al 
Using six pose 
el's origin using 
ther three define 
e and the object 
relevant shape 
ne using the box 
hape parameters, 
of the box, are 
nd footprints of 
me. On the other 
s higher than the 
ne heights of the 
is simplifies the 
he heights of the 
erence points are 
eters from the 
ch determine the 
ith respect to the 
rmal information 
; in this research 
ameters (1.e., the 
and one rotation 
id the two out of 
| of the building). 
nodel parameters 
11). The chosen 
ing edge pixel 
h a least-square 
Recursive MBR 
ne initial model 
rs for the model- 
els are chosen as 
lied to regularise 
decompose them 
h minimum area 
on which contain 
man and Shapira, 
. generation of a 
in Habib et al. 
re comprised of 
can be applied 
lied to the initial 
|* level MBR is 
ts, which do not 
nd then projected 
Using the non- 
cted counterparts, 
rive the 2" level 
until there is no 
1e recursive MBR, 
| by alternating 
inal shape can be 
ontal accuracy of 
initial models for 
cribes how these 
ntially during the 
nagery 
od approximation 
‘the model-based 
    
image fitting is to minimize the normal distance between the 
initial LIDAR-derived model and image edge information by 
refining the model parameters. Habib et al. (2011) already 
confirmed the feasibility of the image fitting process using 
simple rectangular buildings. For complex buildings, 
different levels of MBRs are derived from LiDAR data using 
the recursive MBR procedure described in Section 2.3. These 
MBRs will be adjusted sequentially to improve the 
boundaries. The 1% level MBR is adjusted using the edge 
pixels extracted from the images, and only edges from the 
actual building boundaries will be considered for the 
adjustment. After the 1% level MBR adjustment, the next 
level MBR is adjusted while incorporating the results from 
the previous level, and this process continues until all the 
MBR levels are adjusted. The results are presented in the 
Section 3. 
3. EXPERIMENTAL RESULTS 
To test the proposed methodology, two buildings have been 
selected. Figure 1 shows image and LiDAR data of the 
selected buildings. The building shapes differ in terms of 
complexity which means they are represented using different 
MBR levels. The first selected building, T-shape, is 
comprised of two MBR levels, and the second building 
includes more than two MBR levels. The buildings are 
located on the campus of British Colombia Institute of 
Technology (BCIT) in Canada. Multiple aerial images and 
airborne LiDAR data both captured from flying heights of 
540 m and 1,150 m are available. The ground sampling 
distances for the images are 5 and 10 cm, and the LiDAR 
point densities are 1.5 and 4.0 pts /n? depending on the 
flying height. 
   
(d) 
Figure 1. Aerial images (a), (c), and LiDAR data displayed 
according to the heights (b), (d), of selected buildings 
The proposed plane segmentation methodology successfully 
distinguishes the rooftops of the test buildings. The results 
are shown in Figure 2. Figure 2(a) shows the clustering 
results, and Figure 2(b) presents the ground / non-ground 
classification result. The red colour represents non-ground 
planar points, the green colour - ground planar points, the 
pink colour - non-ground rough points, and the blue colour - 
ground rough points. Groups of planar non-ground points 
Whose height is greater than 4 m and size is larger than 10 m? 
are hypothesized as buildings (Figure 2(c)). Lastly, Boundary 
tracing is performed on the building hypotheses. Figure 3 
shows the traced boundaries of the test buildings projected 
onto the imagery. 
  
   
   
    
      
yh 
A 
i 
em 
    
  
ä 
Y 
         
     
  
   
a 
; PUT A. 
SAE 
lk 
STEEL 
     
(b) 
   
(c) 
Figure 2. Plane segmentation results (a), ground / non-ground 
classification (b), and building hypotheses generation (c) 
  
Figure 3. Initial LIDAR boundaries of the buildings projected 
onto the imagery 
Figure 4 and Figure 5 demonstrate the step-by-step 
procedures of the recursive MBR algorithm for the two test 
buildings. For the first building, the 1* level MBR, i.e., the 
blue rectangle in Figure 4(b) is derived from the initial 
LiDAR boundary (Figure 4(a)). Figure 4(c) shows the non- 
overlapping initial LIDAR boundary points in black circles 
together with the 1* level MBR. These points are projected 
onto the 1% level MBR sides as shown in Figure 4(d) (red 
circles), and then using these points, the MBR algorithm is 
applied one more time. In this case, two 2™ level MBRs, i.e., 
the rectangles in black colour, are derived as seen in Figure 
4(e). The final building shape can be obtained by subtracting 
the 274 level MBRs from the 1? level MBR (Figure 4(f)).