Graphics Reference
In-Depth Information
An advantage of the described local approach is that the three-dimensional recon-
struction result is not affected by additional constraints such as smoothness of the
surface but directly yields the surface gradient vector for each image pixel. A draw-
back, however, is the fact that due to the inherent nonlinearity of the problem, exis-
tence and uniqueness of a solution for
p
uv
and
q
uv
are not guaranteed for both the
albedo-dependent and the albedo-independent case. However, in the experiments
presented in Sect.
5.3.4
and Chap.
6
we show that in practically relevant scenarios
a reasonable solution for the surface gradient field and the resulting depth
z
uv
is
obtained, even in the presence of noise.
5.3.2 Estimation of the Surface Albedo
For the specular surfaces regarded for the experimental evaluations based on syn-
thetic data (cf. Sect.
5.3.4
) and on real-world objects in the context of industrial
quality inspection (cf. Chap.
6
), the three-component reflectance function according
to (
3.14
) is used by d'Angelo and Wöhler (
2005a
,
2005b
,
2005c
,
2008
), correspond-
ing to the reflectance function
cos
θ
i
+
cos
α)
m
n
N
R
I
(θ
i
,θ
e
,α)
=
ρ
σ
n
·
(
2 cos
θ
i
cos
θ
e
−
(5.22)
n
=
1
with
N
2. The term in round brackets corresponds to cos
θ
r
with
θ
r
as the an-
gle between the direction
v
from the surface to the camera and the direction of
mirror-like reflection (cf. (
3.11
)). For
θ
r
>
90
◦
only the diffuse component is con-
sidered. This reflectance function consists of a Lambertian component, a specular
lobe, and a specular spike (Nayar et al.,
1991
). For a typical rough metallic surface,
the measured reflectance function is shown in Fig.
3.4
, where the material-specific
parameters according to (
5.22
)aregivenby
σ
1
=
=
3
.
85,
m
1
=
2
.
61,
σ
2
=
9
.
61, and
m
2
=
15
.
8. The specular lobe is described by
σ
1
and
m
1
, and the specular spike by
σ
2
and
m
2
, respectively.
One possible way to determine a uniform surface albedo
ρ
is its estimation based
on the specular reflections in the images used for three-dimensional reconstruction,
which appear as regions of maximum intensity
I
(l)
spec
as long as the reflectance be-
haviour is strongly specular, i.e. at least one of the parameters
σ
n
is much larger
than 1. Note that the pixel grey values of these regions must not be oversaturated.
For these surface points we have
θ
r
=
0 and
θ
(l)
i
=
α
(l)
/
2. Relying on the previously
determined parameters
σ
n
,(
5.22
) yields
cos
α
(l)
2
−
1
L
N
σ
n
α
(l)
1
L
I
(l)
ρ
=
spec
·
+
.
(5.23)
l
=
1
n
=
1
In principle, a single image is already sufficient to determine the value of
ρ
as long
as it contains specular reflections. Note that in (
5.23
) the dependence of the param-
eters of the reflectance function on the phase angle
α
is explicitly included.
Search WWH ::
Custom Search