Generally, over-segmentation is mainly caused by a smaller 
threshold value. In order to test this, different thresholds of 
parameter 7 (distance to the fitting plane) in RANSAC are used 
to extract planes from roof. As shown in Figure 5(b), the 
appropriate value of ¢ for this data is 0.05, and four planar 
surfaces of the gable roofs are correctly detected. Besides, it 
should be noted that more trivial facets are extracted from roof 
with a smaller value of parameter /. However, it doesn't mean 
that a greater value of / will not cause over-segmented planes. 
Taking Figure 5(c) for example, although the value of t is a little 
greater than the appropriate value in Figure 5(b), it causes two 
over-segmented planes. According to profile (Figure 6) of this 
test data, parts of point clouds on the parallel surfaces can be 
classified into both of them. Without the consideration of 
spatial-domain connectivity, these points will be segmented into 
the planar surface which is first detected. 
  
Figure 6. Profile of roof in Figure 5 
However, no parameters can satisfy any situation. Most of the 
planar surfaces of roof can be detected when the threshold 7 is 
set to 0.1. The number of over-segmented planes wills increases 
if threshold 7 is set too small, although a smaller threshold may 
be appropriate for this data. 
3.2.3  Under-segmented planes: As shown in Figure 2(c), 
the planar surfaces of dorms are coplanar, but they are classified 
into one plane. Actually, most of the under-segmented planes in 
this experiment are planes with a “tail”. The tail can be adjacent 
to (points in red rectangular area in Figure 7(a)) or far away 
(points in the green rectangular area in Figure 7(b)) from the 
“body” plane. 
   
(b) 
Figure 7. Planes detected by RANSAC. (a) under- 
segmented planes. (b) Low point density area on roof 
Because RANSAC tends to detect the best mathematic planes, 
points belong to other roofs or noise may be classified into the 
planes with a large number of points, which will reduce the 
accuracy of boundary of planar surface. However, considering 
spatial connectivity, coplanar planes (Figure 2(c)) and tails far 
way from body plane can be separated from body planes. As far 
as the tails adjacent to body plane, it may be separated based on 
point density. However, parts of the exact planar surface may 
be removed, such as points in the white rectangular area in 
   
Figure 7(b). In that case, topology relationships between 
detected planes may need to be considered. 
3.2.4 Spurious planes: Spurious planes (Figure 2(d)) are 
false planar surfaces detected by RANSAC. They are common 
to most test data. Because points on large planar surfaces tend 
to be first detected and removed from raw data, only a few 
points such as noise, points on edge or small planar surface are 
left. These points, which have low point density and lack of 
spatial connectivity, are segmented into spurious planes. 
  
7 detected planes 
* spurious planes 
  
  
  
  
Figure 8. Plane number plot (x-axis represents building ID, y- 
axis represents number of detected planes) 
   
(b) 
Figure 9. Building images (Cramer, 2010). (a) Dense buildings 
in area |. (b) high-rising residential building in area 2. 
As shown in Figure 8, in the test of 33 buildings, we find that 
spurious planes are related to the number of detected planes. 
The buildings with most detected planes in Figure 8 are 
buildings with complex shapes (Figure 9(a)) or high-rising 
residential buildings (Figure 9(b)). It should be pointed out that 
buildings in the red polygonal area of Figure 9(a) are adjacent 
to each other. It is hard to separate from point clouds. Therefore, 
they are regarded as one building in the test. For further analysis, 
different parameter / is used to detect planes. From Table 1, we 
can see that some of spurious planes can be removed by 
increasing the value of parameter #, but this will lead to more 
non-segmented planes. For over-segmented planes of building 
with complex shapes, it is noted that over-segmented planes 
decrease a lot with the increasing of the value of parameter f. 
But small over-segmented planes are eliminated, which will 
affect the accuracy of boundary of planar surfaces. 
In this experiment, under-segmented planes with tails in Figure 
9(a) are more common than the building in Figure 9(b). That is 
because the former consists of several buildings having a lot of 
  
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