Stefan Growe 
  
  
  
  
  
a) b) Rules Possibilistic Probabilistic 
Judgement Judgement 
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Image #4 
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Figure 6: a) Constructed search tree representing the possible alternatives, the correct path is marked bold. 
(IA = IndustrialArea, Fl=Fairlnactivity, FC=FairConstruction, FA=FairActivity, FD=FairDismantling). 
b) Number of activated inference rules during analysis using the possibilistic and probabilistic judge- 
ment approach respectively. 
approach yields identical values, while the probabilistic approach favours the solution containing the most probable state 
Fairlnactivity. The hypothesis is tested in the data by verifying, whether the parking lots are empty and whether no trucks 
can be found next to the halls. For this purpose, regions of interest are derived from the already detected parking lots and 
halls respectively. Inside these regions vehicles, represented by small rectangular spots of a predefined size and lumi- 
nance, are counted. The number of detected vehicles decides about emptiness and fullness. Finally for the first image the 
state Fairlnactivity can be verified. In order to instantiate the concept Fairground the other states are still missing. Thus, 
the system continues with the second image dated five days later. Hypotheses for the successor state of the site are gener- 
ated according to the temporal knowledge. Within five days only Fairlnactivity and FairConstruction can be reached in 
the state transition diagram. The hypotheses are tested consecutively in the image data until the latter is instantiated be- 
cause of the detection of trucks near the halls. The process repeats for the third and fourth image and the states FairActivity 
and FairDismantling are verified. As all necessary states were detected in the image sequence the concept Fairground 
can be instantiated completely. The goal is reached and the analysis stops. The whole interpretation process is illustrated 
in Fig. 6a. The constructed search tree consists of 13 search nodes, the final scene description contains 888 instances de- 
scribing all the halls and parking lots detected in the four given images. The use of the temporal knowledge and the predic- 
tion of possible successor states restricts the search space, so that the analysis becomes more efficient. 
5.1 Possibilistic vs. Probabilistic Judgement 
In order to compare the two presented judgement approaches the described image interpretation process was performed 
using both methods. The strict separation of knowledge representation and system control permits the exchange of the 
judgement calculus without any modifications of the knowledge base. 
In both cases the correct interpretation result has been reached after having generated 13 search nodes, but the efficiency 
differs considerably. Fig. 6b shows the accumulated number of inference steps, each represented by the number of activa- 
tions of inference rules, needed for the detection of the Fairground. The possibilistic approach does not use the prior proba- 
bilities of states and state transitions. Hence, the search node to be investigated is chosen by random, whenever the evi- 
dence of the alternatives and therefore their judgement is identical. The randomness causes the total number of activated 
rules to vary between 2028 and 2766 rules. In contrast the probabilistic approach is deterministic and requires constantly 
1793 rule activations, a reduction by up to 35%. For the interpretation of the first image (Fairlnactivity) both methods 
need roughly 300 rule activations. During the analysis of the second image, the Bayesian approach favours the more prob- 
able solution of an unchanged state, and therefore follows erroneously the path to search node ny until the observations 
made in the image cause the rejection of this hypothesis. The correct state FairConstruction (search node ng) is found 
after 943 rule activations. If the possibilistic approach selects the correct search node ng by random search, only 622 rule 
activations are needed to reach this intermediate result. During the analysis of the third image the probabilistic method 
focuses immediately on the correct node n;0, so that 493 additional inference steps are sufficient (total 1436) to verify 
the state FairActivity. The other method needs between 469 and 921 rules (accumulated 1091 to 2766 rules) dependent 
on the order of investigated search nodes. For the interpretation of the final image the possibilistic approach fires 623 to 
937 rules compared to 357 rules using the Bayesian network, which again prefers the most probable state transition from 
FairActivity to FairDismantling. 
For the given example, the presented probabilistic judgement calculus takes advantage from the temporal knowledge 
introducing additional information about the probabilities of object states and their transitions. In the absence of such 
probabilities the judgement using Bayesian networks produces results comparable to the possibilistic method at higher 
computational costs due to the more complex propagation algorithm. In such cases the more robust and simple possibilis- 
tic judgement should be chosen. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 349