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.