In the next interpolation, the points with high weights attract the
surface. Others will have a less influence. So interpolated
surface runs nearer to the ground. Off-terrain points are
classified on the basis of given threshold value for residuals.
However, this algorithm is well suited for filtering of datasets,
where outliers are not grouped locally, but spread over a whole
dataset (the case 2 in next article). This situation arrives mostly
by scanning of wooded areas.
2.3 Hierarchic robust interpolation
To make this algorithm applicable for datasets, where off-
terrain points are grouped locally (large buildings, city areas),
the above-mentioned method is applicable, but in a hierarchical
environment. The approach relies on hierarchical using of data
pyramids. At the first, the data are thinned out to the level
where distribution of off-terrain points allows the above-
mentioned filtering method to be applied on the right way. The
thinning is done on a regular grid basis, where the selected
point is the lowest point inside one grid cell. After filtering of
data with robust linear prediction and generating a first
approximation of DTM, the data are compared with data of
higher resolution and points within certain interval are taken
into next iteration. The method iterates with data at higher
resolution level until all data are classified. A result of filtering
is given in figures 4 and 5.
Figure 4. Vaihingen an OEEPE test, original data in a shading
(from Kraus and Pfeiffer 2001)
Figure 5. Vaihingen an OEEPE test, filtered data in a shading
(from Kraus and Pfeiffer 2001)
102
Details of the hierarchical approach, their implementation in
SCOP software and the results of some examples are described
in (Briese et al. 2000) and (Pfeifer et al. 2001)
2.4 Morphological filtering
Another commonly used concept to remove off-terrain points is
morphological analysis. It describes a range of non-linear image
processing techniques that deal with the shape or morphology
of features in an image. Morphological operations use a small
shape or template, known as a structuring element (SE). This
element is positioned at all possible locations in the image and
is compared to corresponding neighborhoods of pixels.
The most primitive morphological operations, the dilation and
erosion, are defined on the domain of a binary image. The
morphological dilation expands or dilates an image. It shrinks
the holes enclosed by a single region and makes the gaps
between different regions smaller.
Figure 6. Morphological erosion, performed by B as a
structuring element
Applied on the greyscale image, the dilation finds a minimum
of the combination of pixel values and kernel function (given
by structuring element) within a specified neighborhood of each
pixel. The erosion returns a maximum on the same way.
Compound morphological operations are combinations of the
elementary operations of erosion and dilation. They are
morphological opening and morphological closing.
Morphological opening involves the application of erosion,
followed by dilation. Moreover, morphological closing does the
dilation first, followed by erosion.
The morphological opening operator is well known and
common used filter for extraction of the “bare” ground from
topographic LIDAR data. It is simple and fast, so therefore is
used by many providers of laser scanner data. However, such
filter, that keeps extreme values only, leaves unwanted gross-
errors in dataset. This often leads to unacceptable results after
DTM interpolation. The impact of filtering a LIDAR dataset
with morphological opening is shown on figure 7. An upper
half is unfiltered data and lower part shows filtered data. As it
can be seen in this shading, the vegetation structures are not
removed completely and negative errors in dataset are stressed
(Notice
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