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DOLOGY 
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International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999 
allow the identification of the two main types of building 
(residential and industrial) . 
In this study, the magnitude of the RMSE for the derived 3D 
models at various grid resolutions is analysed. In addition to the 
RMSE, the value of standard deviation (Std. Dev.) of the building 
heights at various LIDAR DSM grid resolutions is also 
investigated. In the first part of the study, the initial 2m-grid 
LIDAR DSM is degraded to lower resolutions between 4m and 
20m with a 2m-grid interval. Samples that represent residential 
and industrial building are then randomly identified for the 
computation of RMSE and Std. Dev. The number of buildings 
selected to represent residential and industrial buildings is 35 and 
7 respectively. 
In the next stage, 3D models for the study area using the heights 
derived from the LIDAR DSM for resolutions between 2m and 
20m, with a 2m-grid interval, are constructed. As an example, 
Figure 7 and Figure 8 illustrate the basic concept for the 
integrated methodology using the building polygon and the 
LIDAR DSM data for the construction of the 3D model. Figure 7 
shows how the maximum height encountered within the building 
polygon is extracted from the LIDAR DSM and is used to 
construct the 3D model. Figure 8 shows the resulting 3D model. 
Further discussion of this integrated methodology can be found in 
Jaafar et al. (1999b). 
Building Polygon 
  
  
  
15 21 _21 21 
14122 i20 [15] | 
LIDAR DSM i15 120 25 15 
Height 
  
  
  
  
Grid Resolution 
  
15 (21 2 istud 
  
  
  
  
  
  
  
  
  
  
Maximum Height 
Figure 7: Maximum height retrieved from the LIDAR DSM for 
the construction of the 3D model. 
Height (z) 
26m 
     
  
Northing (y) 
  
[Datum Plane] Easting (x) 
Figure 8: 3D model derived from the integrated methodology 
(Maximum height derived from LIDAR DSM). 
3.1 Root Mean Square Error (RMSE) 
Equation 1 shows the formula used for the computation of the 
RMSE. 
RMSE = [1] 
  
where 71 is the number of check points; Z'; is the 3D model height 
at position / and Z; is the value of the ‘control height’ at check 
point i. 
Since the computation of RMSE is based on the discrepancies 
between the height derived from the constructed 3D model and 
the reference height (control height) at specified positions, the 
control heights need to be determined. 
In this study, control heights based on ground survey are not 
available. However, since it is the differences in the complexity of 
the roof structures of residential and industrial buildings that are 
being investigated, and not their absolute heights, the control 
heights were collected as follows; 
Case I 
In Case I, the effects on the 3D model constructed using the 
maximum height derived from the LIDAR DSM at various grid 
resolutions are analysed, using control heights taken as the height 
of a 3D model constructed using the mean height derived from 
the 2m-grid resolution LIDAR DSM. The 2m-grid resolution 
LIDAR DSM acts as a ‘datum’ as the greatest number of LIDAR 
surveyed points (X,Y,Z) are used to represent the DSM. It is 
considered to be the most accurate DSM available in this study. 
Since the mean height is adopted as the control height, the RMSE 
is based on the difference in vertical roof height between the 
maximum and the mean height for the constructed 3D model. 
Figure 9 shows the relationship between the building heights for 
the computation of RMSE. The hypothesis posed is that, if the 
difference in vertical roof height for both building types is not 
significant, the computed roof height will be constant even 
though the 3D models are constructed with varying grid 
resolutions. Section 4.1 discusses the results based on this 
hypothesis. 
  
Maximum Height > | 
Vertical Roof Height | 
2 x Vertical Roof Height 
     
   
Mean Height 
Figure 9: Relationship between the building heights for 
computation of RMSE.