An example where a generic model in the form aggre
gated features are used as a basis for an interpretation is
given in [26], describing buildings with flat roofs by homo
geneous areas with boundaries consisting of polygons
with rectangles only. Then local groups of edges, their
mutual relations (rectangular) and their relation to the
interior of a region is used to generate building hypo
thesis. The model is local, in the sense that the relations
to neighbouring segments are not incorporated. The final
decision on the classification is left to the human analyst.
We do not want to evaluate these techniques with respect
to object modelling in image analysis. Actually all re
presentations are used frequently [9, 11, 16, 32, 38, 50,
67, 70, 85, 86 and 87]. Moreover they may serve as a
sufficiently good description of the object model in not too
complex circumstances.
We only want to comment on two problems which one are
faced when applying generic models to image analysis:
1. there is no commonly accepted methodology to for
malize knowledge, here to establish object, image,
analysis or interpretation models. The problem of
knowledge acquisition is as old as Al. There is no clear
way to avoid the impression of ad-hoc-ery (which may
be not so different also in hard sciences). The ap
propriateness and the predictive power of the model,
being a kind of theory, still is the only way to evaluate
the quality of a chosen model. The advantage of rule-
based descriptions, also useful for representing se
mantic networks of frames, is their flexibility and their
expressive power, especially in case non-specialists
have to use image analysis systems [7],
The problem how to represent uncertainty of data,
relations or classes in a coherent way is not solved yet,
especially if hard decisions during the analysis should
be avoided and the quality of image analysis proce
dures has to be evaluated by comparing the result of
empirical tests with theoretical predictions. This is due
to the lack of an observation theory for fuzzy measures
and belief functions though their mathematics can be
related to the classical probabilistic techniques [1, 47
and 84].
2. the computational complexity of the analysis proce
dures in principle is prohibitively high, as the task of
labelling image features is NP-complete 7). All tech
niques to circumvent this problem therefore are sub-
optimal. Classical examples are decision trees [4],
which require hard decisions, clique formations, which
try to balance the influence of the local and the global
context [85] or techniques based on perceptual group
ing, which exploit the containment hierarchies within
the object models [14 and 64], Parallel techniques are
relaxation [41 and 62] which under certain conditions
guarantee to find the global optimum of an inter
pretation.
Meta-information and fusing object models
The use of a single object model may be sufficient in
some specialized cases. If two or more models of the
object are used within the same image analysis proce
dure the generic problem arises how to fuse different
object models. This problem is even more complex than
7) A problem is called NP-complete (non-polynomial-complete) if its
algorithmic complexity is larger than polynomial, i.e. the compu
tation time grows faster than any polynomial, e.g. exponentially.
380
using object models in a knowledge based interpretation
system, as the semantic consistency between the dif
ferent object models has to be provided. In our context
there are several cases of pairing object models (in
cluding examples):
analyst1, analyst2 (say a geologist and a soil scientist);
analyst, map [42 and 48];
analyst, generic model [26 and 32];
map1, map2 (e.g. having different scale and/or age);
map, generic model [11 and 63];
generic model1, generic model2.
Having two generic models is the one which is equivalent
to having two data-models in federated data bases and is
the case where the problems of model fusion are best
visible [46, 81 and 88]
1semantic equivalence. Two concepts refer to the same
real world object. This is the most simple problem,
E.g. is the point type object in one map the same real
world object as the area type object in the larger scale
map of the same area? Scale differences usually lead
to different granularity of concepts (see below). Some
times it may be possible to establish semantic equiva
lence automatically. Another example is the differently
looking but semantically equivalent result of two analy
sis processes;
2. semantic heterogeneity. This will be the most frequent
situation. Examples for semantic heterogeneity are
manyfold
different context of concepts, e.g. the location of an
object may be described by 2 or by 3 co-ordinates;
different representation, e.g. an area may be re
presented in raster or vector format [66 and 92];
different cardinality of relations, e.g. the relation
visible-from may be defined as a 1 n or as a m
n relation;
different granularity, e.g. a containment hierarchy
is only designed for GIS-analysis not for image
analysis purposes, neglecting details being not es
sential for GIS-applications but essential for auto
matic image interpretation;
unit differences, e.g. feet versus meters.
Semantic heterogeneity thus is related to different re
presentations which, however, refer to similar aspects
of the same object;
3. semantic discrepancy. This is the hardest case as the
same concept/class in different knowledge/informa
tion sources refers to different real world objects. A
typical example is the notion 'road' used in different
analysis procedures, e.g. in case the minimum and
maximum widths differ. This example also reveals that
such discrepancies may occur within the same envi
ronment, in case it changes over time, which is the
normal case in program development: The notion
'road' today is not the notion 'road' tomorrow in case
the algorithm changed.
Semantic consistency only can be achieved if meta-data
are available. Meta-data describe the interpretation of the
data thus are part of the representation (see above). But
meta-data usually are not accessible by the program
which works with the data but (hopefully) contained in the
documentation. A first step to improve semantic consis
tency is the paradigm of object oriented programming,
where changes of objects only can be performed within
specified ranges.
The necessity to explicitly store the semantics of knowl
edge, however, was already stressed in the 70th [13 and
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