The International Archives of the Photogrammetrv. Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beiiine 2008 
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The regions are both static a-priori defined regions with 
political background like cities and districts (solid lines) and 
dynamic regions of the emergency administration, like damage 
sites and operational areas (OA) (dashed lines). 
The binary topological relations of the diverse regions are easy 
to identify for human operators. The fire is inside the 
operational area 3 which is disjoint to the operational area 2 and 
contained by the damage site. The damage site intersects district 
A and B and all regions are inside the city and so on. 
Figure 1. A fire event (AM) and the resulting interactions of 
involved administrative regions (OA - operational area) 
But first of all a definition of the degree of the needed 
topological relations as well as the region characteristic is 
necessary. Based on the situation in the figure above, equation 1 
defines a set fl R of essential topological relations in R 2 , which 
are adequate for representing domain specific spatial scenes. 
ù R ={disjoint, intersect, contain, inside, equal} (1) 
Further possible relations like touch* (OA 2 touches OA3), 
cover (damage site covers OA3) and covered by (inverse 
relation to cover) are excluded deliberately because no benefit 
of gaining further information was found. As a basis restriction 
regions have to be regular closed and without holes. 
For processing, the information content of the scene in Figure 1 
is also represented in a knowledge base, here the domain 
ontology DM 2 . It has to be emphasized that modeling relations 
in such ontologies has a semantic background which is quite 
different from the topological one. Semantic relations are 
focused on entities and objects in general. So, a semantic 
relation is for example the part-of relationship of a fire engine 
and a fire brigade (a composite of engines) which does not 
contain topological information about the spatial situation of 
both. It is not possible to know at a specific point in time, if the 
fire engine is contained by, or disjoint to the convoy of the fire 
brigade. The needed information content for a correct 
* The touch relation is not necessary, because neighbourhood 
relations are defined separately. 
topological representation is derivable by using background and 
context knowledge which is also inherent in the ontology. For 
example it is possible to deduce the location of a fire engine 
based on information of its activity. That means that an engine 
is located, where it extinguishes a fire. Its location is therefore 
independent of the location of the fire brigade. 
The scene information of Figure 1 is modeled in the DM 2 
according to the class-scheme in Figure 2. The five object 
classes of fire, operational area, damage site, district and city 
are obviously required. For modeling the complete semantic of 
this situation, the classes context, building and address are also 
necessary. Semantic modeling means here that more 
information is represented in the knowledge base than is 
inferable by the visualization solely. That way an event in 
general relates to an object which is affected, here a building. 
The relation between building and fire in the DM 2 is affected by 
and the inverse relation is affects. Building itself has a 
geographical location as well as a “semantic” location, the 
address. The relation between them is an instance of 
relationship in the ontology. That way the content given by the 
ontology holds much more potentially useful information for a 
respective reasoning process. 
Figure 2. Part of the class scheme of the DM 2 , in IDEF1X- 
notation 
This kind of object modeling and reasoning is a bit more 
complex than a spatial query function in a GIS for relating a fire 
and the respective city, but it is done with respect to the systems 
semantic and the mental model of the staff members. This is 
important for adopting the reasoning process. 
2.2 Topological Reasoning 
Diverse methods are available for different ways of topological 
reasoning. They can be categorized in the three different groups 
of position based methods, dimension extended methods and 
calculus based methods. Position based methods derive the 
respective topological relation between regions from the 
position to each other. Such methods like the weighted 
walkthroughs model (WWM) (Cicerone and Clementini, 2003) 
as well as the model of ternary projective relations (TPR) 
(Billen and Clementini, 2004) are suitable for topological 
reasoning about dynamic and moving regions. More popular are 
dimension extended methods like the intersection model (IM) 
(Egenhofer and Herring, 1991) and calculus based methods like 
the region connection calculus (RCC) (Renz, 2002). The latter 
two concepts of representing a set of topological relations are 
quite different. 
The formal categorization of topological relations by the IM is 
based on a comparison between the interiors Sx and the 
boundaries x° of objects. That way, a 4-intersection-matrix