J.-H. Hong, M. Egenhofer, and A. Frank
On the Robustness of Qualitative Distance- and Direction-Reasoning
Abstract
This paper focuses on spatial information derived from the
composition of two pairs of cardinal directions (e.g., North and
North-East) and approximate distances (e.g., near and far), i.e.,
given the approximate distances a1 (A, B) and a2 (B, C) and the
cardinal directions c1 (A, B) and c2 (B, C), what are a3 (A, C) and
c3 (A, C)? Spatial reasoning about cardinal directions and
approximate distances is challenging because distance and direction
will affect the composition. This paper investigates the dependency
between qualitative and quantitative inference methods for
reasoning about cardinal directions and approximate distances.
Cardinal directions are based on a 4-sector model (North, East,
South, West), while approximate distance correspond to a set of
ordered intervals that provide a complete partition
(non-overlapping and mutually exclusive) such that the following
interval is greater than or equal to the previous one (for example,
"far" would extend over a distance that is at least as great as
"medium.") We ran comprehensive simulations of quantitative
reasoning, and compared the results with the ones obtained from
quantitative reasoning. The results indicate that the composition
is robust if the ratio between two consecutive intervals of
quantitative distances is greater than 3.
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