d on the plane, the 
all the points of this 
)=0 (2) 
an be taken from the 
d" (x. yz) are 
by calculating the 
=AT-A. 
culated by: 
(4) 
vith one ridge 
ge in three kinds of 
id saltbox roof. For 
is fitted which is 
is the adjusted line 
e points of the roof 
heights along the 
ey are located on a 
rs of 0,55€, and 
o clouds by judging 
. plane: if there is 
) is located on the 
.,C,] ; while it is 
E the plane 
these two clouds to 
ulated respectively. 
ds, those points are 
it are shorter than a 
ered directly as the 
is intersected with 
n a plane is fitted 
current point cloud, 
ated. According to 
nce is smaller than 
he plane patch and 
this plane patch. 
| group. The same 
] as well. 
group is empty, if 
contains points of 
of. In this case, the 
| into two groups 
ay, the points on a 
led or saltbox roof) 
or four (hipped roof) segments which are corresponding to the 
plane patches of the roof. 
3.2.3 The process of segmentation 
The process is described here by taking a complicated roof as an 
example. For instance, there are À (k € R, k » 2) roof ridges 
detected from the point cloud of a roof. The segmentation is 
carried out as follows: 
Step 1: for every detected roof ridge, the points are detected for 
the two plane patches which are intersected at the roof 
ridge. 
Step 2: The rest points are clustered into several groups 
according to the distance of their nearest neighboring 
points, so that the distance of the nearest points 
between two groups is larger than a given distance. 
Step 3: for the points in every group, an adjusted plane is fitted 
at first. If the mean value of the Euclidean distances of 
the points to the adjusted plane is smaller than 0.2 
meter, all the points are belonging to the same segment, 
since they are located on the same plane. Otherwise, the 
points might represent the roof of a dormer window or 
a lower cross gabled/hipped roof. In this case, the roof 
ridge(s) is detected at first, the process goes back to 
step 1. 
Step 4: the process for a group in step 2 terminates, when there 
are fewer than 10 points in the rest group, because a 
plane patch with 10 points is smaller than a roof 
element normally. 
3.2.4 Reconstruction of polygonal roof model 
After the points are clustered for all the roof planes, outline is 
extracted for each cluster of roof plane according to the 
following steps: (i) projecting points on a roof plane (which 
belong to a cluster) on the horizon; (i1) outline is extracted by 
computing a 2D a-shape of the points projected on the horizon; 
(ui) the outline is simplified using the recursive Douglas- 
Peucker line simplification algorithm; (1v) the plane is regressed 
for the original points in the cluster in 3D; (v) project the 
simplified outline extracted the third step on the plane. As a 
result, the simplified roof polygon is obtained. After all the 
polygons are extracted for a roof structure, they could be written 
in CItyGML or AutoCAD format in the further step. 
4. EXPERIMENTAL RESULTS AND DISCUSSION 
The proposed approach has been implemented using Matlab 
(R2010a) and tested on the buildings in area A of the German 
City Vaihingen Enz. The results show that the algorithm can 
segment point cloud of a roof into several clusters, whereby 
points in a cluster should be located on the same roof plane and 
can be used for extracting roof polygon. It works very well for 
buildings that are scanned with high quality (completely 
scanning for every plane patch of roof parts and with few 
noises). The experiments shows high efficiency and low error 
segmentation of the algorithm. 
For a selection of examples see the figures (Figure 3, 4, 5 and 6) 
below. As indicated in Section 3, roof ridges are classified into 
several levels according to their heights at first. In the most 
cases, there is only one level which is corresponding to the main 
roof ridge. In some cases, there are two levels of roof ridges, 
whereby the first level of roof ridge indicates the main roof 
99 
ridge at the highest level while the second level of roof ridge 
refers to the ridges of dormer roof or side house. After the roof 
ridges are detected, the points on the roof planes which are 
intersected in the corresponding roof ridge are extracted and 
segmented. 
Taking the house in Figure 3d as an example, the main roof 
ridge (the intersection line of planes of green and blue points) is 
detected at first. Then the points on the two roof planes along 
this roof ridge are extracted and segmented. After this step, 
there are two groups of points which are corresponding to the 
two dormer roofs. For the points in each group, the roof ridge is 
detected at first, and then the points on the two roof planes are 
extracted and segmented. 
In the following example results, there are four houses (Figure 
2a, 2b, Figure 4 and 6) which have only first level roof ridge, 
while the other three house have two levels of roof ridges. 
  
  
  
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Figure.3. Segmentation for four example houses