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Ta b l e 5 . 2
Comparison of reconstruction results to ground truth data for the synthetic data exam-
ples given in Fig.
5.14
Example
μ
(
1
)
shadow
μ
(
2
)
shadow
μ
1
μ
2
z
RMSE (pixels)
ρ
RMSE (percent)
4
◦
2
.
5
◦
(a)
0
.
043
2
.
0
6
◦
8
◦
2
.
5
◦
(b)
0
.
008
0
.
2
6
◦
8
◦
2
.
5
◦
(c)
0
.
052
5
.
3
5
◦
4
◦
5
◦
(d)
0
.
135
1
.
3
0
.
174
1
.
1
of surface points, the shadow analysis yields accurate depth differences. Dense but
less accurate depth information is obtained with the shape from shading approach;
however, it permits an infinite number of solutions even with the regularisation con-
straint of a smooth or integrable surface. As a first step, a solution which is consistent
with the average depth difference determined by shadow analysis is selected using
the presented iterative scheme. As a second step, the error function to be minimised
is extended by an error term that takes into account the detailed structure of the
shadow.
The second described approach for combining shading and shadow features is es-
pecially suitable for surface reconstruction under coplanar light sources. It is based
on the initialisation of the surface profile by analysis of at least two shadows ob-
served at different illumination angles. In this setting, shadow analysis allows for
deriving the surface gradients in both the horizontal and the vertical image direc-
tion along with the surface albedo for a small surface patch between the shadow
lines. The surface profile is iteratively reconstructed based on the first proposed al-
gorithm, relying on one shading and one shadow image, which is initialised with the
previously obtained result of the analysis of two or more shadows.
Based on synthetic data, we have shown that a high accuracy can be achieved
with the proposed reconstruction techniques. This first evaluation is extended to the
three-dimensional reconstruction of metallic surfaces in Chap.
6
and lunar surface
regions in Chap.
8
.
5.3 Shape from Photopolarimetric Reflectance and Depth
This section introduces an image-based three-dimensional surface reconstruction
method based on simultaneous evaluation of intensity and polarisation features
(shape from photopolarimetric reflectance) and its combination with absolute depth
data (shape from photopolarimetric reflectance and depth). The description is
adopted from d'Angelo and Wöhler (
2005a
,
2005b
,
2005c
,
2006
,
2008
).
A number of approaches for combining stereo and shape from shading have been
proposed in the literature. Cryer et al. (
1995
) combine depth data on large spatial
scales obtained by stereo analysis with depth data on small spatial scales determined
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