Approximate topological relations

Abstract In spatial data models for various applications, such as geographical information systems (GISs), the importance of topological relations is widely recognized. Topology makes very general statements about the structure and the relations of spatial objects. A refinement of topology by means of other geometric aspects can help to bend the various models that have been developed for topological relations towards a more effective description of geographic space. The introduction of broad boundaries is a direction to define approximate topological relations between spatial objects. In this paper, approximate topological relations are destined to capture boundary uncertainty, variations over time, proximity measures, and vector-raster representations. Approximate topological relations are structured in conceptual neighborhood graphs that have a twofold interpretation: two neighboring relations are at topological distance 1 in terms of the nine-intersection model and can be obtained, one from the other, by an elementary continuous deformation.

[1]  Eliseo Clementini,et al.  A Model for Representing Topological Relationships between Complex Geometric Features in Spatial Databases , 1996, Inf. Sci..

[2]  David M. Mark,et al.  Modelling Conceptual Neighbourhoods of Toplogical Line-Region Relations , 1995, Int. J. Geogr. Inf. Sci..

[3]  Wa Mackaness.  Issues in resolving visual spatial conflicts in automated map design , 1994 .

[4]  Max J. Egenhofer,et al.  Reasoning about Gradual Changes of Topological Relationships , 1992, Spatio-Temporal Reasoning.

[5]  Stephan Winter.  Uncertainty of topological relations in GIS , 1994, Other Conferences.

[6]  Derek Thompson,et al.  Fundamentals of spatial information systems , 1992, A.P.I.C. series.

[7]  Soumitra Dutta,et al.  Approximate spatial reasoning: Integrating qualitative and quantitative constraints , 1991, Int. J. Approx. Reason..

[8]  Hans-Peter Kriegel,et al.  Comparison of approximations of complex objects used for approximation-based query processing in spatial database systems , 1993, Proceedings of IEEE 9th International Conference on Data Engineering.

[9]  Anthony G. Cohn,et al.  The ‘Egg-Yolk’ Representation of Regions with Indeterminate Boundaries , 2020 .

[10]  P. D. Felice,et al.  A comparison of methods for representing topological relationships , 1995 .

[11]  Jayant Sharma,et al.  Modeling Topological Spatial Relations: Strategies for Query Processing , 1998 .

[12]  M. Egenhofer,et al.  Topological Relations Between Regions in IR 2 and ZZ 2 * , 1993 .

[13]  Laurent Siklóssy.  Generalized means-ends analysis and artificial intelligence , 1971, Inf. Sci..

[14]  M. Egenhofer.  Categorizing Binary Topological Relations Between Regions, Lines, and Points in Geographic Databases , 1998 .

[15]  Andrew U. Frank,et al.  Concepts and Paradigms in Spatial Information: Are Current Geographical Information Systems Truly Generic? , 1995, Int. J. Geogr. Inf. Sci..

[16]  Michael F. Worboys,et al.  A Design Support Environment for Spatio-Temporal Database Applications , 1995, COSIT.

[17]  Christian Freksa,et al.  Temporal Reasoning Based on Semi-Intervals , 1992, Artif. Intell..

[18]  Max J. Egenhofer,et al.  Topological Relations Between Regions with Holes , 1994, Int. J. Geogr. Inf. Sci..

[19]  David M. Mark,et al.  Naive Geography , 1995, COSIT.

[20]  Jürg Nievergelt.  7 ± 2 Criteria for Assessing and Comparing Spatial data Structures , 1989, SSD.

[21]  Helen Couclelis,et al.  People Manipulate Objects (but Cultivate Fields): Beyond the Raster-Vector Debate in GIS , 1992, Spatio-Temporal Reasoning.

[22]  Anthony G. Cohn,et al.  Representing Spatial Vagueness: A Mereological Approach , 1996, KR.

[23]  Anthony G. Cohn,et al.  Taxonomies of logically defined qualitative spatial relations , 1995, Int. J. Hum. Comput. Stud..

[24]  P. Bruegger,et al.  Spatial Theory for the Integration of Resolution-Limited Data , 1996 .

[25]  Anthony G. Cohn,et al.  Qualitative and Topological Relationships in Spatial Databases , 1993, SSD.

[26]  P. Burrough,et al.  Geographic Objects with Indeterminate Boundaries , 1996 .

[27]  James R. Munkres,et al.  Topology; a first course , 1974 .

[28]  Antony Galton,et al.  Towards a Qualitative Theory of Movement , 1995, COSIT.

[29]  Soumitra Dutta,et al.  Topological Constraints: A Representational Framework For Approximate Spatial And Temporal Reasoning , 1991, SSD.

[30]  Timos K. Sellis,et al.  Topological relations in the world of minimum bounding rectangles: a study with R-trees , 1995, SIGMOD '95.