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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