The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
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Empirical Semivariogram of elevation 
Figure 6. Semivariogram of elevation. 
3.3 Block size and distance threshold 
In the exploratory data analysis, the range of the semivariogram 
of the raw ALS data points was already estimated. It is 25 m, 
that’s to say if the distance between two points exceeds 25 m, 
there should be no spatial autocorrelation between them. So 
when the elevation of a gird is estimated, only the data points in 
the distance of 25 m should be considered. 
The block size is another important parameter for rasterizing the 
raw ALS point clouds. If small block size is used, then the 
result will be more concise. The total number of point cloud in 
the study area (64 m by 64 m) is 5280, so the point density is 
1.23 points/m 2 . On average, there is about one point in every 
square meter. In block Kriging, the covariance between the data 
points in the block and the points in the distance threshold are 
taken into account. Only when at least one point resides in the 
block, block Kriging could be used. In this study, the block 
sizes of 1 w x 1 m, 2 m x 2 m, 4 m x 4 m, are used, respectively. 
3.4 Block Kriging 
Figure 7 demonstrated the step by step procedure to compute 
the elevation of every gird. The input includes the raw ALS 
data point, the gird size, and the distance threshold. The 
distance threshold is used as a window for estimation. Only the 
data point in the window will be used for calculation. Then for 
every grid, First, calculate the covariance every two points the 
window. Second, calculate the covariance between the gird and 
every point. Third, the elevation is calculated by block Kriging 
by Equations (4) and (6) mentioned in Section 2. 
4. RESULTS AND ACCURACY ASSESSMENT 
Table 1 shows the error of ordinary Kriging and block Kriging 
in different block sizes. First, we could see that block Kriging 
did a much better job than ordinary Kriging. The standard error 
of block Kirging is less than 1 m, but the standard error of 
ordinary Kriging is about 4 m, which is unacceptable. 
Figure 7. Flow chart of block Kriging computation. 
Block size 
Min 
Median 
Mean 
Max 
1 m 
0.2098 
0.3320 
0.3353 
0.7549 
2 m 
0.1631 
0.2728 
0.2796 
0.6845 
4 m 
0.1274 
0.1980 
0.2169 
0.5902 
Ordinary 
Kriging 
3.778 
3.906 
3.909 
4.333 
Table 1. Error assessment of different block sizes 
Secondly, for block Kriging in different block size, the error is 
different. As the block size increases from 1 m to 2 m and 4 m, 
the mean standard error decrease from 0.33 to 0.27 and 0.21. 
This is because when bigger block size is used, more data 
points are considered, the estimated results are more likely to 
represent the true value. This could be further demonstrated in 
Figures 8 and 10, they are the 3D graph block Kriging. The 
block size is lm by lm and 2 m by 2 m respectively. As we can 
see, when the block size is 1 m, the result contains quite a lot of 
noise. When the block size increases to 2 m, the result is quite 
good.