A Comparison of Spatio-temporal Interpolation Methods

  • Lixin Li
  • Peter Revesz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2478)


This paper analyzes spatio-temporal interpolation methods based on shape functions, namely, the ST product and the tetrahedral methods. These methods yield data that can be represented and queried in constraint database systems. That is an advantage, because there are many constraint database queries that are not expressible in current geographic information systems. We illustrate and test our approach on an actual real estate database. The interpolations for house prices per square foot are compared on accuracy, storage requirement, error-proneness to time aggregation, and difficulty of representation. It is shown that the best method yields a spatio-temporal interpolation that estimates house prices (per square foot) with approximately 10 percent error, is less error-prone, and uses only linear constraints, which can be implemented in several recent constraint database systems.


Root Mean Square Error Shape Function House Price Interpolation Method Time Aggregation 
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  1. 1.
    N. Adam and A. Gangopadhyay. Database Issues in Geographic Information Systems. Kluwer, 1997.Google Scholar
  2. 2.
    G. Buchanan. Finite Element Analysis. McGraw-Hill, New York, 1995.Google Scholar
  3. 3.
    M. Cai, D. Keshwani, and P. Revesz. Parametric Rectangles: A Model for Querying and Animating Spatiotemporal Databases. In: Proc. 7th International Conference on Extending Database Technology, volume 1777 of Lecture Notes in Computer Science, pages 430–44. Springer-Verlag, 2000.Google Scholar
  4. 4.
    R. Chen, M. Ouyang, and P. Revesz. Approximating Data in Constraint Databases. In: Proc. Symposium on Abstraction, Reformulation and Approximation, volume 1864 of Lecture Notes in Computer Science, pages 124–143. Springer-Verlag, 2000.CrossRefGoogle Scholar
  5. 5.
    M. Demers. Fundamentals of Geographic Information Systems. John Wiley & Sons, New York, 2nd edition, 2000.Google Scholar
  6. 6.
    L. Forlizzi, R. Güting, E. Nardelli, and M. Schneider. A Data Model and Data Structure for Moving Object Databases. In: Proc. ACM SIGMOD International Conference on Management of Data, pages 319–330, 2000.Google Scholar
  7. 7.
    L. Freitag and C. Gooch. Tetrahedral Mesh Improvement Using Swapping and Smoothing. International Journal for Numerical Methods in Engineering, 40: 3979–4002, 1997.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    J. Goodman and J. O’Rourke, editors. Handbook of Discrete and Computational Geometry. CRC Press, Boca Raton, New York, 1997.zbMATHGoogle Scholar
  9. 9.
    S. Grumbach, P. Rigaux, and L. Segoufin. Manipulating Interpolated Data is Easier than You Thought. In: Proc. IEEE International Conference on Very Large Databases, pages 156–165, 2000.Google Scholar
  10. 10.
    S. Hakimi and E. Schmeichel. Fitting Polygonal Functions to a Set of Points in the Plane. Computer Vision, Graphics, and Image Processing, 52(2): 132–136, 1991.Google Scholar
  11. 11.
    D. Hanselman and B. Littlefield. Mastering MATLAB 6: A Comprehensive Tutorial and Reference. Prentice Hall, 2001.Google Scholar
  12. 12.
    J. Jaffar, S. Michaylov, P. Stuckey, and R. Yap. The CLP(R) Language and System. ACM Transactions on Programming Languages and Systems, 14(3): 339–395, 1992.CrossRefGoogle Scholar
  13. 13.
    K. Johnston, J. ver Hoef, K. Krivoruchko, and N. Lucas. Using ArcGIS Geostatistical Analyst. ESRI Press, 2001.Google Scholar
  14. 14.
    P. Kanellakis, G. Kuper, and P. Revesz. Constraint Query Languages. Journal of Computer and System Sciences, 51(1): 26–52, 1995.CrossRefMathSciNetGoogle Scholar
  15. 15.
    G. Kuper, L. Libkin, and J. Paredaens, editors. Constraint Databases. Springer-Verlag, 2000.Google Scholar
  16. 16.
    N. Lam. Spatial Interpolation Methods: A Review. The American Cartographer, 10(2): 129–149, 1983.CrossRefGoogle Scholar
  17. 17.
    R. Laurini and D. Thompson. Fundamentals of Spatial Information Systems. Academic Press, 1992.Google Scholar
  18. 18.
    E. Miller. Towards a 4D GIS: Four-Dimensional Interpolation Utilizing Kriging. In: Z. Kemp, editor, Innovations in GIS 4: Selected Papers from the Fourth National Conference on GIS Research U.K, Ch. 13, pages 181–197, London, 1997. Taylor & Francis.Google Scholar
  19. 19.
    M. Oliver and R. Webster. Kriging: A Method of Interpolation for Geographical Information Systems. International Journal of Geographical Information Systems, 4(3): 313–332, 1990.CrossRefGoogle Scholar
  20. 20.
    F. Preparata and M. Shamos. Computational Geometry: An Introduction. Springer-Verlag, 1985.Google Scholar
  21. 21.
    P. Revesz. Introduction to Constraint Databases. Springer-Verlag, 2002.Google Scholar
  22. 22.
    P. Revesz, R. Chen, and M. Ouyang. Approximate Query Evaluation Using Linear Constraint Databases. In: Proc. Symposium on Temporal Representation and Reasoning, pages 170–175, Cividale del Friuli, Italy, 2001.Google Scholar
  23. 23.
    P. Revesz and L. Li. Representation and Querying of Interpolation Data in Constraint Databases. In: Proc. of the Second National Conference on Digital Government Research, pages 225–228, Los Angeles, California, 2002.Google Scholar
  24. 24.
    P. Revesz and L. Li. Constraint-Based Visualization of Spatial Interpolation Data. In: Proc. of the Six International Conference on Information Visualization, London, 2002 (to appear).Google Scholar
  25. 25.
    J. Shewchuk. Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangu-lator. In: Proc. First Workshop on Applied Computational Geometry, pages 124–133, Philadelphia, Pennsylvania, May 1996.Google Scholar
  26. 26.
    J. Shewchuk. Tetrahedral Mesh Generation by Delaunay Refinement. In: Proc. 14th Annual ACM Symposium on Computational Geometry, pages 86–95, Minneapolis, Minnesota, June 1998.Google Scholar
  27. 27.
    E. Tossebro and R. Güting. Creating Representation for Continuously Moving Regions from Observations. In: Proc. 7th International Symposium on Spatial and Temporal Databases, pages 321–344, Redondo Beach, CA, 2001.Google Scholar
  28. 28.
    J. Westervelt. Introduction to GRASS 4. GRASS Information Center. Army CERL, Champaign, Illinois, July 1991.Google Scholar
  29. 29.
    M. Worboys. GIS: A Computing Perspective. Taylor & Francis, 1995.Google Scholar
  30. 30.
    O. Zienkiewics and R. Taylor. Finite Element Method, Vol. 1, The Basis. Butterworth Heinemann, London, 2000.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Lixin Li
    • 1
  • Peter Revesz
    • 1
  1. 1.University of Nebraska-LincolnLincolnUSA

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