Abstract
A hierarchical spatial reasoning is proposed to determine the topological relation between two regions in independent spatial partitions. Hierarchical partitions considered are raster images as uniform regular partitions — extended to image pyramids —, and quadtrees as hierarchical regular partitions. The hierarchical approach starts at the root level with total uncertainty about a topological relation. A recursive determination level by level refines the results, excluding relations that are definitely not true. The process stops immediately when the refined information is suffcient to answer a given query. The effciency of the approach even can be improved by doing the recursion incrementally, examining only the locations that contribute new information. Both together increases efficiency significantly compared to non-hierarchical procedures.
The topological relation can be determined by intersection sets or by region connection calculus. We apply the method with intersection sets here. Relations are determined for binary classified partition elements, distinguishing the interior and the exterior of a region. By the hierarchic approach mixed partition elements are included.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ackermann, F., and M. Hahn, Image pyramids for digital photogrammetry, in Digital Photogrammetric Systems, H. Ebner, D. Fritsch, and C. Heipke, eds., Wichmann, Karlsruhe, 1991, pp. 43–58.
Bittner, T., Rough Location, ph.d. thesis, Technical University Vienna, 1999.
Burrough, P. A., and A. U. Frank, eds., Geographic Objects with Indeterminate Boundaries, vol. 2 of ESF-GISDATA, Taylor & Francis, 1996.
Cohn, A., B. Bennett, J. Goodday, and N. Gotts, Qualitative spatial re-presentation and reasoning with the region connection calculus, Geoinformatica, 1 (1997), pp. 1–44.
Cohn, A.G., and N. M. Gotts, The ‘egg-yolk’ representation of regions with indeterminite boundaries, in Geographic Objects with Indeterminate Boundaries, P. A. Burrough and A. U. Frank, eds., vol. 2, Taylor & Francis, London, 1996, pp. 171–187.
Egenhofer, M.J., Spatial Query Languages, ph.d. thesis, University of Maine, 1989.
Egenhofer, M.J., and R.D. Franzosa, Point-set topological spatial relations, International Journal of Geographical Information Systems, 5 (1991), pp.161–174.
Frank, A. U., Hierarchical Spatial Reasoning, Technical Report, Department of Geoinformation, Technical University Vienna, 1998.
Knuth, D. E., The Art of Computer Programming, Addison-Wesley, Reading, Massachusetts, 1973.
Kong, T. Y., and A. Rosenfeld, Digital topology: Introduction and survey, Computer Vision, Graphics, and Image Processing, 48 (1989), pp. 357–393.
Kropatsch, W. G., A pyramid that grows by powers of 2, Pattern Recognition Letters, 3 (1985), pp. 315–322.
Randell, D. A., Z. Cui, and A. Cohn, A spatial logic based on regions and connection, in Third International Conference on the Principles of Knowledge Re-presentation and Reasoning, R. Brachmann, H. Levesque, and R. Reiter, eds., Los Altos, CA, 1992, Morgan-Kaufmann, pp. 165–176.
Rosenfeld, A., Digital topology, Am. Math. Month.,86 (1979), pp. 621–630.
Samet, H., Applications of Spatial Data Structures, Addison-Wesley, Reading, Massachusetts, 1990.
The Design and Analysis of Spatial Data Structures, Addison-Wesley, Reading, Massachusetts, 1990.
Sinowjew, A. A., Über mehrwertige Logik, Deutscher Verlag der Wissenschaften, Berlin, 1968.
Tobler, W., Application of image processing techniques to map processing, in International Symposium on Spatial Data Handling, Zurich, Switzerland, 1984, pp. 140–145.
Winter, S., Topological relations between discrete regions, in Advances in Spatial Databases, M. J. Egenhofer and J. R. Herring, eds., vol. 951 of Lecture Notes in Computer Science, Springer, Berlin, 1995, pp. 310–327.
Winter, S., and T. Bittner, Hierarchical topological reasoning with uncertain regions, in International Symposium on Spatial Data Quality, Hongkong, 1999, accepted paper.
Worboys, M., Imprecision infinite resolution spatial data, GeoInformatica, 2 (1998), pp. 257–279.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Winter, S. (1999). Topological Relations in Hierarchical Partitions. In: Freksa, C., Mark, D.M. (eds) Spatial Information Theory. Cognitive and Computational Foundations of Geographic Information Science. COSIT 1999. Lecture Notes in Computer Science, vol 1661. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48384-5_10
Download citation
DOI: https://doi.org/10.1007/3-540-48384-5_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66365-2
Online ISBN: 978-3-540-48384-7
eBook Packages: Springer Book Archive