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An Ordering of Convex Topological Relations
"... Abstract. Klippel has recently identified topological relativity as an important question for geographic information theory. One way of assessing at the importance of topology in spatial reasoning and in spatial theory is to analyze commonplace terms from natural language relative to conceptual neig ..."
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Abstract. Klippel has recently identified topological relativity as an important question for geographic information theory. One way of assessing at the importance of topology in spatial reasoning and in spatial theory is to analyze commonplace terms from natural language relative to conceptual neighborhood graphs, the alignment structures of choice for topological relations. Each of the terms analyzed is found to represent a convex set within the conceptual neighborhood graph of the regionregion relations, giving rise to the construction of the convex ordering of regionregion relations on the surface of the sphere.
A.: Investigating intuitive granularities of overlap relations
 In: Proceedings of the 12th IEEE International Conference on Cognitive Informatics & Cognitive Computing
, 2013
"... Abstract—We present four human behavioral experiments to address the question of intuitive granularities in fundamental spatial relations as they can be found in formal spatial calculi that focus on invariant characteristics under certain (especially topological) transformations. Of particular inter ..."
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Abstract—We present four human behavioral experiments to address the question of intuitive granularities in fundamental spatial relations as they can be found in formal spatial calculi that focus on invariant characteristics under certain (especially topological) transformations. Of particular interest to this article is the concept of two spatially extended entities overlapping each other. The overlap concept has been extensively treated in Galton’s mode of overlap calculus [1]. In the first two experiments, we used a category construction task to calibrate this calculus against behavioral data and found that participants adopted a very coarse view on the concept of overlap, only distinguishing between three general relations: proper part, overlap, and nonoverlap. In the following two experiments, we changed the instructions to explicitly address the possibility that humans could be swayed to adopt a more detailed level of granularity, that is, we encouraged them to create as many meaningful groups as possible. The results show that the three relations identified earlier (overlap, nonoverlap, and proper part) are very robust and a natural level of granularity across all four experiments but that contextual factors gain more influence at finer levels of granularity. I.
Swiss Canton Regions: A Model for Complex Objects in Geographic Partitions
"... Abstract. Spatial regions are a fundamental abstraction of geographic phenomena. While simple regions—disklike and simply connected—prevail, in partitions complex configurations with holes and/or separations occur often as well. Swiss cantons are one highlighting example of these, bringing in addit ..."
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Abstract. Spatial regions are a fundamental abstraction of geographic phenomena. While simple regions—disklike and simply connected—prevail, in partitions complex configurations with holes and/or separations occur often as well. Swiss cantons are one highlighting example of these, bringing in addition variations of holes and separations with point contacts. This paper develops a formalism to construct topologically distinct configurations based on simple regions. Using an extension to the compound object model, this paper contributes a method for explicitly constructing a complex region, called a canton region, and also provides a mechanism to determine the corresponding complement of such a region.
M.J.: From Metric to Topology: Determining Relations in Discrete Space
, 2015
"... Abstract. This paper considers the nineteen planar discrete topological relations that apply to regions bounded by a digital Jordan curve. Rather than modeling the topological relations with purely topological means, metrics are developed that determine the topological relations. Two sets of five su ..."
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Abstract. This paper considers the nineteen planar discrete topological relations that apply to regions bounded by a digital Jordan curve. Rather than modeling the topological relations with purely topological means, metrics are developed that determine the topological relations. Two sets of five such metrics are found to be minimal and sufficient to uniquely identify each of the nineteen topological relations. Key to distinguishing all nineteen relations are regions ’ margins (i.e., the neighborhood of their boundaries). Deriving topological relations from metric properties in ℝ! vs. ℤ! reveals that the eight binary topological relations between two simple regions in ℝ! can be distinguished by a minimal set of six metrics, whereas in ℤ!, a more finegrained set of relations (19) can be distinguished by a smaller set of metrics (5). Determining discrete topological relations from metrics enables not only the refinement of the set of known topological relations in the digital plane, but further enables the processing of raster images where the topological relation is not explicitly stored by reverting to mere pixel counts.
Partitions to Improve Spatial Reasoning
"... The field of spatial reasoning has provided a litany of formal models and reasoning systems aimed at providing users with information about spatial tasks and concepts, ranging from pointtopoint distance measurements coming from sensors all the way to topological information coming from the interac ..."
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The field of spatial reasoning has provided a litany of formal models and reasoning systems aimed at providing users with information about spatial tasks and concepts, ranging from pointtopoint distance measurements coming from sensors all the way to topological information coming from the interaction of multiple sensor readings. In this short paper, the concept of using topology to augment partitions is addressed. Future work within the dissertation includes other partitionbased relation theories, including digital topological relations and surrounds configurations within a collection of objects.
1 Cognitive Evaluation of Spatial Formalisms: Intuitive Granularities of Overlap Relations *
"... We present four human behavioral experiments to address the question of intuitive granularities in fundamental spatial relations as they can be found in formal spatial calculi. These calculi focus on invariant characteristics under certain (especially topological) transformations. Of particular inte ..."
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We present four human behavioral experiments to address the question of intuitive granularities in fundamental spatial relations as they can be found in formal spatial calculi. These calculi focus on invariant characteristics under certain (especially topological) transformations. Of particular interest to this article is the concept of two spatially extended entities overlapping each other. The overlap concept has been extensively treated in Galton’s mode of overlap calculus [1]. In the first two experiments, we used a category construction task to calibrate this calculus against behavioral data and found that participants adopted a very coarse view on the concept of overlap and distinguished only between three general relations: proper part, overlap, and nonoverlap. In the following two experiments, we changed the instructions to explicitly address the possibility that humans could be swayed to adopt a more detailed level of granularity, that is, we encouraged them to create as many meaningful groups as possible. The results show that the three relations identified in the first two experiments (overlap, nonoverlap, and proper part) are very robust and a natural level of granularity across all four experiments. However, the results also reveal that contextual factors gain more influence at finer levels of granularity. 1