The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
Figure 2. Figure placement and numbering. 
3. OUR METHOD 
3.1 Study area and data 
The raw ALS dataset covered the main campus of the 
University of Waterloo (UW), Waterloo, Ontario was acquired 
by the Airborne Laser Terrain Mapper (ALTM) manufactured 
by Optech (http://www.optech.ca/) on March 11, 2006. The 
average flying height was 1,200 m above ground level and the 
flying speed was 66.9 m per second. The scan angle is 20°. The 
desired resolution is 0.908 m. The raw data contain more than 
seven millions point clouds. 
A subset of the raw data (64 m by 64 m) is used in this study. It 
contains 5280 points. So, the point density in the scene is 1.28 
point/m 2 . Figure 3 shows the study area by Orthoimage which is 
part of the UW main campus. This area was selected since it 
offers an ideal site for studying the effectiveness of selected 
spatial statistics approach: it contains different kinds of objects 
such as trees, bare ground, buildings, and parking lots. Figure 4 
shows the raw ALTM data point of the study area. It is shown 
that the point density is not uniformly distributed in the whole 
study area. The point density in the left lower part is bigger than 
other area. Figure 3 shows that the lower left of the study area 
was covered by trees. So the higher density was due to the 
multi-return from trees. 
employed. The histogram shown in Figure 5 illustrates the 
distribution of the height values used in this investigation. The 
histogram displays a slightly skewed towards low elevations. So 
the distribution of the height is fairly normal. 
Semivariogram is a measurement of the spatial autocorrelation 
between the data point. As the distance between two data points 
increases, the value of the semivariogarm increases accordingly. 
When the distance reaches a certain value, the value of the 
semivariogram will increase very slowly, and not exceed a 
certain value. This certain value is called range. Its range is a 
measure of the distance threshold under which the data is 
correlated. 
Raw Lidar Points 
f 
Figure 4. Raw ALTM points. 
By measuring the distance between two locations and plotting 
the difference squared between the elevation values at locations, 
a semivariogram cloud is created. Shown in Figure 6, the x-axis 
is the distance between the locations, and on the y-axis is the 
difference of their elevation squared. Each dot in the 
semivariogram represents a pair of locations, not the individual 
locations on the map. We can see clearly from the 
semivariogram that in a distance of 25 m, the autocorrelation 
between the elevations are gradually decreased. So the range of 
the semivariogram is 25 m.