demand for intermediate representations: especially for en-
vironmental planning a scale 1:50 000 is very favourable
([Winkelhausen 1995]).
Even when the representation of the objects on distinct lev-
els is given, the question arising immediately is how to de-
fine the transitions from one scale to the next. For small
changes in scale smoothing operation can be applied (cf.
processes in digital image processing: gaussian smoothing
([Sester 1990]) or morphological operations). At a certain
level however, there are abrupt changes in the representa-
tion which cannot be reflected by elementary processes, but
have to be represented by a set of rules (e.g. transition from
geometric to symbolic representation).
1.3 Sketch of proposed approach
The idea of this contribution is to use an object oriented
representation in conjunction with techniques from Machine
Learning. The elementary representation of the objects of
the catalogue is straightforward. The object-class hierarchy
can be transferred directly. Each object has a set of methods,
which define its behaviour, namely the range of its possible
actions. Among these, there are e.g. methods for represen-
tation. In this way also methods for generalization can be
implemented. The question is however how to define such
methods. E.g. the aggregation of a set of houses can de-
pend on the distance of the individual houses, on the fact
that a street is nearby, .... Which factors are relevant is not
easy to determine. One possibility is to use knowledge ac-
quisition techniques to determine generalization rules. Tra-
ditionally Knowledge Acquisition this is done by interviewing
experts [Weibel, Keller & Reichenbacher 1995]. This process
can be automated by methods from Machine Learning. The
technique of "Learning from Examples" e.g. uses a set of
examples to derive a general rule which describes the struc-
ture inherent in the examples. Ideally such techniques are
applied when there is no explicit knowledge about the given
fact available, or no rules of thumb are known. The examples
to feed the learning algorithms can be taken from existing
maps. In the learning procedure, e.g. a set of houses can be
given as example, whereas the system then has to derive all
the relevant objects, the relations between them and thus the
criteria when and how to aggregate the buildings to a larger
complex.
Generalization highly depends on relations between objects,
thus the problem is to define such relations. The paper
first presents an approach of supervised learning of object
models in terms of an object hierarchy (including attributes
and relations of object classes, and corresponding methods)
[Sester 1995], which was developed for the application in im-
age and map interpretation. Starting from this approach,
a transfer to the generalization in multiple representation is
straightforward - since the object models and the methods
needed are similar. Thus a concept for learning generaliza-
tion rules is presented. In the approach the learning program
ID3 [Quinlan 1986] is applied.
770
2 GENERALIZATION OPERATIONS AND
DATA STRUCTURES
Generalization bases on distinct operations, like selection, fil-
tering, smoothing, abstraction, aggregation, collapse, scal-
ing and displacement (cf. [Mdller, Weibel, Lagrange &
Salge 1995], [Beard & Mackaness 1991]).
These operations operate on dedicated data structures,
which include all the details necessary for the generaliza-
tion. This concerns especially the representation of topol-
ogy (neighborhood, relations, adjacency) - a fact which is
obvious for the displacement operator. To this end several
data structures are proposed, which can be characterized as
raster structures :
> A triangulation of the given data set ([Bundy, Jones &
Furse 1995], [Ruas & Lagrange 1995]) directly reveals
the neighborhood of the objects.
> Another approach applies a raster-vector transforma-
tion. In a so-called displacement mountain, the im-
portance of the object, the range and also the direc-
tion of displacement can be coded in the gray-values
[Jager 1990].
These representations however take only geometric neigh-
borhood into consideration. Semantic proximity or adjacency
over other objects is not considered. For some applications
however different types of neighborhood are required.
Thus another structure can be used, namely an object ori-
ented approach, where the object-specific neighborhood is
explicitly stored for each object (or object class).
3 APPROACHES FOR TRANSITION
BETWEEN MULTIPLE LEVELS OF
DETAIL
A well known and popular approach for generalization of
line structures is the Douglas-Peucker-Algorithm. Line data
structures like the strip-tree or binary line generalization tree
(BLG) base on this type of algorithm and guarantee quick ac-
cess to line objects on various levels of detail.
Concerning generalization of areal features there is an ap-
proach by van Oosterom [1995]. He presents the concept
for map generalization on-the-fly. The aim of his approach
is the derivation of a temporary generalization (mainly for the
purpose of screen display), thus not the creation of a sec-
ond, redundant dataset. In order to get quick responses he
relies on so-called reactive data structures (i.e. geometric
data structure with detail levels). As a data structure for the
area partitioning process, he introduces the GAP (general-
ized area partitioning) tree. Area partitioning starts from the
assumption, that each point in the 2D domain belongs exactly
to one of the areas, thus there are no gaps or overlaps.
Generalization of an areal object can on one hand be re
duced to the generalization of its constituent polygon lines.
This however can result in overlaps or gaps when no topo-
logical data structure is used. The alternative is to select ob-
jects what are to be deleted. In order to prevent having gaps,
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996
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