The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
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Figure 6: Detected non-ground points 
2.3. Using a Statistical Filter to Remove the Effects of 
Surface Roughness 
We want to use the potential non-ground points outputted from 
the previous procedure to extract non-ground points, so surface 
roughness and noise should be removed. When comparing the 
resulting potential ground points with potential non-ground 
points, the potential ground point results are more reliable, and 
thus would make a good reference set of points. The terrain can 
be considered a random field, in which the elevation can be 
approximated to be normally distributed with a mean p and a 
variance o 2 . 
In most cases, the surface of the terrain is supposed to be 
continuous; therefore, the distribution of terrain points is more 
suitable for being our reference than the distribution of non 
ground points. In analyzing the histogram of the elevations of 
the detected ground points in a local area, we consider the 
points located beyond 2 STD from the mean of the distribution, 
where the probability of having a terrain point is only 2%, to be 
wrongly classified non-ground points that need to be corrected. 
These points are classified as ground points in the previous 
procedure because of the rough and uneven surfaces of the non 
ground objects. We consider the points located within 1.5 STD 
from the mean of the distribution, where the probability of 
having a terrain point is 93%, to be reliable signals that should 
be kept. These points could have been identified as non-ground 
points because of the roughness of the ground surface. 
The concept above can be implemented as a filter. Only the 
center of the filter window is examined, using the distribution of 
the neighboring ground pixels within the window. In order to 
have enough samples to generate a reliable distribution for re 
classification, the filter window size should be adaptively 
increased if the number of potential terrain samples in this local 
neighborhood is less than a pre-defined number which is chosen 
to be 100 in our case. Through the moving window procedure, 
all the pixels can be checked. The statistical filter is used to 
remove the defects caused by the false hypotheses in the surface. 
The ground points extracted are shown in Figure 6. 
order to handle the terrain with various slope angles, more 
constraints are needed to improve refinement of the classified 
points. Combining plane fitting with the statistical filter together 
(Fig. 7), a new method for correcting false hypotheses has been 
developed. Using potential ground points after occlusion 
detection in the local block as an input, the plane fitting 
procedure estimates the most probable plane which can be used 
to represent the terrain. The plane fitting procedure is performed 
through a least squares adjustment process by minimizing the 
summation of normal distances between the potential terrain 
points and the estimated plane. In order to determine where the 
higher probability of having a terrain points could happen, the 
standard deviation of normal distances between the estimated 
plane and the potential terrain points within the local block is 
first computed. Then using a multiple of the standard deviation, 
we create a buffer around the computed plane (Fig. 8 and Fig. 9). 
The central point of the local block is defined as non-ground if 
the point is located outside the buffer. Otherwise, the point is 
taken to be a ground point. If the estimation procedure for plane 
fitting cannot be convergent, a statistical filter can be used to 
correct false hypotheses. 
A procedure for the classification of a regularly spaced surface 
model has been introduced above. After classifying the DSM 
into ground and non-ground pixels, we can classify the original 
LiDAR points based on their proximity to the classified DSM 
cells. Each cell, however, can contain more than one LiDAR 
point, and thus we must consider that only the lowest point 
within each cell was used in creating the DSM. If several 
LiDAR points lie in a DSM cell, which has been classified as a 
terrain point, then the lowest LiDAR point is classified as 
terrain. The classification of the remaining points depends on 
their height relative to the lowest LiDAR point. If the heights of 
the other points are significantly higher than the height of the 
lowest LiDAR point, these points are classified as non-ground. 
In the case that a cell is classified as non-ground, then all 
LiDAR points in this cell are classified as non-ground. 
o 
Figure 7: Potential ground points and potential non-ground 
points in the local block 
o 
When dealing with the terrain with very large slope angle, a 
standard deviation of a histogram could become very huge. In 
Figure 8: Plane fitting using potential ground points in the local 
block