Graphics Reference
In-Depth Information
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
 
Search WWH ::




Custom Search