Graphics Reference
In-Depth Information
I
uv
−
G
uv
∗
R
I
(ρ
uv
,p
uv
,q
uv
,α)
2
e
PSF
I
=
(5.25)
u,v
Φ
uv
−
R
Φ
(p
uv
,q
uv
,α)
2
e
PSF
Φ
=
G
uv
∗
(5.26)
u,v
D
uv
−
R
D
(p
uv
,q
uv
,α)
2
e
PSF
D
=
G
uv
∗
(5.27)
u,v
describing the mean square deviation between the observed intensity and polarisa-
tion values and the modelled reflectances convolved with the PSF
G
uv
extracted
from the image as described in Sect.
4.2.2
. This approach is related to the shape
from shading scheme for blurred images introduced by Joshi and Chaudhuri (
2004
).
In that work, however, the PSF radius is estimated simultaneously with the surface
gradients, while we independently determine the PSF radius for every position in
the image during the depth from defocus analysis. The iterative update rule (
5.21
)
then becomes
∂R
I
∂p
+
∂R
Φ
∂p
p
(n
+
1
)
p
(n)
=¯
+
λ(I
−
G
∗
R
I
)G
∗
μ(Φ
−
G
∗
R
Φ
)G
∗
∂R
D
∂p
+
ν(D
−
G
∗
R
D
)G
∗
,
(5.28)
where the dependence of the surface gradients and the PSF on
u
and
v
has been
omitted for clarity. An analogous expression is readily obtained for
q
.
5.3.3.2 Integration of Accurate but Sparse Depth Information
One possible method to obtain depth information about the surface is stereo image
analysis. In the experiments by d'Angelo and Wöhler (
2008
), the correlation-based
blockmatching method described in Sect.
1.5.2
is used. Apart from blockmatching
techniques, one might think of employing a dense stereo algorithm which computes
a depth value for each image pixel independent of the presence of texture (Horn,
1986
; Scharstein and Szeliski,
2001
; Hirschmüller,
2006
). However, parts of the
surface may show no surface texture at all, or corresponding parts of the stereo im-
age pair do not display a similar structure. The latter behaviour occurs e.g. as a
consequence of specular reflectance properties leading to a different appearance of
the respective surface part in the stereo images. In such cases of missing or contra-
dictory texture information, dense stereo algorithms usually interpolate the surface
across the ambiguous image parts, leading to an inaccurate three-dimensional re-
construction result for the corresponding region. Hence, we prefer to compute depth
points only in places where point correspondences can be established unambigu-
ously and accurately and to compute dense depth data in a subsequent step based on
an integration of the available photometric or photopolarimetric information.
Another technique well suited to determine a three-dimensional point cloud of
the surface to be combined with the SfPR analysis is structure from motion (cf.
Search WWH ::
Custom Search