Skip to main content
SpringerLink
Log in

Map Algebraic Characterization of Self-adapting Neighborhoods

  • Conference paper
Spatial Information Theory (COSIT 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5756))

Included in the following conference series:

Abstract

A class of map algebraic operations referred to as “focal” characterizes every location as a function of the geometry and/or attribute of all locations that belong to the “neighborhood” of that location. This paper introduces a new type of map algebraic neighborhood whose shape is unspecified but required to have a specified size. This paper explores how the use of such neighborhoods affects the design of focal operations, as well as their implementation and application. It is suggested that the proposed operations can contribute to site selection analyses, which are often subject to size restriction (e.g. due to limited budgets or environmental concerns), but needs more theoretical investigation for them to be fully operational in practice.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aerts, J.C.J.H., Heuvelink, G.B.M.: Using simulated annealing for resource allocation. International Journal of Geographical Information Science 16, 571–587 (2002)

    Article  Google Scholar 

  2. Benabdallah, S., Wright, J.R.: Shape considerations in spatial optimization. Civil Engineering Systems 8, 145–152 (1991)

    Article  Google Scholar 

  3. Benabdallah, S., Wright, J.R.: Multiple subregion allocation models. ASCE Journal of Urban Planning and Development 118, 24–40 (1992)

    Article  Google Scholar 

  4. Brookes, C.J.: A parameterized region-growing programme for site allocation on raster suitability maps. International Journal of Geographical Information Science 11, 375–396 (1997)

    Article  Google Scholar 

  5. Bruns, T., Egenhofer, M.: User Interfaces for Map Algebra. Journal of the Urban and Regional Information Systems Association 9(1), 44–54 (1997)

    Google Scholar 

  6. Burrough, P.A., McDonnell, R.A.: Principles of Geographical Information Systems, 2nd edn. Oxford Press, Oxford (1998)

    Google Scholar 

  7. Cerdeira, J.O., Gaston, K.J., Pinto, L.S.: Connectivity in priority area selection for conservation. Environmental Modeling and Assessment 10(3), 183–192 (2005)

    Article  Google Scholar 

  8. Church, R.L., Gerrard, R.A., Gilpin, M., Sine, P.: Constructing Cell-Based Habitat Patches Useful in Conservation Planning. Annals of the Association of American Geographers 93, 814–827 (2003)

    Article  Google Scholar 

  9. Cova, T.J., Church, R.L.: Contiguity Constraints for Single-Region Site Search Problems. Geographical Analysis 32, 306–329 (2000)

    Article  Google Scholar 

  10. Cova, T.J., Goodchild, M.F.: Extending geographical representation to include fields of spatial objects. International Journal of Geographical Information Science 16, 509–532 (2002)

    Article  Google Scholar 

  11. Diamond, J.T., Wright, J.R.: Design of an integrated spatial information system for multiobjective land-use planning. Environment and Planning B 15, 205–214 (1988)

    Article  Google Scholar 

  12. Dorenbeck, C., Egenhofer, M.: Algebraic Optimization of Combined Overlay Operations. In: Mark, D., White, D. (eds.) AutoCarto 10: Technical papers of the 1991 ACSM-ASPRS annual convention, Baltimore, Maryland, USA, pp. 296–312 (1991)

    Google Scholar 

  13. Egenhofer, M.J., Bruns, H.T.: Visual map algebra: a direct-manipulation user interface for GIS. In: Proceedings of the third IFIP 2.6 Working Conference on Visual Database Systems, Lausanne, Switzerland, pp. 235–253 (1995)

    Google Scholar 

  14. Frank, A.U.: Map Algebra Extended with Functors for Temporal Data. In: Akoka, J., Liddle, S.W., Song, I.-Y., Bertolotto, M., Comyn-Wattiau, I., van den Heuvel, W.-J., Kolp, M., Trujillo, J., Kop, C., Mayr, H.C. (eds.) ER Workshops 2005. LNCS, vol. 3770, pp. 194–207. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  15. Fischer, D., Church, R.L.: Clustering and Compactness in Reserve Site Selection: an Extension of the Biodiversity Management Area Selection Model. Forest Science 49, 555–565 (2003)

    Google Scholar 

  16. Gilbert, K.C., Holmes, D.D., Rosenthal, R.E.: A multiobjective discrete optimization model for land allocation. Management Science 31, 1509–1522 (1985)

    Article  Google Scholar 

  17. Heuvelink, G.B.M.: Error Propagation in Environmental Modelling with GIS. Taylor & Francis, London (1998)

    Google Scholar 

  18. Heuvelink, G.B.M., Burrough, P.A., Stein, A.: Propagation of errors in spatial modelling with GIS. International Journal of Geographical Information Systems 3, 303–322 (1989)

    Article  Google Scholar 

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

    Article  Google Scholar 

  20. Li, X., Hodgson, M.E.: Data model and operations for vector fields. Geographic Information Sciences and Remote Sensing 41(1), 1–24 (2004)

    Google Scholar 

  21. Mcdonnell, M.D., Possingham, H.P., Ball, I.R., Cousins, E.A.: Mathematical Methods for Spatially Cohesive Reserve Design. Environmental Modeling and Assessment 7, 107–114 (2002)

    Article  Google Scholar 

  22. Mennis, J., Viger, R., Tomlin, C.D.: Cubic Map Algebra Functions or Spatio-Temporal Analysis. Cartography and Geographic Information Science 32(1), 17–32 (2005)

    Article  Google Scholar 

  23. Nalle, D.J., Arthur, J.L., Sessions, J.: Designing Compact and Contiguous Reserve Networks with a Hybrid Heuristic Algorithm. Forest Science 48, 59–68 (2003)

    Google Scholar 

  24. Önal, H., Briers, R.A.: Incorporating Spatial Criteria in Optimum Reserve Network Selection. In: Proceedings of the Royal Society of London: Biological Sciences, vol. 269, pp. 2437–2441 (2002)

    Google Scholar 

  25. Önal, H., Briers, R.A.: Designing a conservation reserve network with minimal fragmentation: A linear integer programming approach. Environmental Modeling and Assessment 10(3), 193–202 (2005)

    Article  Google Scholar 

  26. Önal, H., Wang, Y.: A Graph Theory Approach for Designing Conservation Reserve Networks with Minimum Fragmentation. Networks 51(2), 142–152 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  27. Roy, A.J., Stell, A.J.: A qualitative account of discrete space. In: Egenhofer, M.J., Mark, D.M. (eds.) GIScience 2002. LNCS, vol. 2478, pp. 276–290. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  28. Shirabe, T.: Modeling Topological Properties of a Raster Region for Spatial Optimization. In: Fisher, P. (ed.) Developments in Spatial Data Handling: Proceedings of the 11th International Symposium on Spatial Data Handling, pp. 407–420. Springer, Heidelberg (2004)

    Google Scholar 

  29. Shirabe, T.: A Model of Contiguity for Spatial Unit Allocation. Geographical Analysis 37, 2–16 (2005)

    Article  Google Scholar 

  30. Takeyama, M.: Geo-Algebra: A mathematical approach to integrating spatial modeling and GIS. Ph.D. dissertation, Department of Geography, University of California at Santa Barbara (1996)

    Google Scholar 

  31. Takeyama, M., Couclelis, H.: Map dynamics: integrating cellular automata and GIS through Geo-Algebra. International Journal of Geographical Information Science 11, 73–91 (1997)

    Article  Google Scholar 

  32. Tomlin, C.D.: Geographic information systems and cartographic modeling. Prentice-Hall, Englewood Cliffs (1990)

    Google Scholar 

  33. Tomlin, C.D.: Map algebra: one perspective, Landscape and Urban Planning 30, 3–12 (1994)

    Google Scholar 

  34. Williams, J.C.: A Zero-One Programming Model for Contiguous Land Acquisition. Geographical Analysis 34, 330–349 (2002)

    Article  Google Scholar 

  35. Winter, S.: Topological relations between discrete regions. In: Egenhofer, M.J., Herring, J.R. (eds.) SSD 1995. LNCS, vol. 951, pp. 310–327. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  36. Winter, S., Frank, A.U.: Topology in raster and vector representation. Geoinformatica 4, 35–65 (2000)

    Article  MATH  Google Scholar 

  37. Wright, J., Revelle, C., Cohon, J.: A multipleobjective integer programming model for the land acquisition problem. Regional Science and Urban Economics 13, 31–53 (1983)

    Article  Google Scholar 

  38. Xiao, N.: An evolutionary algorithm for site search problems. Geographical Analysis 38, 227–247 (2006)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geoinformation and Cartography, Vienna University of Technology, 1040, Vienna, Austria

    Takeshi Shirabe

Authors
  1. Takeshi Shirabe
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Geography, University of Iowa, 316 Jessup Hall, 52242, Iowa City, IA, USA

    Kathleen Stewart Hornsby

  2. Naval Academy Research Institute, 29240, Brest Naval, France

    Christophe Claramunt

  3. Groupe Cognition Humaine, LIMSI-CNRS, Université de Paris-Sud, 91403, Orsay, France

    Michel Denis

  4. LIMSI-CNRS, Université de Paris-Sud, 91403, Orsay, France

    Gérard Ligozat

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Shirabe, T. (2009). Map Algebraic Characterization of Self-adapting Neighborhoods. In: Hornsby, K.S., Claramunt, C., Denis, M., Ligozat, G. (eds) Spatial Information Theory. COSIT 2009. Lecture Notes in Computer Science, vol 5756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03832-7_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03832-7_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03831-0

  • Online ISBN: 978-3-642-03832-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation