International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
with Matlab 6 (Vesanto et al. 2000). Although the number of
output vectors (neurons) of a SOM can be arbitrarily
determined, usually we choose a number that is smaller than
that of the input vectors. Through the training process, each
point is supposed to have a BMU from the set of neurons within
the SOM. It helps to set up a linkage between a SOM and the
corresponding point cloud. The specific procedure for setting up
such a linkage in ArcView GIS platform is as follows (Figure
3):
e Create a polygon theme in which each polygon has a
hexagonal shape, representing a neuron with output
vectors as attributes in a table (SOM table)
e Create a link table (LINK table) with two fields,
namely BMU and point ID
e Link the SOM table and LINK table (note fields
SOM-ID and BMU are equivalent)
e Link the LINK table and NETWORK table through
the common field street-ID
Through the above procedure, a linkage that is set up between a
SOM and corresponding point cloud will help to select points
belonging to different spatial objects.
POINT CLOUD table
SOM table LINK table
SOM-ID| X |Y |Z | !
1
D|x[|vizl!
1
2 — 2
—
Figure 3: Linkage between a SOM and point cloud
3.2 An interactive environment for clustering and selection
Based on the above procedure, an interactive environment for
clustering and selection can be built in a GIS platform. The
trained SOM is imported into a GIS to setup a linkage to the
point cloud that is represented as both 2D theme and 3D scene.
In order to detect various clusters with the SOM, a unified
distance matrix between a neuron and its neighbouring neurons
(Ultsch and Siemon 1990) is computed. The distance matrix
reflects the level of similarity between a neuron and its
neighbouring neurons. With color scales for representing the
distance matrix, we can easily detect clusters, i.e. those neurons
tied closely. From the view entitled as SOM4029 in figure 4,
we note that those neurons with light colors are supposed to be
clusters, while those neurons with dark colors are neurons that
are far from various centres of clusters. With the same figure, a
cluster is selected with yellow, and the corresponding set of
points is highlighted in both 2D view and 3D scene, from which
we note the points are those from forest rather than from the
ground.
p BET
Figure 4: An interface with three connected visual components:
SOM, 2D view and 3D scene of a point cloud
4. A CASE STUDY
To validate the approach, we carried out a case study applied to
a dataset that consists of 9072 points (figure 5). The dataset was
a part of a larger dataset captured using a terrestrial laser
scanner by the GIS institute at the University of Gávle. The
reason why we choose the dataset is that the GIS institute has
already manually filtered the dataset. Different spatial objects
such as clay-road, stones, spruce and ground are extracted. Thus
it provides a base to validate the model.
Using a heuristic way, we decided a SOM with the size of
40 x 29 to train the dataset. The process is performed in the way
as follows with reference to the description in section 2. The
1160 neurons are initialised by randomly giving some values of
Xyz coordinates and the return intensity; and each of the
neurons compares to the individual points with the point cloud
to determines its best match unit using equation [1]; Then the
winning neurons and its neighbourhood are adjusted their
values of xyz coordinates and the intensity according to
equation [2]. Details on parameter settings for the training
process are shown in table 1. Once a pre-determined
convergence is reached, the training process is finished with a
trained SOM. The trained SOM is supposed to retain the initial
structure of the point cloud. Figure 6 is the component
visualizations of the SOM, and the smooth color transitions
reflect the fact that similar neurons are being closer than those
dissimilar.
Internati
Table 2:
Param
| Dime
Neigh
Learn
Initial
Traini
(T)
Initial
radius
Final 1
Figure
Figu
coordina