International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
Figure 4: Example of laser scanner point cloud of a branch on
a coniferous tree. Scattering of the points in the top-to-bottom
direction in the image can partly be caused by the wind, other
possible sources are the mixing of ranges to targets within one
laser beam.
In the following a simple algorithm for the reconstruction of the
outer hull is described, requiring that the stem axis is known. The
outer hull is defined as a collection of closed polygons. Each
polygon describes the hull at a certain height, and the polygons
are sorted with ascending height. The vertices of such a polygon
represent the outermost point of the tree in a specific direction
and height. The height interval (e.g., 20cm) and the number
of directions (e.g., 12, corresponding to equally spaced angular
sectors of 30°) are user-specified values. It is chosen based on
point density and, for coniferous trees, the average distance of
branches in vertical direction. Each point of the outer hull has 3
co-ordinates (x,y,z).
The outer hull is computed by first aggregating the points of the
given point cloud in the height slices and the angular sectors. If
the outer hull is to be determined for a plot of trees standing close
together, points are first assigned to a tree by choosing the one
where it has the minimum horizontal distance to the axis. Taking
the outermost point in each sector is not sufficiently robust for
computing the outer hull, because measurement errors, or points
from neighboring trees, without reconstructed axis, may fall into
that sector as well. A simple analysis considering the distances of
the points to the axis is performed, starting from the points closest
to the axis. If large gaps (i.e., large distance differences) are
found between point in the sector, the outer points are discarded
and considered to be measurement errors or originating from other
trees. From the accepted points, the one with the largest distance
to the axis is taken.
This algorithm provides the outer hull in the form of polygons in
different heights.
4 EXAMPLES AND DISCUSSION
The set of presented algorithms can be used differently. A fully
automatic reconstruction of leaf trees can be performed in the
following way. After removing spurious points in the original
point cloud the segmentation algorithm in the voxel domain is
carried out, and for each found segment (i.e., a set of points)
cylinder following is applied.
In Fig. 5 the result of the segmentation (45 segments) and the
reconstruction of an oak tree are shown. The segmentation per-
formed very well, but it can be seen that some smaller branches
were grouped to larger segments. The tree was scanned from all
sides, using 4 scans, summing up to 2.4 million points. Not all
branches could be reconstructed, but the 36 found branches are
correct — based on visual comparison to the point cloud. Ap-
parently some failures in the segmentation process (mentioned
above), but also the fact, that some branches are only covered
Figure 5: Automatic estimated branches of a leaf tree. The
inserted shows the result of the segmentation in voxel space,
the large image shows the reconstructed branches.
poorly with points cause these results. In these cases it should —
at least — be possible to estimate rough start and end points of the
branch. During the cylinder following all together 90 cylinders
were determined, with minimum and maximum r.m.s.e. of 1.1cm
and 3.0cm, respectively. The average fitting accuracy (r.m.s.e.)
is 1.8cm.
In Fig. 6 the fully automatic reconstruction of 3 coniferous trees
with their outer hulls is shown. Left the point clouds are shown (5
scans, all together 7 million points), each scan is given a different
color for each tree. Right, the reconstructed stems and the hulls
are shown. For the stem reconstruction one point was selected
manually on each ofthe three trees. As the registration was not ac-
curate enough, leading to distances of the tree axis in higher parts
of 10cm, each scan was processed individually. After running the
cylinder following, the branches were aligned automatically and
a model of linear decreasing radius was fit to the sets of cylinder
start and end points and radii. This yielded the stems shown in the
right part of Fig. 6. For computing the outer hulls, the slices were
given a height of Im, and split up into 16 sectors (22.5? each).
The hulls are shown as closed polygons around the tree axes.
These results demonstrate that the method works well, but it can
also be seen, that the upper part of the stem of the left tree was
not reconstructed. A lower part of the stem is occluded by lower
points on the side branches and needles, and the cylinder following
could not bridge this gap. Tuning the parameters of the cylinder
following can help here, but this makes the process less automatic.
Another application (not shown) is to apply cylinder following
to manually selected point clouds. This can give results in short
time, too, and a quality check can be performed during the work.
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