The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
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vertices are determined by accomplishing the intersection
between adjacent straight lines, according to the topology of the
projected LiDAR roof contour polygon. The final result is
better than the projected LiDAR polygon because most parts of
the refined polygon are improved to some degree. The proposed
methodology was not able to provide satisfactory results along
four sides of the refined polygon. The roof gable defined by the
straight lines 4 and 5 remains with a poor geometric description.
The reasons for this poor results are twofold: 1) the deficiency
of the proposed approach in finding the correct matching for the
projected LiDAR straight line 5; and 2) the lack of a valid
candidate for the projected LiDAR straight line 4. The roof
details neighboring the straight lines 13 and 15 were poorly
described due to a basic reason. The geometric descriptions of
the corresponding parts of the polyhedron extracted from the
3D laser data are not enough to be handled by the proposed
approach properly. Finally, based on the above analysis, the
completeness and correctness of the result are 100% and 79%
(= 15/19), respectively.
4. CONCLUSIONS AND OUTLOOK
In this paper a methodology was proposed for geometric
refinement of LiDAR roof contour project onto the image-space.
An MRF description for groupings of image-space roof contour
straight lines was developed, assuming that each building roof
contour reconstructed from the LiDAR data is topologically
correct, but its geometry needs to be improved. The MRF
description is formulated based on relations (length, proximity,
and orientation) between straight lines extracted from the image
and the projected roof contour polygon. The groupings of
straight lines are obtained by optimizing an energy equation
associated to the MRF description. The topology of the
projected LiDAR roof contour is used to get the polygon
representing the refined image-space roof contour.
The preliminary results showed that the proposed methodology
is promising. Although only a test was presented and discussed,
it involves a building with a relatively complex geometry and a
low contrast with the background. Most sides of the refined
polygon are geometrically better then corresponding projected
LiDAR straight lines. The general quality of the obtained result
can be expressed by the completeness and correctness
parameters, which were 100% and 79%, respectively.
Some directions for future developments are the improvements
of the energy function and the use of more appropriate
optimization methods (as, e.g., the simulated annealing
algorithm) of the energy function, mainly to allow high
dimensional problems to be treated properly. The energy
function can be improved tanking into account the shadow
information, the comer information, the laser heights, besides
other cues.
ACKNOWLEDGEMENTS
This paper was carried out with support of CNPq, National
Council for the Scientific and Technological Development -
Brazil, and FAPESP, Sao Paulo State Foundation for Research
Development - Brazil. The available building polyhedron model
used in the experiment was previously extracted from LiDAR
data supplied by LACTEC - Technological Institute for
Development, Brazil.
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