Reasoning about Gradual Changes of Topological Relationships
Max Egenhofer and Khaled Al-Taha Theory and Methods of Spatio-Temporal Reasoning in Geographic Space, Pisa, Italy,
A. Frank, I. Campari, and U. Formentini (eds.), Lecture Notes in Computer Science, Vol. 639, Springer-Verlag, pp. 196-219, September 1992.
Abstract
Geographic objects and phenomena may gradually change their
location, orientation, shape, and size over time. A qualitative
change occurs if the deformation of an object affects its
topological relationship with respect to another object. The
observation of such changes is particularly interesting, because
qualitative changes frequently require different decisions or
trigger new actions. Investigations of a closed set of mutually
exclusive binary topological relationships led to a formal model to
determine for each topological relationship the relationships
closest to it. Applied to the entire set of binary topological
relationships between spatial regions, this model describes a
partial order over topological relationships and provides a measure
to assess how far two relationships are apart from each other. The
changes to the binary topological relationship caused by such
deformations as translation, rotation, reduction, and expansion of
an object are mapped onto this graph. The graphs show
characteristic traverses for each kind of deformation. Using these
characteristic traverses as knowledge about deformations, one can
infer from multiple observations the kind of deformation that
caused the change and predict the next topological relationship.
Particularly, it provides answers to three kinds of qualitative
space-time inferences: (1) Given a process and a state, what is the
next most likely state? (2) Given an ordered pair of states, what
process may have occurred? (3) Given an ordered pair of states and
a process, in what states must the two objects have been in
between?
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Max Egenhofer and Khaled Al-Taha