hips between 
ure 2(d)) are 
/ are common 
surfaces tend 
i only a few 
ar surface are 
y and lack of 
lanes. 
  
  
ilding ID, y- 
28) 
  
se buildings 
1 area 2. 
we find that 
ected planes. 
igure 8 are 
r high-rising 
nted out that 
are adjacent 
is. Therefore, 
ther analysis, 
Table 1, we 
removed by 
lead to more 
; of building 
ented planes 
parameter f. 
which will 
ils in Figure 
9(b). That is 
ving a lot of 
  
  
slope roofs with different directions. Because of the probable 
intersection of plane defined by point sets, some points may 
belong to several mathematical planes, which can lead to tails. 
On the contrary, most of planar surfaces of the latter building 
are parallel and discontinuous in height, so points tend to 
belong to one mathematical plane. Because there are some 
points on the surfaces of facade, a few points may be classified 
into the planar surfaces of flat roof. But these points are very 
rare and far away from the body planes, they are easy to be 
separated. 
  
  
  
  
  
  
  
  
  
  
  
building |/ Non- | Over- | Under- | Spur- 
a 8 0 3 19 8 
a 16 5 2 18 4 
a 24 3 0 16 2 
a 32 7 0 14 4 
a 40 8 0 14 3 
b 8 0 0 3 26 
b 16 3 0 5 14 
b 24 3 0 5 7 
b 32 3 0 5 5 
b 40 4 0 3 4 
  
  
  
  
  
  
  
  
Table 1. Numbers of detected planes. (a) Building with 
complex shapes in Figure 9(a). (b) high-rising residential 
building in Figure 9(b). 
From above, quality problems are very common in RANSAC- 
based roof facets extraction. It is hard to get an accurate 
building model without improve the quality of extracted planes. 
Although spatial connectivity can improve the quality of planes 
extracted by RANSAC, it cannot solve all the problems. More 
factors or strategies need to be considered. 
4. CONCLUSION 
Roof facets extraction is the basis of 3D building reconstruction 
based on polyhedral model. It has been the focus of research all 
the time. As a robust method for model estimation, RANSAC is 
widely used in the extraction of geometry primitives. This paper 
gives a comprehensive evaluation of RANSAC-based approach 
for roof facets extraction 
We give four detail categories of inaccurate planes detected by 
RANSAC. Based on some experiments, the reasons for quality 
problems are discussed. Experiments show that non-segmented 
planes are sensitive to the number of points on planar surface. 
Small planes tend to be discarded. Over-segmented planes are 
susceptible to the parameters of RANSAC. Whether the value 
of parameter is too smaller or a little bigger, an inappropriate 
value will lead to over-segmentation. Under-segmented planes 
are sensitive to the shape of building. Complex shapes mean 
that points belonging to several mathematical planes are more 
likely to be segmented into the larger plane, which will cause 
under-segmentation. Spurious surfaces are common in all test 
data. It is related to the number of detected planes. Buildings 
with complex shapes tend to have more spurious planes. 
Increasing the related threshold of RANSAC can reduce the 
number of spurious planes, but this will affect the accuracy of 
plane detection. Most of the quality problems above can be 
improved, if spatial-domain connectivity is considered. 
However, some problems such as the tail adjacent to body plane 
can't be solved. And there are still many issues to be studied. 
     
   
  
  
   
  
  
   
  
   
    
  
   
   
    
  
   
     
  
  
   
   
   
   
  
  
  
   
  
  
  
   
   
   
   
  
   
  
   
    
   
  
  
   
  
    
   
   
    
   
   
   
   
    
    
Point density and topology relationships between planes are 
suggested to be considered. 
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