„father“-area, all the others were derived from. This graph -
which in this case is reduced to a tree - mirrors the generation
process. The nodes in the tree form the structure elements
of the model. Each node has certain attributes (like form
and size) and certain relations to other nodes (the fields it
is divided into). Thus the node information states, how a
parcel with certain attributes is divided into smaller ones.
The nodes are considered as an outcome of a random exper-
iment. An estimation procedure is applied in order to gain
the structuring parameters (i.e. the parameters of the par-
celling) and their probabilities. In that way the variability
of the structure is evaluated with the help of a statistical
analysis. Since the parcelling is relating spatial entities, the
evaluation makes use of statistical spatial processes: the sub-
division of a bigger parcel into smaller ones is modelled with
a Renewal Process, i.e. the partitions are distributed with a
common parameter of the Poisson distribution À and the in-
dividual cuts are independent of each other. This modelling
is motivated by the fact, that the size of an individual parcel
is determined by factors that cannot be estimated from by
visual knowledge alone, but mainly depends on legal aspects,
namely the claims of its owner. In that way the sizes of the
parcels can be considered independent.
Thus the generation tree reveals that parcelling is a recur-
sive process: new parcels originate by dividing a big par-
cel into smaller ones. This recursive structure favours the
representation scheme of formal grammars, where the model
information is coded with an attributed stochastic grammar.
6.1 Structural analysis
The clustering process is a mixture between structural and
parametric approaches. First the structure of the data is
gained, then numerical values expressing the relations be-
tween the object parts are calculated in order to guide the
clustering process.
Starting with line segments, in a first step the individual
parcels are extracted by looking for a trace of segments
forming closed contours. To this end the list of lines is cy-
cled twice: the points are traversed clockwise for the outer-
boundary of a region and counter-clockwise for an inner
boundary.
In order to cluster the parcels a measure of similarity or
connectedness has to be given. In this case the measure is
defined by the adjacency of the parcels. Only parcels which
are neighbored can be grouped together. Furthermore, the
more complete the common border between two parcels is,
the more ,similar^ the parcels are, the closer they are to-
gether. In a region-adjacency graph the neighbored parcels
(see Figure 2) are shown, where the degree of similarity is
visualized by the thickness of the connecting lines.
This graph structure is subjected to a clustering procedure
where similar regions (in sense just defined) are merged. A
simple hierarchical clustering method is successively group-
ing parcels which share one common border. In that way
a dendrogram is produced with the single parcels as leaves
and the ,father"-parcel at the top. Nodes in between form
subparcels, which are further divided (see Figure 3). This
tree reflects the generation process of the individual parcels:
starting from a big area and dividing it successively.
A
i)
:
Figure 2: Region-Adjacency Graph: thick lines denote close
relation
level = 1
PARCEL n=3
=2 level = 2 level = 2
-2 PARCEL na 5 PARCEL = 5
PARCEL"
1 2 115 8 9 4 7 6 93 10 12
Figure 3: Dendrogram of grouped parcels
The information contained in these nodes (the nodes’ at-
tributes) are the size and the form of the parcel, the direc-
tion of the partition, the number of its successors and the
number of previous partitions. This information is analyzed
statistically in the next step.
6.2 Statistical analysis
Up to now the analysis produced a production rule for each
individual parcel. The desired information is a set of stochas-
tic production rules which state, how individual parcels are
