International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences
Vol XXXV, Part B5. Istanbul 2004
3.7 Orthogonal lines configuration
This solution requires the specification of the projection of
three edges assumed to be orthogonal in the 3-D space. It
fixes the three object orientation parameters, letting unde-
termined the translation.
Figure 10: Orthogonal lines geometry.
Let S1 (A; B1 ), Sa(Aa Ba), S'3(.43 B3) be the selected seg-
ments. The director vector Vi of the 3-D edge D; that
projects in S; can be expressed as a linear combination of
i; =CA A, and b; = = CR, As its length is not constrained,
a scalar k; exists so that:
d
—
=.
i
>
He i € [1,3]
The orthogonality of the 3-D edges is given by:
We must then solve the following system:
ky ko J by : bo HE kı : b, : as oF ko 1 dy + bo + ay : d = ()
ki ka : bi 2 ba s ky y bi : 3 = ka . di : ba + d x üa zs)
ka ka * ho > ba mm ka T ba ; da = ka : d» . ba zi da : as = 0
ko is extracted from thc first equation and k4 from the
second one. Substitution in the third equation provides a
quadratic equation in k;. This system may admit two real
solutions that can be used to der ive ko and ks, and then the
three vectors V;. Each solution corresponds to the direct or
the inverse interpretation of the built reference frame. If the
equation has no real root, the provided segments configu-
ration cannot be associated to a set of orthogonal segments.
This may come from numerical errors when the viewpoint
configuration is close to some limit condition. Our imple-
mentation displays the closest solution to the configuration
where the built reference frame faces towards the viewer
with a vertical Z axis. RK, is built over E, 1, V and Va, with
PSP.
Figure 11 example displays the selected features (a) and
the matched object on the computed solution (b). Then
successive Interactive actions are:
- 1) parallel translation to the image plane / (c),
- 2) translation along PP, interpretation line (d).
This solution is quite general and in particular, each seg-
ment may be indifferently selected in a separate view. Ac-
tually our experience showed that finding a view with a
Figure 11: Orthogonal lines example.
long edge in each orthogonal direction can be a really hard
constraint. Two long orthogonal edges may be easily dis-
played, but most often the third one is short and may dete-
riorate the solution accuracy.
4 ADDITIONAL ASSISTANCES
4.1 Semi-automatic segment extraction
All these solutions require the extraction of image seg-
ments. This task repetition could become tedious and soon
impede the system performance. Therefore we have im-
plemented a semi-automatic segment extraction function
in which the operator firstly draws a rough initial segment
close to the relevant edge, and lets it be attracted towards
the best contour found in the surrounding area (Even and
Malavaud, 2000). The way it was integrated is particularly
well suited to cope with the many possible failures of the
automatic attraction function, so that this assistance actu-
ally contributes to speed up the modelling work.
4.2 Estimation of the solution consistency
A selection of the fewest image features possible makes
our technique very sensitive to the many error sources that
are linked to sensor definition, interior and exterior orien-
tation inaccuracy, selected image features quality (sharp-
ness, contrast) and care of the interactive delineation tasks.
Moreover computer vision algorithms are viewpoint de-
pendent and these primary error sources are amplified by
geometrical conditions such as the features spatial distri-
bution or the viewpoints relative position. The operator
has not always a good perception of the actual geometrical
configuration. This drawback is amplified by the exper-
tise level required. In a given situation, estimating if the
features distribution and viewing conditions are favourable
or not requires a fine knowledge of the implemented algo-
rithm.
Some estimation of the geometrical configuration quality
must be computed and provided to the operator to help him
decide on the registration reliability according to the task
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