ISPRS Commission III, Vol.34, Part 3A ,,Photogrammetric Computer Vision", Graz, 2002 
  
3D RESAMPLING FOR AIRBORNE LASER DATA OF URBAN AREAS 
S. Zinger, M. Nikolova, M. Roux, H. Maitre 
Ecole Nationale Supérieure des Télécommunications 
46 rue Barrault, 75634 Paris Cedex 13, France 
zinger@tsi.enst.fr, nikolova@tsi.enst.fr, mroux@tsi.enst.fr, henri.maitre@enst.fr 
KEY WORDS: laser scanning, urban areas, irregular sampling, DEM 
ABSTRACT 
We consider the problem of resampling for the data obtained by laser scanning on an irregular grid. The data obtained by 
airborne laser scanning are scattered, and the resampling on a regular grid is needed for the generation of digital surface 
models (DSM). Some well-known methods are considered in this article: triangle-based linear interpolation, triangle- 
based nearest neighbor interpolation and kriging. An energy minimization approach is proposed which allows to avoid 
the drawbacks relevant to these methods. This approach allows to impose a model of surface corresponding to urban 
areas. The energy function is adapted to deal with the scattered data, and its parameters are chosen to fit the model of 
a urban area. A correlation coefficient is used to compare the results. The methods are tested on real data - irregularly 
spaced 3D points - laser scanner data of Brussels. Visual and numerical experimentation results are presented. 
1 INTRODUCTION 
Laser scanning allows to measure the height of the terrain 
from an aircraft sending a pulse towards the ground and 
measuring the time for the reflected pulse to come back. 
As an output it gives coordinates of 3D points of the ter- 
rain. We will consider the data representing urban areas. 
Due to the acquisition technique, these points are irregu- 
larly spaced while one needs to have them on a regular grid 
for most of possible applications. In this paper we con- 
sider methods of 3D resampling applied for urban areas. 
Images of urban areas are characterized by homogeneous 
zones (roofs, streets), separated by edges. In an altimetric 
image height values are represented by gray level values. 
Let us emphasize that edges contain critical information, 
especially for urban images, since they delimit streets and 
buildings. 
Classical approaches for the resampling of laser data on a 
regular grid are nearest neighbour and linear interpolation. 
In (Behan, 2000), both approaches are tested and evaluated 
with regards to the grid size and the DSM quantization to- 
wards the problem of overlapping strips matching. The 
grid size is recommended to be very similar to the original 
density of the data, the better results are reached with linear 
interpolation. Statistical interpolation methods, like krig- 
ing and linear prediction, are also proposed for the resam- 
pling over non-urban areas (Lohmann et al., 1999). The 
main drawback of these different approaches is either to 
oversmooth or to deform the building edges. 
The suitable approach is supposed to give horizontal or 
oblique surfaces, i.e. roofs of buildings, and strong discon- 
tinuities, 1.e. differences between roofs and ground, which 
are usually presented by straight lines, because of the form 
of facades. In order to cope with this problem we define the 
sought image to be a minimizer of a regularized cost func- 
tion. We describe this approach and its implementation. 
Then we make experiments to determine the performance. 
We check the relevance of our results comparing with the 
altimetric data obtained from the optical images. 
2 SOME RESULTS OF CLASSICAL APPROACHES 
The classical methods for scattered data interpolation are 
triangle-based linear interpolation, triangle-based nearest 
neighbour interpolation (Watson, 1992) and kriging (Noel, 
1991). Triangle-based linear interpolation gives results which 
have problems with edges and represents facades with non- 
vertical surfaces (Figure 1). 
  
Figure 1: Result of linear interpolation based on the De- 
launay triangulation of the initial data (city of Brussels, 
(©FEurosense). 
The drawback of triangle-based nearest neighbour inter- 
polation is that the surface is very rough, i.e. there are 
no slopes, and changes between groups of values are very 
steep. Then oblique surfaces like some roof facets are rep- 
resented with discontinous surface (Figure 2). 
Kriging gives smooth areas, where edges are blurred (Fig- 
ure 3). For this approach the spatial dependencies are ex- 
pressed by the variogram (Noel, 1991), which has three 
parameters to be fit according to the data. 
The aerial image of the area we are working on is shown 
on Figure 4. Its resolution is 8 cm per pixel. 
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