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Figure 4. Recursive MBR procedure of the first building 
The second test building includes 3 MBR levels. Figure 5 
illustrates the recursive MBR results of the second test 
building. The initial LIDAR boundary points and the 1* level 
MBR are presented in Figure 5(a) and Figure 5(b), 
respectively. Figure 5(c) displays the non-overlapping points 
in black circles with the 1* level MBR, and Figure 5(d) 
shows their projection onto the 1* level MBR in red circles. 
The 2™ level MBR, i.e., the black rectangle in Figure 5(e), is 
derived using the points in Figure 5(d). The same procedure 
is repeated to find the non-overlapping LiDAR points with 
the 2™ level MBR (i.e., pink circles in Figure 5(f)) and their 
projection onto the 2™ level MBR (i.e., red circles in Figure 
5(g)). Figure 5(h) shows the 3 level MBR in green color. 
The final shape can be derived by alternating subtraction and 
addition of different levels (1° level MBR — 2™ level MBR + 
3" level MBR) as seen in Figure 5(i). 
  
  
  
  
  
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Figure 5. Recursive MBR procedure of the second building 
Before following the Boolean operation of different MBR 
levels, the rectangular models determined from the LiDAR 
data undergo a refinement process using the sequential 
adjustment. Figure 6 shows the two MBR levels (red and 
yellow) derived from LiDAR data and the final adjusted 
MBRs after the model-image fitting projected onto the image. 
The adjustment was performed using two aerial images that 
cover the building. Please note that there is no limitation in 
terms of number of images used. The use of a single image 
produces satisfactory results; however, the use of more 
images provides various views of the building which 
decreases the chance of occlusion. 
  
   
  
    
   
    
  
   
  
   
  
  
  
   
  
   
  
   
    
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