GeoInformatica

, Volume 9, Issue 3, pp 211–236 | Cite as

Indeterminacy and Spatiotemporal Data: Basic Definitions and Case Study

  • Dieter Pfoser
  • Nectaria Tryfona
  • Christian S. Jensen
Original Article

Abstract

For some spatiotemporal applications, it can be assumed that the modeled world is precise and bounded, and that also our record of it is precise. While these simplifying assumptions are sufficient in applications like a land information system, they are unnecessarily crude for many other applications that manage data with spatial and/or temporal extents, such as navigational applications. This work explores fuzziness and uncertainty, subsumed under the term indeterminacy, in the spatiotemporal context. To better illustrate the basic spatiotemporal concepts of change or evolution, it is shown how the fundamental modeling concepts of spatial objects, attributes, and relationships and time points and periods are influenced by indeterminacy and how they can be combined. In particular, the focus is on the change of spatial objects and their geometries across time. Four change scenarios are outlined, which concern discrete versus continuous change and asynchronous versus synchronous measurement, and it is shown how to model indeterminacy for each. A case study illustrates the applicability of the paper’s general proposal by describing the uncertainty related to the management of the movements of point objects, such as the management of vehicle positions in a fleet management system.

Keywords

spatiotemporal uncertainty spatiotemporal indeterminacy spatiotemporal fuzziness moving objects spatiotemporal data trajectories 

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References

  1. 1.
    B.D. Anderson and J.B. Moore. Optimal Filtering. Prentice-Hall: Englewood Cliffs, NJ, 1979.Google Scholar
  2. 2.
    R. Bartels, J. Beatty, and B. Barsky. An Introduction to Splines for Use in Computer Graphics and Geometric Modeling. Morgan Kaufmann Publishers: Los Altos, CA, 1987.Google Scholar
  3. 3.
    I. Bloch. “On fuzzy distances and their use in image processing under imprecision,” Pattern Recognition, Vol. 32(11):1873–1895, 1999.CrossRefGoogle Scholar
  4. 4.
    S. Brakatsoulas, D. Pfoser, and N. Tryfona. “Modeling, storing and mining moving object databases,” Proceedings of the IDEAS Conference, 68– 77, 2004.Google Scholar
  5. 5.
    P.A. Burrough and R.A. McDonnell. Principles of Geographical Information. Oxford University Press: Oxford, 1998.Google Scholar
  6. 6.
    P.A. Burrough, “Fuzzy mathematical methods for soil survey and land evaluation,” Journal of Soil Science, Vol. 40:477–492, 1989.Google Scholar
  7. 7.
    P.A. Burrough, R.A. MacMillan, and W. vanDeursen. “Fuzzy classification methods for determining land suitability from soil profile observations and topography,” Journal of Soil Science, Vol. 43:193–210, 1992.Google Scholar
  8. 8.
    T. Cheng and M. Molenaar. “Diachronic analysis of fuzzy objects,” GeoInformatica, Vol. 3(4):337–355, 1999.CrossRefGoogle Scholar
  9. 9.
    N. Chrisman. “A theory of cartographic error and its measurement in digital databases,” Proceedings of Auto-Carto 5, EGIS Foundation, Utrecht, 159–168, 1982.Google Scholar
  10. 10.
    C. Claramunt and M. Theriault. “Managing time in GIS: an event-oriented approach,” Recent Advances in Temporal Databases, Springer-Verlag: Berlin, 142–161, 1995.Google Scholar
  11. 11.
    C. Claramunt, C. Parent, S. Spaccapietra, and M. Theriault. “Database modelling for environmental and land use changes,” in S. Geertman, S. Openshow, and J. Stillwell (Eds). Geographical Information and Planning: European Perspectives. Chapter XX. Springer-Verlag: Berlin, 1998.Google Scholar
  12. 12.
    D. Dubois and H. Prade. “Fuzzy sets and probability: misunderstandings, bridges, and gaps,” Proceedings of the 2nd IEEE International Conference on Fuzzy Systems, 1059–1068, 1993.Google Scholar
  13. 13.
    C.E. Dyreson and R.T. Snodgrass. “Valid-time indeterminancy,” Proceedings of the 9th IEEE International Conference on Data Engineering, 335–343, 1993.Google Scholar
  14. 14.
    C.E. Dyreson, M. Soo, and R.T. Snodgrass. “The data model for time,” The TSQL2 Temporal Query Language. Kluwer Academic Publishers: Boston, 97–101, 1995.Google Scholar
  15. 15.
    P. Fisher. “Boolean and fuzzy regions,” Geographic Objects with Indeterminate Boundaries. Taylor & Francis: London, 87–94, 1996.Google Scholar
  16. 16.
    M. Goodchild and S. Gopal. Accuracy of Spatial Databases. Taylor & Francis: London, 1989.Google Scholar
  17. 17.
    R.H. Gütting, M. Böhlen, M. Erwig, C.S. Jensen, N. Lorentzos, M. Schneider, and M. Vazirgiannis. “A foundation for representing and querying moving objects,” ACM Transactions on Database Systems, Vol. 25(1): 1–42, 2001.CrossRefGoogle Scholar
  18. 18.
    T. Hadzilacos. “On layer-based systems for undetermined boundaries,” Geographic Objects with Indeterminate Boundaries, Taylor & Francis: London, 237–256, 1996.Google Scholar
  19. 19.
    T. Hadzilacos and N. Tryfona. “A model for expressing spatiotemporal integrity constraints,” Proceedings of the International Conference GIS—From Space to Territory: Theories and Methods of Spatio-Temporal Reasoning, 252–268, 1992.Google Scholar
  20. 20.
    K. Hornsby and M. Egenhofer. “Modeling moving objects over multiple granularities,” Special issue on Spatial and Temporal Granularity, Annals of Mathematics and Artificial Intelligence, Vol. 36:177–194, 2002.CrossRefMathSciNetGoogle Scholar
  21. 21.
    R.E. Kalman. “A new approach to linear filtering and prediction problems,” Transaction of the ASME–Journal of Basic Engineering, Vol. 82(Series D):35–45, 1960.Google Scholar
  22. 22.
    E.J. Krakiwsky, C.B. Harris, and R. Wong. “A Kalman filter for integrating dead reckoning, map matching, and gps positioning,” Proceedings of the IEEE Position Location and Navigation Symposium, 39–46, 1988.Google Scholar
  23. 23.
    G. Kollios, D. Gunopulos, V. Tsotras, A. Delis, and M. Hadjieleftheriou. “Indexing animated objects using spatio-temporal access methods,” IEEE Transactions on Knowledge and Data Engineering, Vol. 13(5):742–777, 200l.CrossRefGoogle Scholar
  24. 24.
    I. Lazaridis, K. Porkaew, and S. Mehrotra. “Dynamic queries over mobile objects,” Proceedings of the 8th International Conference on Extending Database Technology, 269–286, 2002.Google Scholar
  25. 25.
    A. Leick. GPS Satellite Surveying. John Wiley & Sons: New York, 1995.Google Scholar
  26. 26.
    J. Moreira, C. Ribeiro, and J. Saglio. “Representation and manipulation of moving points: An extended data model for location estimation,” Cartography and Geographic Information Science, Vol. 26(2):109–123, 1999.Google Scholar
  27. 27.
    D. Pfoser and N. Tryfona. “Requirements, definitions, and notations for spatiotemporal application environments,” Proceedings of the 6th International Symposium on Advances in Geographic Information Systems, 124–130, 1998.Google Scholar
  28. 28.
    D. Pfoser and C.S. Jensen. “Capturing the uncertainty of moving-object representations,” Proceedings of the 6th International Symposium on the Advances in Spatial Databases, 111–132, 1999.Google Scholar
  29. 29.
    D. Pfoser, C.S. Jensen, and Y. Theodoridis. “Novel approaches in query processing for moving objects data,” Proceedings of the 26th International Conference on Very Large Data Bases, 395–406, 2000.Google Scholar
  30. 30.
    D. Pfoser and N. Tryfona. “Capturing fuzziness and uncertainty of spatiotemporal objects,” Proceedings of the 5th East European Conference on Advances in Databases and Information Systems, 149–162, 2001.Google Scholar
  31. 31.
    D. Pfoser. “Indexing the trajectories of moving objects,” IEEE Data Engineering Bulletin, Vol. 25(2):3–9, 2002.Google Scholar
  32. 32.
    S. Saltenis, C.S. Jensen, S. Leutenegger, and M.A. Lopez. “Indexing the positions of continuously moving objects,” Proceedings of the ACM SIGMOD Conference on Management of Data, 331–342, 2000.Google Scholar
  33. 33.
    M. Schneider. “A design of topological predicates for complex crisp and fuzzy regions,” Proceedings of 20th International Conference on Conceptual Modeling, 103–116, 200l.Google Scholar
  34. 34.
    M. Schneider. “Uncertainty management for spatial data in databases: Fuzzy spatial data types,” Proceedings of the 6th International Symposium on the Advances in Spatial Databases, 330–351, 1999.Google Scholar
  35. 35.
    R. Shibasaki. “Handling spatiotemporal uncertainties of geo-objects for dynamic update of gis databases from multi-source data,” in Advanced Geographic Data Modeling, Publications on Geodesy, Netherlands Geodetic Commission, Vol. 40, pp. 228–243, 1994.Google Scholar
  36. 36.
    P.A. Story and M.F. Worboys. “A design support environment for spatio-temporal database applications,” Proceedings of the International Conference on Spatial Information Theory, 413–430, 1995.Google Scholar
  37. 37.
    Y. Tao and D. Papadias. “Mv3R-tree: A spatiotemporal access method for timestamp and interval queries,” Proceedings of the 27th International Conference on Very Large Databases, 431–440, 2001.Google Scholar
  38. 38.
    N. Tryfona and C.S. Jensen. “Conceptual data modeling for spatiotemporal applications,” Geoinformatica, Vol. 3(3):245–268, 1999.CrossRefGoogle Scholar
  39. 39.
    M. Vazirgiannis. “Uncertainty handling in spatial relationships,” Proceedings of the ACM Symposium on Applied Computing, Vol. 1:494–500, 2000.Google Scholar
  40. 40.
    M. Worboys. “Imprecision in finite resolution spatial data,” GeoInformatica, Vol. 2(3):257–279, 1998.CrossRefGoogle Scholar
  41. 41.
    M. Worboys. “Computation with imprecise geospatial data,” Computers, Environment, and Urban Systems, Vol. 22(2):85–106, 1998.Google Scholar
  42. 42.
    L. Zadeh. “Fuzzy sets,” Information and Control, Vol. 8:338–353, 1965.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Dieter Pfoser
    • 1
  • Nectaria Tryfona
    • 1
  • Christian S. Jensen
    • 2
  1. 1.Research Academic Computer Technology InstituteAthensGreece
  2. 2.Department of Computer ScienceAalborg UniversityAalborgDenmark

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