Case II 
Here, the averaging effect on the LIDAR DSM within the 
building polygons used to construct the 3D model is analysed. In 
this case, 3D models are constructed using the mean height 
derived from the LIDAR DSM at various grid resolutions. The 
control height adopted is similar to Case I. The hypothesis posed 
is that, if the building roof is not complex (flat roof), the RMSE 
should be constant even though the 3D model was constructed 
with varying grid resolutions. The advantages in this case will be, 
apart from understanding the nature of the vertical roof height 
through analysing the effect of RMSE, the RMSE will also give an 
accuracy estimate of the derived model with respect to the control 
height. The role of grid resolution in preserving the accuracy 
estimates of the constructed model using mean height derived 
from the LIDAR DSM at various grid resolutions can be 
examined. Section 4.2 contains a discussion of the result of this 
analysis. 
Case III 
For Case III, the 3D model was constructed using the maximum 
height derived from the LIDAR DSM at various grid resolutions. 
A 3D model constructed using the maximum height from the 2m- 
grid resolution LIDAR DSM was adopted as control. The 
hypothesis posed is that, for roof with one dominant height the 
RMSE computed will be constant, even though the model is 
constructed with varying grid resolutions. The computed 
discrepancies in this case are of the same order. Therefore, the 
role of grid resolution in preserving the accuracy estimates of the 
constructed model using maximum height derived from the 
LIDAR DSM at various grid resolutions can also be examined 
(section 4.3). 
The procedure for the computation of RMSE is shown in Figure 
10. Due to the potential locational mismatch between the building 
polygons and the LIDAR DSM, the derived heights (mean height 
from LIDAR DSM) used to construct the 3D model could be in 
error. Figure 11 shows an example of the mismatch between the 
building polygons and the corresponding buildings on the LIDAR 
DSM. Due to the mismatch, errors in the retreived heights at 
building edges on the LIDAR DSM could affect the computation 
of the derived height, where the height of the ground surface 
could be incorperated in the computation (Figure 11). 
  
LIDAR DSM 
Various grid resolution 
(2m, 4m, 6m. . ..20m) 
| | 
i 
3D Model Control Height 
Feichtfroml IDARDSM 3D derived from 2m LIDAR 
(mean and maximum height) DSM (mean and maximum 
height) 
  
Building Polygon 
  
  
  
  
  
  
  
  
  
  
  
i 
RMSE 
RMSE between ‘control height” 
and 3D derived from LIDAR 
DSM (mean and maximum 
height) 
  
  
  
  
Figure 10: The procedure for the computation of RMSE. 
       
  
   
  
  
  
  
  
  
  
  
  
  
  
   
  
  
  
   
  
   
  
   
    
    
   
   
  
   
   
   
   
  
  
   
  
   
  
   
    
    
  
   
  
   
   
   
  
  
  
   
    
  
   
   
   
   
   
   
International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999 
  
Figure 11: Mismatch between the building polygons and the 
LIDAR DSM. 
3.2 Standard Deviation (Std. Dev.) 
For the computation of Std. Dev., the formula used is as shown in 
Equation 2. The "Zonalstat" function available within ARC/INFO 
is used to compute the Std. Dev. using the building polygon as a 
‘mask’. As stated above, the potential locational mismatch 
between the building polygon and the LIDAR DSM could also 
affect the computation of the Std. Dev. because the heights of 
ground surface locations may erroneously be placed within the 
building polygon (Figure 10). 
Std. Dev. (0 )= [2] 
  
where n is the number of grid within a building polygon , Z is 
the mean height for the building polygon and z is the height value 
for each grid within the building polygon. 
Further discussion of the variation of Std. Dev. on the building 
heights at various LIDAR DSM grid resolutions can be found in 
section 4.5. 
4 RESULTS AND DISCUSSION 
4.1 Maximum height derived from LIDAR DSM and mean 
height as control 
It was noted in 3.1 (Case I) that the RMSE is not related to the 
‘absolute’ accuracy estimates but rather is used to detect relative 
height changes. Figure 12 shows the vertical roof heights for 
residential and industrial buildings for the derived 3D model at 
different grid resolutions. 
The vertical roof height for both residential and industrial 
buildings decreases gradually as the grid resolution of the LIDAR 
DSM increases (Figure 12). However, there is a difference 
between the vertical roof heights of residential and industrial 
buildings, the vertical roof height of residential buildings 
decreases from 2.4m to 1.3m as the LIDAR DSM grid resolution 
increases from 2m to 20m (Figure 12). On the other hand, even 
  
   
Internatio 
though the vertical rc 
the grid resolution 
vertical roof height c 
for the computed ver 
as the grid resolution 
12, that industrial b 
compared to residet 
building types by ana 
resolutions between 
that, the maximum d: 
height (1.70m) is 
suggested that differ 
resolution (less than 
the fact that more hei 
DSM and the possibi 
of both building ty] 
relation to this effect 
that the vertical rc 
buildings is higher th 
  
  
  
  
Height (m) 
64 
E Po 
24e 
05 
2m 4m 
—@— Residential 24 1.7 
—Q-— Industrial | 4.1 32 
  
  
  
  
Figure 12: Vertical r 
buildings (Maximu 
construct the 3D 
constructed using 
42 Mean height c 
height as contre 
As noted in Section £ 
height from the LID/ 
of mean height is 
understanding the r 
building types, accure 
mean height from the 
grid resolution in the 
constructing the 3D 
building types cons 
LIDAR DSM increas 
13). 
RMSE (m) 
2: 
  
a HH 
| —@— Residential 0 
  
  
| —~o— Industrial | © 05 
Figure 13: RMSE for 
height derived from t