International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
  
  
  
Figure 4 The pattern of errors in the bilinear and nearest 
neighbour surfaces at 1m, 2m and 4m grid resolutions. 
4. SUMMARY OF TECHNICAL CONCLUSIONS 
This investigation has shown that there is significant 
variation between the forms of DSMs created using different 
interpolation algorithms and different grid sizes. It was found 
that the most error was introduced by the nearest neighbour 
algorithm, and the least error was introduced by the bilinear 
and bicubic methods, with some evidence that the 
biharmonic spline may produce lower errors where used with 
a buffer zone to reduce the strongest oscillations in the 
unconstrained regions. Despite being shown to produce the 
least overall error, bilinear and bicubic interpolation were 
observed to over smooth building edges and may therefore be 
unsuitable for some applications. Ultimately the choice of 
optimal algorithm for a particular application must be 
decided by the user — understanding spatial variations in 
accuracy can therefore promote better informed decision 
making. 
This investigation has also shown that changes in grid sizes 
have very different effects on the magnitude of error 
introduced by different interpolation algorithms. "Where 
accuracy is the most important factor, optimal grid spacing 
for any interpolation method should be as close as possible to 
(or slightly less than) the original point spacing. This 
supports Behan's (2000) conclusions. The pattern of highest 
magnitude error appeared to occur in the areas of greater 
surface roughness. There is some potential for this pattern to 
be used in subsequent image segmentation as an indicator of 
surface roughness. This is currently being investigated by the 
authors. 
5. SIGNIFICANCE OF THE FINDINGS AND REAL 
WORLD APPLICATIONS 
One common application of LiDAR DEMs is in flood 
modelling and flood inundation prediction. Small differences 
in values in the DEM used as an input to the flood modelling 
program can have a large effect on the predictions. The effect 
of these differences are shown in figure 5, in which the four 
surfaces created are ‘flooded’ at 4m and then at 5m. Figure 5 
1000 
shows the marked difference between the flood predictions, 
particularly the limited flooding in the nearest neighbour 
surface. This is caused by the ‘stepped’, or blocky, nature of 
this surface which was noted in section 2.1. In the nearest 
neighbour flood prediction it is clear that the level of the 
‘step’ must be exceeded in order for the flood to propagate, 
In this instance the ‘step’ characteristic of this surface clearly 
acts as a flood break, altering the results, and producing a 
potentially erroneous prediction. In contrast, the biharmonic 
splined surface, which was noted to produce a very smooth 
surface, permitted the largest flood prediction. Despite these 
noted differences it is, of course, impossible to comment on 
which of the predictions is closest to reality. Clearly, 
however, if these models were to be used in the calculation 
and mapping of tlood risk areas, the use of different gridding 
techniques could substantially alter the results. The same 
argument holds for the use of DEMs in similarly sensitive 
applications, such as mobile phone wave propagation 
modelling, and noise pollution modelling. Thus differences 
in the height values of DEMs can have significant 
implications where the models are used in a predictive or 
analytical capacity. 
6. SUMMARY 
The introduction of errors in the gridding of data remains 
only one source of error in the process of modelling from 
LiDAR data. It has been the purpose of this paper to 
demonstrate how these gridding errors may be introduced, 
and how the magnitude and the spatial structure of these can 
change with different methodologies. Whilst differences have 
been highlighted between different interpolation methods, it 
should be noted that there is no optimal creation 
methodology, as the final decision regarding interpolation 
algorithm, grid spacing, filtering method, and segmentation 
procedure must be driven by the requirements of the 
application for which the DEM is intended. However, what 
has been shown is that in order that informed decisions can 
be made regarding the specific modelling processes, users 
must be provided with error information which may come in 
the form of a map of the spatial structure of error — such as 
those presented in this paper. The provision of this error 
information further requires that there are software processes 
which are able to cope with the communication of the error, 
and with the incorporation of this information in subsequent 
analysis. This in turn requires that the data users understand 
the error information, and can use this intelligently in order 
to reduce the introduction of error in their LiDAR 
processing. 
Interna 
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