hether they 
r, RANSAC 
ibdivide the 
discussed. 
iatical plane 
le does not 
rcome this 
s proposed 
process of 
> minimum 
final fitted 
f RANSAC 
DAR data is 
| set after a 
> errors and 
algorithm is 
; represents 
IS à process 
xplained in 
sensitive to 
ie unstable 
AC. What's 
y classical 
cations for 
liscussed. 
rmany and 
assification 
three areas 
  
e earth. (a) 
vith small 
res in this 
area | and 
ure 1, area 
Vaihingen, 
ex shapes. 
with a few 
. data are 
\R data is 
rence. For 
  
further information about data of "ISPRS Test Project", please 
refer to (http//www.itc.n/ISPRS, WGllI4/tests datasets.html). 
32 Experiment and analysis 
With the help of 2D building plans of test areas, buildings can 
be extracted from LIDAR data. There are about 25 buildings in 
area 1 and 8 buildings in area 2. Then, classical RANSAC 
algorithm coded by Peter Kovesi (Kovesi, 2006) is used in this 
experiment for roof facets extraction. 
Inaccurate planes detected by RANSAC from roof can be 
classified into the following categories: 
1) Non-segmented planes: Planes, which have been 
classified as parts of planar surfaces of roof, are not 
segmented into any of the detected planes. 
2) Over-segmented planes: A planar surface of roof is 
segmented into more than one plane. 
3) Under-segmented planes. Two or more planar 
surfaces of roof are segmented into one plane. 
4) Spurious planes. Planes, which are detected from 
point clouds, are not true planar surfaces of roof. 
  
Figure 2: Planes detected by RANSAC. (a) Non-segmented 
planes (white square area). (b) Over-segmented planes (white 
polygonal area). (c) Under-segmented plane (blue points). (d) 
Spurious plane (blue points). 
3.21 Non-segmented planes: In Figure 2(a), points in the 
white square area presents a slope roof of a high-rising 
residential building. However, without consideration of spatial- 
domain connectivity, points on the slope roof are classified into 
other planar surfaces by RANSAC, which leads to a non- 
segmented plane. Profile of this building (Figure 3) can prove it. 
The flat roof with most points is first detected and removed 
from the point clouds of building. In the end, there are no points 
left for the slope roof. In addition, there is another cause for no- 
segmented planes. As shown in Figure 4(b), there is a certain 
chance that planar surfaces in the hip roof are not detected. That 
is because 3 points, not on the same planar surface of roof, are 
randomly selected in the initial process of RANSAC, which 
may lead to a spurious plane (green points in Figure 4(b)). As a 
    
   
  
   
  
   
   
  
  
  
   
   
   
   
   
   
   
   
   
  
   
   
   
   
  
   
  
  
   
  
  
  
   
  
  
   
    
  
  
   
  
  
  
    
  
   
   
   
   
   
   
    
  
   
    
   
    
result, some of points on the same planar surface are removed, 
and the plane may not be detected because of fewer points 
(white points in the larger rectangular area in Figure 4(b)). 
  
Figure 4. Hip roof. (a) Image. (b) Detected planes (white 
class represents noise) 
From above analysis, although fewer remaining points on 
the surface lead to a non-detected plane, the ultimate cause 
of non-segmented plane is random sample without spatial- 
domain connectivity. However, this explanation only 
applies to the small planar surfaces of roof. Large planar 
surfaces can be always detected from roof by RANSAC. 
3.2.2 Over-segmented planes: From Figure 2(b), in the 
white polygonal area, it is noted that the region has two planar 
surfaces but is segmented into four planar surfaces. In fact, there 
are two gable roofs adjacent to each other, but it is hard to 
separate them from LIDAR data. As a result, parts of the two 
planar surfaces of gable roof in the white polygonal area are 
classified into the gable roof outside the white polygonal area 
by RANSAC. 
  
(b) 
  
   
(c) (d) 
Figure 5. Planes detected by RANSAC. (a) # =0.02. (b) : 
—0.05. (c) t —0.1. (d) t -0.2.