eX- 
'SS, 
ith 
re, 
om 
for 
where S denotes a Startsymbol, Vr and Vy the Terminal and 
Nonterminal vocabulary (symbols), and P a set of rules (pro- 
duction rules) describing, which symbols may be replaced by 
other symbols. Given a startsymbol, any structure can be 
derived within the domain of the grammar, simply by replac- 
ing the nonterminal symbols with the help of the production 
rules. This procedure stops, ie. a structure is generated, 
when only terminal symbols (which cannot be replaced) oc- 
cur in the sentence. 
In general, formal grammars allow both for generation of 
new structures and for deciding, if an unknown structure is 
explainable with the given grammar [Cohen and Feigenbaum 
1982]. 
Formal grammars rely on noise and error-free data. However, 
when real physical processes are involved, the grammar has 
to cope with non perfect data. To this end the concept of 
formal languages is extended to a stochastic grammar, where 
each production rule is assigned a probability of occurrence. 
With an attributed grammar, functional dependencies of the 
nonterminal symbols of the rules can be coded in a compact 
way. 
5 SPATIAL PROCESSES 
Spatial data processing deals with the analysis of spatially 
distributed patterns. The task is to find regularities among 
the data or to make assumptions on the underlying mecha- 
nism that generated the pattern [Ripley 1981]. 
A frequently applied model are stochastic processes, espe- 
cially Poisson processes. In the scope of this paper, so-called 
Renewal Processes are of importance. Primal assumption of 
Renewal Processes is that a random experiment is repeated 
with the same assumptions and probabilities as the first ex- 
periment. Thus with the repetition the process really starts 
from anew. The model of a Renewal Process is usually ap- 
plied in the analysis of defects of machine parts. Such parts 
may break down now and then. A break-down at one time 
instance does not affect the next defect, a feature denoted as 
the , lack of memory“-property. The probability of a defect 
itself is distributed with certain parameters (usually Poisson: 
A). The probability of an event at time instance j is given 
by the following formula: 
Aj 
P(X 2j) = Zep; BX) =) (3) 
Instead of discrete time instances, also discrete spatial pa- 
rameters can be modelled with this process. 
6 AUTOMATIC ACQUISITION 
OF PARCEL STRUCTURE 
The visible regularities in the agricultural parcel structure 
are due to fact that the subdivision was ruled by certain cri- 
teria: the parcels are of a reasonable size and of a simple 
form (e.g. rectangles with one „long“ side), in order to be 
manageable with machines. Possible other aspects like his- 
tory, sociology or aesthetics will not be considered in this 
context, as only observable features are taken into account. 
859 
In spite of the underlying planning, the aggregation struc- 
ture is not unique, a model is not easy to determine. At a 
first glimpse, a simple model could be a collection of parcels, 
each of which is represented by a polygonal boundary. This 
representation however contains no information about the re- 
lations of the parcels. Without specifying relations, a parcel 
structure would just be a random parcel puzzle, neglecting 
the neighborhood relations which are quite obvious: most 
parcels are connected to at least one other parcel of similar 
form and size, sharing one common border completely. Thus 
a more elaborate model is required, taking the structure of 
the object into account. 
In maps or images there is a lot of exemplary data avail- 
able, thus the idea is to use structural and statistical learn- 
ing techniques to automatically derive a parcel model from 
examples. 
The task is to turn specific knowledge (examples) into gen- 
eral one (model). In the spirit of Winston's approach, first a 
structural description of the examples is generated, then this 
structure is generalized to a model. The resulting model de- 
scription should intuitively fit the description humans have. 
This can be verified by using the model to generate new 
objects, ie. simulate the generation process and compare 
the outcome with real data. In the following, the automatic 
acquisition of a generic parcel model is sketched. 
The program starts with the observable information: an ex- 
ample of a parcel aggregation represented as line segments 
(see Figure 1). 
? 
  
  
  
Figure 1: Input data: digitized line segments 
The structure, namely the individual parcels and the rela- 
tions between them, has to be extracted with the help of 
a learning strategy. A clustering process is applied, which 
is grouping parcels which are similar in the sense of neigh- 
borhood. A iterative grouping leads to a graph, where the 
leaves represent the individual parcels, while the nodes stand 
for groups of neighbored parcels. The top node finally is the