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Some
structures may be conceived as hierachical, so that "square"
may imply "geometrical". If structured concepts are admit-
ted, it becomes possible to represent intersections, relation-
ships and dependencies between concepts and groups of con-
cepts. Since, however, most transmission of knowledge uses
the discrete medium of language, we must accept the con-
straints of approximation imposed by linguistic communica-
tion. Therefore Sager (1990) postulates that the value of a
concept with respect to a given axis is generally defined as
a range and only exceptionally as a point. A concept must
therefore normally be considered as occupying a region or a
set of points in space and not a single point.
3 CONCEPTUAL LEVELS AND THEIR
TRANSFORMATION IN IMAGE PROCESSING
We shall not indulge here in philosophical thinking about the
nature of the " real world" since it would go beyond the scope
of this paper. We shall just consider that the real world may
be viewed from three conceptual levels, according to Figure
1: the level of reality, the iconic level and the symbolic level.
The step from one level to the other occurs through transfor-
mations, here called " Projection" and "Semantic Modelling".
In Linguistics we speak in this case of " Representation" and
"Coding".
The explanation for transformation reality-photographic im-
age (iconic level) is attained by means of physical models.
Other transformations of this type are, for example, topo-
graphic maps. In any case we are faced with generalisation,
i.e. geometrically and sematically reduced representations.
Both the level of reality and the iconc level are readily recog-
nizable by man since they involve analogue information.
Semantic modelling as far as this paper is concerned, is the
transformation of the iconic level into the symbolic level. The
result is a symbolic description of the real world. This allows
the direct comparison of different types of images, maps, mas-
ter plans, etc. in a way in which it had not been possible at
the iconic level. Comparison and interaction are now feasible
with the aid of a digital computer, the procedure being based,
for instance, on declarative languages.
Transformations themselves require linguistic elements since
they proceed following topological and logical interrelation-
ships, with the help of grammars, graphs, semantic nets or
production systems. At this level new abstractions are re-
quired, but the most important factor is the transformation
(coding) of the fundamental information of the iconic level
into the symbolic level with the least possible loss of infor-
mation.
À very particular significance should here be assigned to lan-
guage as a carrier of information. The degree of generaliza-
tion, grammar, methodology and logical interrelation of signs
and sounds also places language at the symbolic level. When
speakers or writers/readers interact using the same semantic
model, communication can be established. But this is not
enough to ensure correct communication: another very im-
portant variable enters the game when context is taken into
account. Yet, there is no general consensus about the rel-
ative importance of context and linguists are still discussing
whether transference of meaning is possible without context
(Sager, 1990).
Transferred to the understanding of images, this would mean
to question "absolute symbolization". If context is so im-
9
Reality 5 Real World
| Projection
Transformation ( >} Laws, Cartographical Rules, 4 B. )
lconiclevel ^5 liadel] | Mon] ...-.
nd = cs
Semantic rz
( Topological and Logical Buildings ,
Transformation Grammatics , Graphs , Semantic Networks..... )
pe
4——————— UO[[DSI[DIQUEHG —s I
Symbolic Level | - — |
( Vector Form ) Symbolic Description
Fig. 1 : Conceptual levels and their transfomations
portant to emit and understand a message correctly at the
linguistic level, this means that there could be more to it than
mere geometry and attributes at the image processing level .
4 THE SYMBOLIC LEVEL: SEMANTIC NETS AND
INTELLIGIBILITY
Fig. 2 shows a semantic net, how it is used to describe the
modelling of parts of an image on the symbolic level (Bahr,
Quint, Stilla, 1995). The scheme consists of nodes and links.
Objects contained in an image or a map are represented by
nodes (terms, concepts); their relationships are represented
by different types of lines: part links, specialization links and
intstance links each of which express different functions.
The logical structure of the semantic net depicted in Fig. 2
may be verbalised in the following way:
"Vegetation, sealed surfaces and water are com-
ponents of the concept "park" (connected to it
by part links). Trees and grass are also to be
found in a park (part links). Trees and grass are
special types of vegetation (specialization links).
Bariloche National Park and Hyde Park are lo-
cal instances of park (instance links). Hyde Park
Corner is a sector of Hyde Park (part link). It
is a " meeting place" which is part of the con-
cept "park" like, for example, " playing ground" .
Hyde Park Corner is a unique and localized in-
stance of " meeting place" (instance link).
Compared to the iconic level, the structuring of a semantic
net at the symbolic level is conceptually much clearer. It
becomes evident, however, that both objects and their rela-
tionships are influenced to the highest degree by verbalization
(terms and concepts) and thus are subject to imprecisions.
These imprecisions are not only transferred together with
transformations but also reproduce themselves negatively in
the logical structure of the whole semantic net. No rigor-
ous theory of this type of "error propagation” has yet been
formulated but such a theory would be a prerequisite for se-
mantic modelling not only of the deterministic but also of the
stochastic component of the semantic net.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B6. Vienna 1996
