laplace operator by Horn (
1989
) occurring as a result of the
inclusion of the integrability error
e
int
. If the algorithm is initialised by a smooth
surface, small surface details tend to be less pronounced in the final solution than
their real counterparts. Hence, Grumpe and Wöhler (
2011
) propose an extended
photoclinometry approach which performs a pixel-wise independent minimisation
of the error term
¯
g
˜
=
e
i
+
δe
DEM
(5.42)
with respect to the surface gradients
p
PHCL
uv
and
q
PHCL
uv
based on an optimisation by
gradient descent. The surface is initialised with
z
DEM
uv
, while the albedo map is ob-
tained based on the surface gradients derived from to
z
DEM
uv
according to steps 2-4
described above. The corresponding surface
z
PHCL
uv
is then obtained using the itera-
tive scheme of Horn (
1986
) according to (
3.32
). Generally, the appearance of small-
scale details is more realistically pronounced in
z
PHCL
uv
than in the solution obtained
by (
5.38
) initialised with a smooth surface. Hence, the surface
z
PHCL
uv
obtained by
the extended photoclinometry scheme is favourably used as an initialisation to the
variational approach described above.
The extended shape from shading method described in this section, which relies
on the integration of dense depth data with an effective lateral resolution which is
significantly lower than that of the available images, will be applied to the three-
dimensional reconstruction of metallic surfaces in an industrial metrology scenario
in Sect.
6.3.5
and to the construction of DEMs of the lunar surface in Sects.
8.2
and
8.4
.
5.6 Three-Dimensional Pose Estimation Based on Combinations
of Monocular Cues
This section describes the integrated approach to the problem of three-dimensional
pose estimation (cf. Sect.
2.1
) proposed by Barrois and Wöhler (
2007
). The presen-
tation in this section is adopted from that work. Most appearance-based approaches
to three-dimensional pose estimation explicitly rely on point features or edges. How-
ever, in the presence of a cluttered background or low contrast between object and
background, edge information tends to be an unreliable cue for pose estimation. This
method applies the principles of combining several sources of complementary in-
formation for three-dimensional surface reconstruction, which have been derived in
the previous sections of this chapter, to the problem of three-dimensional pose esti-
mation. It relies on the comparison of the input image to synthetic images generated
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