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RASTERIZING AIRBORNE LASER SCANNING POINT CLOUDS BY BLOCK KRIGING 
Wenxia Tan*, Jonathan Li, Yu Li 
Department of Geography & Environmental Management, Faculty of Environment, University of Waterloo 
200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada -{twenxia, junli, y621i}@fes.uwaterloo.ca 
KEY WORDS: Airborne laser scanning, Point clouds, Rasterization, Block Kriging, Geostatistics 
ABSTRACT: 
Airborne laser scanning (ALS) is increasingly becoming a standard method for the collection of dense elevation models, especially 
in 3D urban mapping. However, automation in processing of ALS point-clouds involves handling huge datasets, irregular point 
distribution, multiple views, and relatively low textured surfaces. Since raster data structure is the most commonly used data 
representation method and is relatively easy to store and process, there comes a need to convert the ALS point clouds into raster data 
format. Since the ALS point clouds are rarely at the same location as the centre of the discretization grid, approximation is therefore 
required. A simple and most often used method is selecting a known point value to represent the grid. Such a point-to- point 
transformation often leads to serious information loss. Transformation of the ALS point clouds to grid is known as a special case of 
the change of support, because it changes the data volume from point to area. In this paper, we present block Kriging to model this 
kind of change of support towards rasterization of the ALS point clouds. The mathematic and algorithmic formulations are 
illustrated. Results from the UW campus show that the proposed method can better preserve the information in the ALS point clouds 
than the point-to-point transformation. Quality assessment is designed and conducted to evaluate the performance of block Kriging. 
Detailed error analysis is also provided to illustrate the accuracy of the proposed method. 
1. INTRODUCTION 
Airborne laser scanning (ALS) or light detection and ranging 
(LIDAR) is a rapidly emerging technology in photogrammetry, 
remote sensing, surveying and mapping communities, which 
provides high accurate Earth’s surface contour information for 
the generation of digital elevation models (DEMs), three- 
dimensional (3D) city models, and 3D vegetation mapping 
(Ackermann, 1999; Baltsavias, 1999; Wehr and Lohr, 1999; 
Haala, and Brenner, 1999; Shan, and Sampath, 2005; Koch et 
al., 2006). A typical ALS system consists of a platform (e. g., a 
helicopter or an aircraft) and an integrated sensor system 
including a laser scanner, a Global Positioning System (GPS) 
receiver, and an inertial measurement unit (IMU). Raw ALS 
data acquired by an ALS system is usually characterized as a 
set of sub-randomly distributed points in three-dimensional (3D) 
space, called 3D point clouds, with the x, y coordinates 
specifying the geographical location and the z coordinate the 
elevation. Recently, many methods have been proposed to use 
the data acquired by the ALS system to generate dense digital 
elevation models (DEMs) (Brovelli and Cannata, 2002; Sithole 
and Vosselman, 2004; Ma, 2005). 
Generally, ALS data are represented with three basic data 
structures: point clouds, raster models, and triangulated 
irregular network (TIN). Point clouds contain all the original 
information, but the data volume is very huge and this makes 
the processing and application of ALS data difficult. While TIN 
is more flexible and fewer point is needed to be stored to 
present the terrain, it is not suitable for information extraction. 
Compared to the point clouds and TIN, raster models are the 
most common data representation method and are relatively 
easy to store and process. Moreover, most of the existing digital 
image processing algorithms can be used for raster data 
processing. To this end, there comes a need to convert the ALS 
point clouds into raster data format. 
Although ALS enables point sampling at very small separation 
distances, subsequent prediction from points to a grid (altitude 
matrix) is subject to much uncertainty. This research focuses on 
the use of Kriging, an optimal technique for unbiased spatial 
prediction, to derive a digital surface model (DSM) from ALS 
point clouds. Although ordinary Kriging and universal Kriging 
have been used for this purpose (Stein, 1999), there is no 
systemic investigation on the effects of terrain morphology, 
sampling density, and different Kriging techniques for ALS 
point clouds on the accuracy of interpolated heights in a raster 
DSM. This research will focuses on this issue. As shown in 
Figure 1, irregularly distributed point clouds (left) are 
interpolated into gird (right). 
Figure 1. Rasterizing ALS points 
2. BACKGROUND 
2.1 Spatial interpolation and Geostatistics 
Since the ALS point clouds are rarely at the same location as 
the centre of the discretization grid, spatial interpolation should 
be used. It is a procedure of estimating the value of a field 
* Corresponding author. Wenxia Tan, PhD student,- twenxia@fes.uwaterloo.ca.