A Completeness of Metrics for Topological Relations in 3D Qualitative Spatial Reasoning

 

Chaman L. Sabharwal and Jennifer L. Leopold

 

Missouri University of Science and Technology, USA (e-mail: chaman@mst.edu, leopoldj@mst.edu).

 

Manuscript received on June 6, 2015
Accepted for publication on August 18, 2015
Published on October 15, 2015

 

Abstract

For qualitative spatial reasoning, there are various dimensions of objects. A considerable amount of effort has been devoted to 2D representation and analysis of spatial relations. Here we present an exposition for 3D objects. There are three types of binary relations between pairs of objects: topological connectivity, cardinal directions, and distance relations. The combinations of these relations can provide additional useful knowledge. The spatial databases include data and the spatial relations to facilitate end-user spatial querying, it also is important to associate natural language with these relations. Some work has been done in this regard for line-region and region-region topological relations in 2D, and very recent work has initiated the association between natural language, topology, and metrics for 3D objects. However, prior efforts have lacked rigorous analysis, expressive power, and completeness of the associated metrics. Herein we present a detailed study of new metrics required to bridge the gap between topological connectivity and size information for integrating reasoning in spatial databases. The complete set of metrics that we present should be useful for a variety of applications dealing with 3D objects including regions with vague boundaries.

Key words: Region connection calculus, metrics, spatial reasoning, qualitative reasoning.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

REFERENCES

[1] D. A. Randell, Z. Cui, and A. G. Cohn, "A Spatial Logic Based on Regions and Connection." Proceedings of the 3^rd International Conference on Knowledge Representation and Reasoning, Cambridge, MA, pp. 156-176, 1992.         [ Links ]

[2] M. J. Egenhofer and J. Herring, "Categorizing binary topological relations between regions, lines, and points in geographic databases." NCGIA Technical Reports 91-7, 1991.         [ Links ]

[3] S. Schockaert, M. De Cock, and E. E. Kerre, "Spatial reasoning in a fuzzy region connection calculus," Artificial Intelligence, 173(2), pp. 258-298, 2009.         [ Links ]

[4] D. Hernandez, E. C. Clementini, and P. Di Felice. "Qualitative Distances," 2nd Int. Conf. on Spatial Information Theory, LNCS 988, Springer-Verlag, pp. 45-57, 1995.         [ Links ]

[5] R. Shariff, M. J. Egenhofer, and D. M. Mark, "Natural-Language Spatial Relations Between Linear and Areal Objects: The Topology and Metric of English-Language Terms." International Journal of Geographical Information Science, 12, pp. 215-246, 1998.         [ Links ]

[6] M. Schneider, "Vague topological predicates for crisp regions through metric refinements," P. F. Fisher (Eds.) Developments in Spatial Data Handling, 11^th International Symposium on Spatial Data Handling, 1 Springer, pp. 149-162, 2005.         [ Links ]

[7] J. Leopold, C. Sabharwal, and K. Ward, "Spatial Relations Between 3D Objects: The Association Between Natural Language, Topology, and Metrics". Proceedings of the Twentieth International Conference on Distributed Multimedia Systems Pittsburgh DMS 2014, August 27-29, pp. 241 -249, 2014.         [ Links ]

[8] J. Albath, J. L. Leopold, C. L. Sabharwal, and A. M. Maglia, " RCC-3D: Qualitative Spatial Reasoning in 3D," Proceedings of the 23rd International Conference on Computer Applications in Industry and Engineering, pp. 74-79, 2010.         [ Links ]

[9] C. L. Sabharwal and J. L. Leopold. "Cardinal Direction Relations in Qualitative Spatial Reasoning," International Journal of Computer Science & Information Technology (IJCSIT) 6(1), pp. 1-13, 2014. DOI 10.5121/ijcsit.2014.6101        [ Links ]

[10] C. Sabharwal and J. Leopold, "Reducing 9-Intersection to 4-Intersection for Identifying Relations in Region Connection Calculus," Proceedings of the 24th International Conference on Computer Applications in Industry and Engineering (CAINE 2011), pp. 118-123, 2011.         [ Links ]

[11] C. Sabharwal and J. Leopold, "Modeling Cardinal Direction Relations in 3D for Qualitative Spatial Reasoning," Proceedings of Mining Intelligence and Knowledge Exploration, MIKE 2014, in Lecture Notes in Artificial Intelligence 8891, pp. 199-214, 2014.         [ Links ]