Advertisement

Map Algebra Extended with Functors for Temporal Data

  • Andrew U. Frank
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3770)

Abstract

This paper shows how to extend and generalize Tomlin’s Map Algebra to apply uniformly for spatial, temporal, and spatio-temporal data. A specific data layer can be seen as a function from location to a value (Goodchild’s geographic reality). Map layer but also time series and other similar constructions are functors, mapping local operations to layers, time series, etc. Tomlin’s Focal Operations are mostly convolutions and the zonal operations are summaries for zones. The mathematical framework explained justifies polymorphic overloading of operation names like + are made to work for layers, time series, etc. There is also a uniform method to apply user-defined local functions to them. The result is a consistent extension of Map Algebra with a simplified user interface. The implementation covers raster operations and demonstrates the generality of the concept.

Keywords

Time Series Category Theory Local Operation Geographic Information System Data Constructor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Asperti, A., Longo, G.: Categories, Types and Structures - An Introduction to Category Theory for the Working Computer Scientist. The MIT Press, Cambridge (1991)zbMATHGoogle Scholar
  2. Bird, R., de Moor, O.: Algebra of Programming. Prentice Hall, Europe (1997)zbMATHGoogle Scholar
  3. Cardelli, L.: Type Systems. Handbook of Computer Science and Engineering, pp. 2208-2236. A.B. Tucker, CRC Press (1997)Google Scholar
  4. Cardelli, L., Wegner, P.: On Understanding Types, Data Abstraction, and Polymorphism. ACM Computing Surveys 17(4), 471–522 (1985)CrossRefGoogle Scholar
  5. Church, R.L., Gerrard, R.A., et al.: Constructing Cell-Based Habitat Patches Useful in Conservation Planning. Annals of the Association of American Geographers 93(4), 814–827 (2003)CrossRefGoogle Scholar
  6. Couclelis, H., Gale, N.: Space and Spaces. Geografiska Annaler 68(1), 1–12 (1986)CrossRefGoogle Scholar
  7. ESRI, Understanding GIS - The ARC/INFO Method. The Bath Press, Harlow, Longman (1993)Google Scholar
  8. Frank, A.U.: GIS for Politics. GIS Planet 1998, Lisbon, Portugal, September 9 - 11, IMERSIV (1998)Google Scholar
  9. Frank, A.U.: One Step up the Abstraction Ladder: Combining Algebras - From Functional Pieces to a Whole. In: Freksa, C., Mark, D.M. (eds.) COSIT 1999. LNCS, vol. 1661, pp. 95–107. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  10. Goodchild, M.F.: A Geographical Perspective on Spatial Data Models. GIS Design Models and Functionality, Leicester, Midlands Regional Research Laboratory (1990)Google Scholar
  11. Goodchild, M.F.: Geographical Data Modeling. Computers and Geosciences 18(4), 401–408 (1992)CrossRefGoogle Scholar
  12. Horn, B.K.P.: Robot Vision. MIT Press, Cambridge (1986)Google Scholar
  13. Lifschitz, V. (ed.): Formalizing Common Sense - Papers by John McCarthy. Ablex Publishing, Norwood (1990)Google Scholar
  14. Loeckx, J., Ehrich, H.-D., et al.: Specification of Abstract Data Types. John Wiley, B.G. Teubner, Chichester, UK, Stuttgart (1996)zbMATHGoogle Scholar
  15. Mac Lane, S., Birkhoff, G.: Algebra. Macmillan, New York (1967)Google Scholar
  16. McHarg, I.: Design with Nature. Natural History Press (1969)Google Scholar
  17. Peyton Jones, S., Hughes, J., et al.: Haskell 1998: A Non-strict, Purely Functional Language (1999)Google Scholar
  18. Snodgrass, R.T.: Temporal Databases. In: Frank, A.U., Formentini, U., Campari, I. (eds.) GIS 1992. LNCS, vol. 639, pp. 22–64. Springer, Heidelberg (1992)Google Scholar
  19. Stroustrup, B.: The C++ Programming Language. Addison-Wesley, Reading (1991)Google Scholar
  20. Tomlin, C.D.: Digital Cartographic Modeling Techniques in Environmental Planning, Yale Graduate School, Division of Forestry and Environmental Studies (1983a)Google Scholar
  21. Tomlin, C.D.: A Map Algebra. Harvard Computer Graphics Conference, Cambridge, Mass (1983b)Google Scholar
  22. Tomlin, C.D.: Geographic Information Systems and Cartographic Modeling. Prentice Hall, New York (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Andrew U. Frank
    • 1
  1. 1.Dept. of Geoinformation and CartographyTechnical UniversityVienna

Personalised recommendations