![](bg8.png)
ground truth than the AAV — both in terms of mean
and variance of the difference.
Figure 13: Histograms of the elevation difference between
the tested method variants and the ground truth.
Table 1: A comparison of the different methods’ results to
the ground truth. “coverage” refers to all the points with at
least one trace covering it.
Vatiant Data Mean Variance
RAV all points (6606) +0.59 1.51
RAV coverage (4923) +0.47 1.63
AAV coverage (4923) +3.56 6.88
One should note that since the GPS receiver is typ-
ically not located at the ground level while recording,
it is expected that the AAV will results with some off-
set in z above the ground truth, but this should not
affect the variance of the comparison with the ground
truth.
7 CONCLUSIONS AND FUTURE
WORK
In this paper, we presented an approach for the recon-
struction of 3D graphs from 3D positional traces and
2D graphs, and shown that this method can provide
good results in the application of road interchanges.
We believe that the RAV method might also be ap-
plied to other applications such as medical reconstruc-
tion, cave mapping, or flight paths. In order to adapt
this method to other applications, we suggest a vari-
ation to the problem as follows. Since we use in this
method the graph’s 2D positions only for the purpose
of registering the traces, we could think of a variation
of the problem in which the nodes’ 2D positions are
not known, and instead other information is available
to allow us to register the traces to the graph, or the
2D positions are not accurate but can still be used for
registration. In that case, instead of calculating the
nodes’ elevations, every coordinate of the nodes’ po-
sitions is calculated separately and independently in
the same manner.
For the application of 3D road network recon-
struction from traces, we suggest a semi-automatic
method to provide more topologically-accurate re-
sults than existing methods that reconstruct a road net-
work from traces alone. With the evident success of
OpenStreetMap and other commercial 2D maps, we
believe that using our method on existing 2D datasets
to ameliorate them to 3D can provide with results that
are more robust, due to the high quality of these exist-
ing datasets. In general, the system would consist of
the following steps:
1. Reconstruction of a 2D graph from the univari-
ate traces using an existing 2D reconstruction
method, such as (Guo et al., 2007; Cao and
Krumm, 2009; Chen et al., 2010).
2. Augmentation of the 2D graph into 3D using the
method presented in this work.
This proposed approach also allows one to make use
of traces that have only 2D information in the first
step, and to achieve reasonably good results with a
small amount of 3D traces.
Finally, a more comprehensive data analysis on
the GPS output signal might provide with an ap-
propriate filtration and noise-removal method, which
might improve the reconstruction quality for the in-
terchanges application. Still, the basic property of a
global trace error will still manifest in traces recorded
by consumer devices, and thus the method presented
in this paper or an equivalent method is still required.
ACKNOWLEDGEMENTS
This research was supported in part by the E. and J.
Bishop Research Fund, Technion.
We would also like to thank Armi Grinstein –
Geodetic Engineering Ltd (http://www.armig.co.il/)
for kindly providing us with the ground truth data for
the ‘Mesubim’ interchange.
REFERENCES
Aanjaneya, M., Chazal, F., Chen, D., Glisse, M., Guibas, L.,
and Morozov, D. (2012). Metric graph reconstruction
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Cao, L. and Krumm, J. (2009). From gps traces to a routable
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