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ISPRS Commission III, Vol.34, Part 3A ,,Photogrammetric Computer Vision“, Graz, 2002 
  
  
  
  
  
  
  
   
   
(c) 
  
  
  
Figure 4. (a) first return height minus last return height (b) 
gradient based on last return heights (c) filtered 
discrepancy map between first and last 
2.2 Local statistical analysis and interpretation 
The surface smoothness was tested through local statistical 
interpretation. The height variation over a small region is an 
excellent tool in LIDAR data segmentation (Mass, 1999). Each 
height group that lies within a small square area will be fit to a 
plane. The iteratively reweighed least squares adjustment 
algorithm was used to solve the overdetermined system and 
obtain the surface parameters (Mikhail, 1976). Weights were 
assigned to each observation based on its residual, except in 
the first iteration all observations were weighted equally. After 
the last iteration in the adjustment procedure, the root mean 
square error (RMSE) was computed for each square window 
and recorded at the center of that window. 
The number of height points that are included in the surface 
fitting procedure depends on the window size. For example, if 
we have a window of 3x3, then the number of observations is 
equal to nine. Moreover, each of the nine observations is 
included in the adjustment nine times in nine different 
windows. Each one of those windows has a different RMSE 
since it was calculated using different observations. So, the 
height point might belong to any of the windows that contain 
this point. The attribute used to classify the point is the RMSE. 
So, the point will belong to the window that has the minimum 
RMSE, in order to obtain the best fit to maximize the surface 
smoothness. A high RMSE indicates an irregular surface that 
can be interpreted as a characteristic of a tree or a rough 
surface, since most buildings have smooth roof surfaces. With 
a few number of iterations, all high variability surfaces were 
detected and filtered using a minimum filter with a size equal 
to the fitting window or larger. The resulting digital surface 
model (DSM) of the two filtering steps is shown in figure 6. 
  
  
(b) 
  
  
Figure 5. (a) last return heights before first step filtering, (b) 
result after first step filtering 
  
  
  
  
  
Figure 6. the filtered last return image heights 
3. BUILDING FOOTPRINT DETECTION AND 
DELINEATION 
Detecting buildings directly from the raw LIDAR data is not a 
straightforward problem. This is due to the ambiguity of other 
vertically extended features which are not buildings in the raw 
data. Filtering “noise” such as trees and other extraneous 
objects facilitates the detection of building footprints and 
consequently the reconstruction procedure. Using the ground 
plans as in (Brunn and Weidner, 1997) or utilizing a 
multispectral reflectance for the segmentation as in (Haala and 
Brenner, 2000) are alternatives to the filtering step to obtain