International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
the surface-part of the tensor.
The algorithm compares each location to its direct neigh-
bors and computes a value for each pair by applying the
homogenity criterion. These values are ranked then and
the couples which fit best together will be merged. For the
merged locations the homogenity criterion is again applied
in combination with each of the new neighbors. This pro-
cedure is repeated until no fitting pairs are found anymore.
The metioned homogenity criterion is based on the mini-
mum-description-length (MDL) principle (Rissanen, 1987).
The goal of the MDL principle is to select the simplest
model that explains the data. This is based on the informa-
tion theory (Shannon, 1948) where it is possible to express
the likelihood of an event with the length necessary to en-
code its occurance. In this case we have two models to
compare: two neighbors fit or dont fit. therefore the plane,
its uncertainity of orientation in space and the length of
the boundary of the two single regions are compared to the
hypotheticaly merged case. The value of saving if coding
length in case of a merging is the desired value. The higher
is it the earlier the neighbors are merged.
3.3 Segmentation of curves
For the segmenation of 3D curves there are also diverse
methods to find in literature (Lindeberg and Li, 1997). In
our case we define simple region growing like in the plane
segmenter, but so far we dont apply a mathematical model
for the curve. As homogenity criterion we define the sim-
ple constraint that neighbored locations are merged, if the
distance and the difference of the orientation of the curve-
part does not exceed a certain value. By applying this cri-
terion we get a collection of points defining a 3D curve.
For visualisation we take these points as sampling points
for splines.
4 RESULTS
In this section we present three different datasets. The first
one is a synthetical one. It containes a dice with a bor-
derlength of five fig. (5). It consists of equally distributet
points on the surface of the dice. These points are con-
tamined with gaussian noise. After the first, sparse voting
step the points have influenced each other fig. (6). The re-
sult of the second voting step is shown in fig. (7), which
are the decomposed fields after the maximum search.
The second data set is data of an airborn laser scanner, that
contains high voltage power lines fig. (8). In fig. (9) there
is an enlargement of the scene where the arcs of the power
lines are replaced by a spline which has been created with
the segmented points.
The third data set is taken by a terrestrial laser scanner and
contains a facade fig. (10). In fig. (11) there are the points
replaced by the planes found by the segmenter of 3.2
5 CONCLUSION AND OUTLOOK
We presented a segmentation algorithm which yields good
results for the processing of terrestrial or airborne LIDAR-
data.
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Figure 5: The test dice
Figure 6: Result after the first voting step
The advantage of the preprocessing with the tensor voting
framework is that featured like edges, even if it is only im-
plicitly contained in the data, emerge from the point cloud
by continuing the tensor field. By this the decision of fit-
ting data points to one or an other mathematical model in
the segmentation step can be avoided, and the segmenta-
tion algorithm can be kept simple.
A problem is the value of c, the range of influence inside
the tensor voting. It has to be chosen in the context of the
data-characteristics and can destroy the results if it is badly
chosen.
Here it is solved in the knowledge that the data have the
characteristics of LIDAR-data. So they are eugally dis-
tributed in a grid-like structure in x-y-plane and can be tri-
angulated in 2D in the view from the Laser scanner. The
value of the dense grid and the c variable is calculated as
mean value over all distances of the triangulated Network
over the point cloud. More investigation is necessary at
this point.
Some improvement can also be done by implementing dif-
ferent geometrical models in the segmentation procedures.
In this context it would be interesting to extract for exam-
ple general surfaces and chain lines.
Internat
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