Stefan Growe
4.2 Judgement of Competing Scene Interpretations
In order to use Bayesian networks for the judgement of a semantic net, a transformation between both types has to be
defined that states how the nodes, attributes, and edges of the semantic net are mapped to Bayes nodes and edges. In the
presented approach all instances and hypotheses of the semantic net are interpreted as Bayes nodes. Each Bayes node X
models a binary random variable and thus possesses a two dimensional belief vector BEL(X) = (P(x), P( ^x)) represent-
ing the probabilities for the verification and falsification of the event X. The node attributes of the semantic net, which
mainly introduce the evidence, are transformed to special nodes of the Bayesian net that send exclusively A-messages
and are not influenced by zt-messages of their parent nodes. Part—of— and con—of relations are mapped to Bayes links
inverting the direction of the edge, because the concretizations and parts are understood as diagnostic support for their
parents. Temporal relations are mapped unchanged to an edge of the Bayesian network. Arrributed relations are not mod-
elled by a Bayes link, but the contained attributes are considered as normal node attributes during the propagation process.
After mapping the semantic net to a Bayesian network, the root nodes are initialized by a top-down —message, which
is the ignorance vector (0.5, 0.5) by default. If a prior probability is known for the node, like for example for object states
as part of the temporal knowledge, this value is used instead. Consequently a predefined belief is assigned to these nodes
from the beginning, which is an important way to prefer more probable hypotheses during the analysis. After initialization
the evidence, represented by the attribute values measured so far, is introduced into the Bayesian network and propagated
according to the mentioned algorithm. Similar to the possibilistic judgement approach the degree of compatibility be-
tween attribute value and range is determined and used as A-message of the Bayes node representing the attribute. Hence,
the two corresponding fuzzy sets u ; and u y are superimposed and the normalized ratio of intersecting and total area is
calculated (s. Eq. (6)). If a node possesses multiple attributes, the individual A—values are combined by a weighted geo-
metric mean according to Eq. (7).
aL PA
Lys rire 7 x) ic
1 w. I
Ax) = d | lacs with: W = Sw, (7)
ixl i=1
Figure 5: Computation of the diagnostic support A(x) from attribute values (ug) and attribute ranges (ug).
|
The evidence is propagated through the Bayesian network considering the conditional probabilities attached to the Bayes
links. Here, the state transition probabilities of the temporal knowledge are taken into account. The nodes of the semantic
layer are used to derive an overall judgement of the scene description. Their belief values are again combined by a geomet-
ric mean. The essential differences to the possibilistic approach mentioned in Chapter 2.2.1 are: The information is propa-
gated both, bottom-up and top-down through the network. Therefore the belief of an object part, for example, influences
the belief of the remaining parts and vice versa. Prior probabilities of objects, like temporal states, are considered within
the judgement procedure via a corresponding z-message. This enables the system to prefer the more probable solution,
even if the evidence is identical for all alternatives. The same effect cause the defined conditional probabilities of the
temporal state transitions. The benefit of the Bayesian approach is illustrated in the following example.
5 RESULTS: EXTRACTION OF AN INDUSTRIAL FAIRGROUND
To validate the capabilities to a multitemporal image analysis of the AIDA system the mentioned example of the industrial
fairground was chosen. The knowledge base illustrated in Fig. 3 was implemented including the necessary image process-
ing algorithms to extract halls and parking lots. The application was tested for a set of aerial images of the Hannover fair-
ground. The images, dated from 1995 to 1998, cover all states of the site (inactivity, activity, and construction/disman-
tling). Unfortunately, no continuous image sequence exists which depicts all phases of a single fair, but the given images
are suitable to simulate the whole cycle by manipulating the time-stamps accordingly.
The analysis starts with the first image of the sequence looking for an industrial fairground. The system searches for the
obligatory parts Hall and ParkingLot. Halls are recognized by right-angled polygons in elevation data, which is derived
by stereo or is given by a DEM including buildings and vegetation. A hall candidate is accepted, if the region meets prede-
fined expectations about shape, area, compactness, and neighbourhood to other halls. Parking lots are characterized by
clusters of parallel lines representing the individual lanes. Only those clusters are selected to represent a parking lot that
lie outside the fairground area surrounded by the halls. After the detection of at least three halls and two parking lots the
IndustrialArea is instantiated completely. As the interpretation goal is to find a fairground, the system proceeds and tries
to replace the IndustrialFairground by a more special concept. There are four possible specializations (Fairlnactivity to
FairDismantling) and the search tree splits into five leaf nodes which are judged individually. The possibilistic judgement
348 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
