r the task of au-
retation requires
a few vectors in
Yodeling.
at these models
Il kinds of roads
ave no problems
the large variety
aerial Imagery.
describes a road
pology, function-
ribe a road only
5. E.g. a road is
in elongated ho-
ion, a side walk,
:h, and probably
s a road. Some
olour or texture
expected if the
context of a road is also considered.
Cars on a road, houses and trees alongside the road, shadows
of fly-overs, junctions with other roads, road markings, and
traffic signs are all clues that help an operator to identify a
road. The description of all these objects may in turn require
some other context information. The question then rises how
extended the context of a road should be and how detailed
each of the objects needs to be described. The answer is not
known, but it is clear that a lack of modeled knowledge about
the objects and their context is a major source for the un-
certainty in the outcome of image interpretation procedures.
Instead of finding support in the presence of cars, houses,
road markings, etc., most road detection schemes consider
these objects as noise which leads to detection failures.
4.3 Image data
The image data itself and the feature extraction process are
also sources of uncertainty. In the imaging process uncer-
tainties are introduced by the sensor noise and the imaging
circumstances. Due to a different perspective or changed
(weather) conditions object appearances may change drasti-
cally and thereby systematically affect the number and shape
of the extracted features.
When propagating the image noise to the parameters of ex-
tracted features, the assumed noise level is usually taken
much higher than the sensor noise (which is almost ne-
glectable). This higher noise level is required to account
for small violations of the image models used in the feature
extraction algorithms. E.g. many edge extraction operators
assume ideal straight step edges with constant grey values on
both sides of the edge. When extracting the side of a road,
small grey level variations due to structures in the concrete
or clumps of grass are ignored and (incorrectly) considered
as noise. Such incomplete or simplifying image models give
rise to a substantial amount of uncertainty in the extracted
features.
Due to the complexity of feature extraction a straightforward
error propagation is often not possible. In those cases exten-
sive experiments are required on either simulated [Fuchs et
al., 1994] or real [Vosselman, 1992] imagery in order to cap-
ture the stochastic properties of the feature extraction pro-
cess. Transition matrices with conditional probabilities have
proven to be adequate for describing the uncertainty. Once
extraction probabilities of some basic features are known,
some probabilities of detecting more complex features can
be derived theoretically. E.g., Fuchs et al. [1994] determine
the probability of detecting line junctions by propagating the
probability of detecting edge pixels.
In the previous paragraph it was argued that many road mod-
els are to poor for a successful recognition. This recognition
is based on a comparision between object models and image
features. Like for the objects, it is largely unknown how to
describe an image such that the description is suitable for in-
terpretation purposes. Many feature extraction processes do
not preserve the information that would be very helpful for
interpretation and thus complicate the high level reasoning.
5 PROCESSING UNCERTAIN DATA
Image interpretation tasks have to combine several knowl-
edge sources. To assess the final quality the uncertainty in
the knowledge sources needs to be propagated. Related to
the different methods of representing uncertainty (section 3),
913
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Figure 2: Edges do not contain sufficient information to dis-
tinct roads from other linear features.
several techniques for combining uncertain knowledge and
propagating uncertainty have been developed.
e Probabilities
Most computations with probabilities are in some way
related to Bayes’ theorem
_ P(BIA)P(A)
un FORD.
in which the probability of the event A, given that
B has been observed is derived. Beside prior prob-
abilities P(A) and P(B), also the conditional proba-
bility of observing B in case of the event A has to be
known. This conditional probability corresponds to the
stochastic model used in adjustments, i.e. the assump-
tion of a Gaussian distribution with a certain standard
deviation. Error propagation with Bayes' theorem or
least squares adjustments of linearized models are very
common in photogrammetric calculations, but still find
little attention when dealing with GIS data. Heuvelink
et al. [1989] and Goodchild and Gopal [1989] give a
few examples of error propagation in GIS.
e Probabilistic networks
Associated with the links of a probabilistic network
are conditional probabilities. The probability of each
proposition (node) may depend on the probability of
several neighbouring nodes. So-called relaxation meth-
ods update the probability of a proposition by using the
probabilities at the adjacent nodes together with the
conditional probabilities [Rosenfeld et al., 1976]. In
its simplest form, the probability of proposition A is
derived from neighbouring propositions Bj ... B5 by
P(A) =} [P(A|B:)P(B:) 4 P(AI-B)P(^B;)] /n
i=1
