teration several
ent weights for
y. The following
m of all weights
> weights of all
of 3D points is
nean differences
1 and maximum
weights from
. Table 3 shows
n maximum
2.7354
3.5491
4.4104
) 4.8409
m maximum
9 14.5787
5 16.8064
6 19.1585
8 19.5025
ce
te surface
Figure 7. Two residual images of concrete surface
Besides statistical data about the geometry of both surfaces
given in the tables above, also visualisation of the surfaces, e.g.
fig. 6, combined with information on point distribution, figures
4 and 5, and especially residual images, e.g. fig. 7, are valuable
sources of information on the properties of the approach.
3.2 Discussion of the results
A comparison of the results of computations with different
weights and the reference data given by stripe projection clearly
shows, that there are only very small changes in Zmean in both
data sets. Also the largest negative differences (column
minimum in tables 2 and 3) are almost constant while the largest
positive differences (maximum) moderately increase when the
weights of 3D points diminish. Obviously there is almost no
contradiction between 3D points and the surfaces derived from
the intensity images.
The remaining differences which can clearly be seen from
minimum and maximum in tables 2 and 3 and also from Zmean
in table 3 seem to be caused by various other reasons. One
reason is the uneven distribution of 3D points acquired by the
stripe projecting device. Figure 3 shows dense point clouds at
the edge of the test surface and gaps in the curved centre. Also
the concrete surface, cf. fig. 4, shows gaps on the gravel. These
areas are much larger than the resolution of the surface
description (1 mm) and, thus, require either supporting image
data or some kind of regularisation. As the image data does not
contain sufficient gradients, cf. fig 5, in the same region of the
surface it does not contribute to the determination of the surface
parameters. The effect of specular reflection on the object is an
additional error source.
First experiments with regularisation by curvature reduction
with varying weights did not yield satisfying results. Figure 6
shows a colour coded height model of the surface reconstruction
revealing gross errors in areas without texture and 3D points.
Depending on the strategy used for processing (with or without
hierarchical object model and image pyramid) the influence of
the approximate values on the final result is difficult to balance
by choosing appropriate weights.
Figure 7 finally shows the effect of an unsuitable surface model.
The large positive and negative residuals (coded black and
white in the figure) in two out of seven images each lie on parts
of the surface which are not projected in all digital images and
leading to contradictions in the reconstruction process.
4. CONCLUSIONS
In the presented paper the approach of combined adjustment of
3D point data and digital photogrammetric images has been
applied to close range applications for the first time. The results
are promising under the aspect of mutual support of the
different data.
It could clearly be shown that in case of smooth surfaces the
chosen 2 1/2 D surface model delivers highly precise results and
an excellent representation of the surface. Larger differences
between the photogrammetric results and the true surface given
by stripe projection are most likely caused by faint image signal
or un-modelled specular reflection on the surface.
In the case of rough and structured surfaces a refinement of the
surface model to a true 3D representation seems to be
unavoidable.
Further research work still has to be done considering the
determination of adequate weights for 3D points, intensity
observations and regularisation functions.
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GOM 2002: Product information ATOS.
http://www.gom.com/En/Products/atos vars.html (accessed 15
June 2002)
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