Modeling Spatial Relations Between Lines and Regions: Combining
Formal Mathematical Models and Human Subjects Testing
David Mark and
Max Egenhofer Cartography and Geographical Information Systems 21 (3): 195-212, 1994.
Abstract
This paper describes the results of a series of human-subjects
experiments to test how people think about spatial relations
between lines and regions. The experiments are centered on a formal
model of topological spatial relations, called the 9-intersection.
For unbranched lines and simply-connected regions, this model
identifies 19 different spatial relations. Subjects were presented
with two or three geometrically-distinct drawings of each spatial
relation (40 drawings in all), with the line and region said to be
a road and a park, respectively. In the first experiment, the task
was to group the drawings so that the same phrase or sentence to
describe every situation in each group. A few subjects
differentiated all 19 relations, but most identified 9 to 13
groups. Although there was a great deal of variation across
subjects in the groups that were identified, the results confirm
that the relations grouped by the 9-intersection model are the ones
most often grouped by the subjects. No consistent language-related
differences were identified among 12 English-speaking subjects, 12
Chinese-speaking subjects, and 4 other subjects tested in their own
native languages. A second experiment presented the subjects with a
short sentence describing a spatial relation between a road and a
park, and the same 40 diagrams. Each subject was asked to rate the
strength of their agreement or disagreement that the sentence
described each relation. For each of the two different predicates
tested--"the road crosses the park" and "the road goes into the
park"--there was a great deal of consensus across the subjects. The
results of these experiments suggest that the 9-intersection model
forms a sound basis for characterizing line-region relations, and
that many spatial relations can be well-represented by particular
subsets of the primitives differentiated by the 9-intersection.
Full article
David Mark and
Max Egenhofer
