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Fig. 5.11
Temperature-induced relative systematic error of the depth from defocus measurements,
corresponding to
(z
f
(T )
−
z
0
)/z
0
. The focal length is set to
f
=
20 mm
curvature of
(z)
is high (cf. Fig.
4.11
). This effect can be observed when the on-
line algorithm is applied to the lava stone sequence, for which Fig.
5.10
shows the
correlation between the error of the estimated absolute scale and the average PSF
radius
σ
. Measurement errors occurring when the last three images are included,
which are strongly blurred with
σ>
2 pixels, appear to have a substantial effect on
the accuracy of the estimated absolute scale. These considerations suggest that fea-
tures with large associated PSF radii
σ
should be excluded from the analysis, where
the favourable
σ
range depends on the depth-defocus function
S
(z)
.
According to Wöhler et al. (
2009
), systematic errors may also be introduced
by the thermal expansion of the body of the lens, which leads to a temperature-
dependent principal distance
b(T )
and thus a temperature-dependent depth
z
f
(T )
,
which yields a sharp image. The resulting 'shift' of the depth-defocus func-
tion (
4.15
) along the
z
axis leads to a relative systematic depth error of
S
[
z
f
(T )
−
z
0
]
/z
0
. As long as
|
T
−
T
0
|
T
0
and
z
0
f
, this systematic error is proportional
to
z
0
and
(T
−
T
0
)
(cf. Fig.
5.11
). For a lens with
f
=
20 mm, a temperature dif-
ference of
T
10 K leads to systematic deviations of the estimated absolute
scale of a few percent when the lens body is assumed to consist of aluminium with
a typical relative thermal expansion coefficient of 2
.
3
−
T
0
=
10
−
5
K
−
1
.
Other sources of systematic deviations are variations of the appearance of the ex-
tracted ROIs across the image sequence, especially when the surface exhibits spec-
ular reflectance properties.
×
5.1.4 Discussion
This section has described a method for combining triangulation-based and PSF-
based methods for monocular three-dimensional reconstruction of static scenes at
absolute scale. The proposed algorithm is based on a sequence of images of the ob-
ject acquired by a monocular camera from different viewpoints under constant fo-
cus settings. A varying degree of defocus is obtained by tracking feature points over
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