International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
building boundary. The final squared building and the original 
building points are also shown in Figure 3, with the original 
lidar points overlaid atop. Presented in Figure 4 are examples 
of regularized building footprints with their ortho image 
displayed beside. 
  
  
Figure 3. Boundary points (left) and parametric lines overlaid 
with original lidar points (right). 
  
  
Figure 4. Some examples of regularized buildings 
There are several characteristics of this least squares based 
hierarchical building squaring approach. First, it is robust to 
possible errors in building segmentation and boundary tracing. 
This is because of the hierarchical implementation of the 
solution, shorter line segments being processed after longer 
lines. Second, the errors of final extracted building can be 
evaluated through the least squares adjustment process, using 
either the residual values between estimated coordinates and 
the observed coordinates of the points or determining the 
distance of each of these points from the parametric lines. 
  
   
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Third, it provides a global optimization solution to the building 
squaring problem. No points or line segments are taken as fixed 
reference. The longer line segments receive larger weights than 
shorter ones. All points and line segments are subject to certain 
adjustment in position depending on their contribution to the 
line segments Figure 4 present the results of several squared 
buildings along with their ortho-images. They are obtained 
from the above described regularization process. 
Once the building footprints have been regularized, we can use 
the *Z" dimension of lidar data to obtain elevations for the 
parametric lines of the edges that we have determined. The 3D 
visualization of buildings that have flat roofs or “multiple 
layers of flat roofs" is accomplished by segmenting those 
portions of the roof that have similar "Z" values. Then these 
segmented parts are individually “regularized” in the manner 
described above. The parametric lines that define the 
regularized segments of the roof are given elevation values 
based on the average elevation of that segment of points. 
As for the ridge buildings, a similar process is developed. In 
this case, slopes of each roof points are calculated based on a 
triangulation of roof points. Points with similar slope will be 
used to model the slant roof plane. The similar regularization is 
applied to form the slant roof plane. Reconstructed 3D 
buildings are shown in Figure 5. 
  
Figure 5. 3D reconstructed buildings 
6. CONCLUSION 
We have tried to show that lidar data can be used as a tool to 
model the urban environment. The series of steps described 
above can process raw lidar data and can be used to create 
building models that closely resemble the reality. 
We used a novel approach to initially label the data as ground 
and building points. Then, we described a series of steps to 
segment the building point dataset, such that 3D points can be 
mapped to each building. This building detection and 
   
  
  
  
  
  
  
  
  
  
   
   
  
   
  
   
   
   
  
  
   
   
  
  
  
  
  
  
  
  
  
  
  
   
   
  
  
  
  
  
  
   
  
   
   
    
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