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Towards a formal model for multiresolution spatial maps

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Advances in Spatial Databases (SSD 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 951))

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Abstract

Topological and metric aspects of the multiresolution representation of geographic maps are considered. The combinatorial structure of maps is mathematically modelled through abstract cell complexes, and maps at different detail are related through continuous functions over such complexes. Metric aspects of multiresolution are controlled through the concept of homotopy. Two alternative multiresolution models are proposed, which are implicitly defined by a sequence of map simplifications that fulfil both topological and metric consistency rules.

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References

  1. Bertolotto, M., De Floriani,L., Puppo, E.: Multiresolution topological maps. In Advanced Geographic Data Modelling — Spatial Data Modelling and Query Languages for 2D and 3D Applications, M. Molenaar, S. De Hoop (eds.), Netherland Geodetic Commission, Publications on Geodesy — New Series, 40, pp.179–190

    Google Scholar 

  2. Bruegger, B., Frank, A.: Hierarchies over topological data structures. Proceedings ASPRS-ACSM Annual Convention, Baltimore, MD, 1989, pp. 137–145

    Google Scholar 

  3. Bruegger, B., Kuhn, W.: Multiple topological representations. Technical Report 91–17, National Center for Geographic Information and Analysis, Santa Barbara, Ca, 1991

    Google Scholar 

  4. De Floriani, L., Puppo E.: A hierarchical triangle-based model for terrain description. In Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, eds. A.U. Frank, I. Campari, U. Formentini, Lecture Notes in Computer Science 639, Springer-Verlag, 1992, pp.236–251

    Google Scholar 

  5. De Floriani, L., Marzano, P. Puppo, E.: Spatial queries and data models. In Spatial Information Theory — A theoretical basis for GIS, A.U. Frank, I. Campari (Eds.), Lecture Notes in Computer Science 716, Springer-Verlag, 1993, pp.113–138

    Google Scholar 

  6. Dettori, G., Puppo, E.: Simplification of combinatorial maps through continuous mappings. Technical Report, 3-95, Istituto per la Matematica Applicata, C.N.R., 1995, Genova, Italy

    Google Scholar 

  7. Egenhofer, M., Frank, A.U., Jackson, J.P.: A topological model for spatial databases. In Design and Implementation of Large Spatial Databases, (SSD'89), Lecture Notes in Computer Science, 409, 1989, pp. 271–286

    Google Scholar 

  8. Egenhofer, M., Herring, J.: A mathematical framework for the definition of topological relationships. Proceedings 4th International Symposium on Spatial Data Handling, Zurich, Switzerland, 1990, pp.803–813

    Google Scholar 

  9. Egenhofer, M., Franzosa, R.: Point-set topological spatial relations. International Journal of Geographical Information Systems, 5 (2), 1991, pp. 161–174

    Google Scholar 

  10. Egenhofer, M., Sharma, J.: Topological consistency. Proceedings 5th International Symposium on Spatial Data Handling, Charleston, SC, 1992, pp.335–343

    Google Scholar 

  11. Egenhofer, M., Al-Taha, K.: Reasoning about gradual changes of topological relationships. In Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, A.U. Frank, I. Campari, U. Formentini (Eds.), Lecture Notes in Computer Science 638, Springer-Verlag, 1992, pp.196–219

    Google Scholar 

  12. Egenhofer, M., Clementini, E., Di Felice, P.: Topological relations between regions with holes. International Journal of Geographical Information Systems, 8 (2), 1994, pp. 129–142

    Google Scholar 

  13. Egenhofer, M., Clementini, E., Di Felice, P.: Evaluating inconsistencies among multiple representations. Proceedings 6th International Symposium on Spatial Data Handling, Edinburgh, Scotland, 1994, pp.901–920

    Google Scholar 

  14. Frank, A., Kuhn, W.: Cell graph: a provable correct method for the storage of geometry. Proceedings 2nd International Symposium on Spatial data Handling, Seattle, WA, 1986

    Google Scholar 

  15. Frank, A., Timpf, S.: Multiple representations for cartographic objects in a multiscale tree — An intelligent graphical zoom. Computers & Graphics, 18, 6 (1994) pp. 823–829

    Google Scholar 

  16. Hadzilacos, T., Tryfona, N.: A model for expressing topological integrity constraints in geographic databases. Lecture Notes in Compute Science, 639, Springer-Verlag, 1992, pp.252–268

    Google Scholar 

  17. Kainz, W.: Spatial relationships — Topology versus order. Proceedings 4th International Symposium on Spatial Data Handling, pp.814–819, Zurich, Switzerland, July 1990

    Google Scholar 

  18. Kelly, J.L.: General Topology. D. Van Nostrand Co., 1955

    Google Scholar 

  19. Kovalevsky, V.A.: Finite topology as applied to image analysis. Computer Vision, Graphics, and Image Processing, 46, 1989, pp. 141–161

    Google Scholar 

  20. Lundell, A.T., Weingram, S.: The Topology of CW Complexes. Van Nostrand Reinhold Comp., 1969

    Google Scholar 

  21. Molenaar, M.: Single valued vector maps — a concept in GIS. Geo-Informations-systeme, 2 (1), 1989

    Google Scholar 

  22. Pigot, S.: A topological model for a 3D spatial information system. Proceedings 5th International Symposium on Spatial Data Handling, Charleston, SC, August 3–7, 1992

    Google Scholar 

  23. Pigot, S.: Generalized singular 3-cell complexes'. Proceedings 6th International Symposium on Spatial Data Handling, Edinburgh, Scotland, 1994, pp.89–111

    Google Scholar 

  24. Rourke, C.P., Sanderson, B.J.: Introduction to Piecewise-linear Topology. Springer-Verlag, 1972

    Google Scholar 

  25. Timpf, S., Volta, G.S., Pollock, D.W., Egenhofer, M.: A conceptual model of wayfinding using multiple levels of abstraction. In Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, eds. A.U. Frank, I. Campari, U. Formentini, Lecture Notes in Computer Science 639, Springer-Verlag, pp.348–367

    Google Scholar 

  26. Worboys, M.F., Hearnshaw, H.M., Maguire, D.J.: Object-oriented data modelling for spatial databases. International Journal of Geographical Information Systems, 4 (4), 1990, pp. 369–383

    Google Scholar 

  27. Worboys, M.F.: A generic model for planar geographic objects. International Journal of Geographical Information Systems, 6 (5), 1992, pp. 353–372

    Google Scholar 

  28. Worboys, M.F., Bokafos, P: A canonical model for a class of areal spatial objects. Advances in Spatial Database (SSD93), D. Abel, B.C. Ooi (Ed.s), Lecture Notes in Computer Science, Springer-Verlag, 1993, pp.36–52

    Google Scholar 

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Authors and Affiliations

  1. Istituto per la Matematica Applicata Consiglio Nazionale delle Ricerche, Via De Marini, 6, 16149, Genova, Italy

    Enrico Puppo & Giuliana Dettori

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  1. Enrico Puppo
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  2. Giuliana Dettori
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Max J. Egenhofer John R. Herring

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© 1995 Springer-Verlag Berlin Heidelberg

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Puppo, E., Dettori, G. (1995). Towards a formal model for multiresolution spatial maps. In: Egenhofer, M.J., Herring, J.R. (eds) Advances in Spatial Databases. SSD 1995. Lecture Notes in Computer Science, vol 951. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60159-7_10

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  • DOI: https://doi.org/10.1007/3-540-60159-7_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60159-3

  • Online ISBN: 978-3-540-49536-9

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