Skip to main content
SpringerLink
Log in

Triangulation of Gradient Polygons: A Spatial Data Model for Categorical Fields

  • Conference paper
Spatial Information Theory (COSIT 2007)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 4736))

Included in the following conference series:

  • 1393 Accesses

Abstract

The concept of the categorical gradient field is introduced to encompass spatially continuous fields of probabilities or membership values in a fixed number of categories. Three models for implementing categorical gradient fields are examined: raster grids, epsilon bands and gradient polygons. Of these, the gradient polygon model shows promise but has not been fully specified. A specification of the model is developed via a four-step process: 1) the constrained Delaunay triangulation of the polygon is created, 2) vertices are added to the polygon edge to ensure consistency, 3) a skeleton of the medial axis is produced and flat spurs are identified, and 4) additional vertices are added along each flat spur. The method is illustrated on a hypothetical transition zone between four adjacent regions, and evaluated according to five general criteria. The model is efficient in terms of data storage, moderately flexible and robust, and intuitive to build and visualize.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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.

Similar content being viewed by others

References

  1. Amenta, N., Bern, M., Eppstein, D.: The crust and the (-skeleton: Combinatorial curve reconstruction. Graphical Models and Image Processing 60(2), 125–135 (1998)

    Article  Google Scholar 

  2. Bailey, R.G.: Ecoregions: the ecosystem geography of the oceans and continents. Text volume (176 pp.) and two folded maps. Springer, New York (1998)

    Google Scholar 

  3. Bailey, R.G.: Identifying ecoregion boundaries. Environmental Management 34(1), S14–S26 (2005)

    Article  Google Scholar 

  4. Bennett, B.: Introduction to special issue on spatial vagueness, uncertainty and granularity. Spatial Cognition and Computation 3(2/3), 93–96 (2003)

    Google Scholar 

  5. Bittner, T., Smith, B.: Vague reference and approximating judgements. Spatial Cognition and Computation 3(2/3), 137–156 (2003)

    Google Scholar 

  6. Burrough, P.A.: Natural objects with indeterminate boundaries. In: Burrough, P.A., Frank, A.U. (eds.) Geographic Objects with Indeterminate Boundaries, Taylor & Francis, London (1996)

    Google Scholar 

  7. Burrough, P.A., Frank, A.U.: Geographic Objects with Indeterminate Boundaries. Taylor & Francis, London (1996)

    Google Scholar 

  8. Castilla, G., Hay, G.J.: Uncertainties in land use data. Hydrology and Earth System Science Discussions 3, 3439–3472 (2006)

    Article  Google Scholar 

  9. Cohn, A.G., Gotts, N.M.: The ‘egg-yolk’ representation of regions with indeterminate boundaries. In: Burrough, P.A., Frank, A.U. (eds.) Geographic Objects with Indeterminate Boundaries, pp. 171–187. Taylor & Francis, London (1996)

    Google Scholar 

  10. Equihua, M.: Fuzzy clustering of ecological data. Journal of Ecology 78, 519–534 (1990)

    Article  Google Scholar 

  11. Fisher, P.F.: Sorites paradox and vague geographies. Fuzzy Sets and Systems 113(1), 7–18 (2000)

    Article  Google Scholar 

  12. Foody, G.M.: A fuzzy sets approach to the representation of vegetation continua from remotely sensed data: An example from lowland heath. Photogrammetric Engineering and Remote Sensing. 58, 221–225 (1992)

    Google Scholar 

  13. Goodchild, M.F., Chih-chang, L., Leung, Y.: Visualizing fuzzy maps. In: Hearnshaw, H., Unwin, D. (eds.) Visualization in Geographical Information Systems, John Wiley and Sons, New York (1994)

    Google Scholar 

  14. Goodchild, M.F.: Introduction: Special issue on Uncertainty in geographic information systems. Fuzzy Sets and Systems 113, 3–5 (2000)

    Article  Google Scholar 

  15. Hengl, T., Walvoort, D.J.J., Brown, A., Rossiter, D.G.: A double continuous approach to visualization and analysis of categorical maps. International Journal of Geographical Information Science 18, 183–202 (2004)

    Article  Google Scholar 

  16. Kronenfeld, B.J., Mark, D.M., Smith, B.: Gradation and Objects with Indeterminate Boundaries. Short-term research priority, University Consortium for Geographic Information Science (UCGIS) (2002)

    Google Scholar 

  17. Kronenfeld, B.J.: Implications of a data reduction framework for assignment of fuzzy membership values in continuous class maps. Spatial Cognition and Computation 3(2/3), 221–238 (2003)

    Google Scholar 

  18. Kronenfeld, B.J.: Incorporating gradation as a communication device in area-class maps. Cartography and Geographic Information Science 32(4), 231–241 (2005)

    Article  Google Scholar 

  19. Kronenfeld, B.J.: Gradation and map analysis in area-class maps. In: Mark, D.M., Cohn, A.G. (eds.) Proceedings of the Conference on Spatial Information Theory (COSIT), Ellicottville, NY, USA, Springer, Berlin (2005)

    Google Scholar 

  20. Leung, Y., Yan, Y.: A Locational Error Model for Spatial Features. International Journal of Geographical Information Science 12(6), 607–620 (1998)

    Article  Google Scholar 

  21. McBratney, A.B., Moore, A.W.: Application of fuzzy sets to climatic classification. Agricultural and Forest Meteorology 35, 165–185 (1985)

    Article  Google Scholar 

  22. McBratney, A.B., Odeh, I.O.A.: Applications of fuzzy sets in soil science: fuzzy logic, fuzzy measurements and fuzzy decisions. Geoderma 77, 85–113 (1997)

    Article  Google Scholar 

  23. Peuquet, D.J., Smith, B., Brogaard, B.: The ontology of fields: Report of a specialist meeting held under the auspices of the Varenius Project. Santa Barbara: National Center for Geographic Information and Analysis (1998)

    Google Scholar 

  24. Risser, P.G.: The status of the science examining ecotones. Bioscience 45(5), 318–325 (1994)

    Article  Google Scholar 

  25. Robinson, V.B.: A perspective on the fundamentals of fuzzy sets and their use in geographic information systems. Transactions in GIS 7(1), 3–30 (2003)

    Article  Google Scholar 

  26. Rosch, E.: Principles of categorization. In: Rosch, E., Lloyd, B.B. (eds.) Cognition and Categorization, Lawrence Erlbaum Associates, Hillsdale, NJ (1978)

    Google Scholar 

  27. Thibault, D., Gold, C.M.: Terrain reconstruction from contours by skeleton reconstruction. GeoInformatica 4, 349–373 (2000)

    Article  MATH  Google Scholar 

  28. Usery, E.L.: A conceptual framework and fuzzy set implementation for geographic features. In: Burrough, P.A., Frank, A.U. (eds.) Geographic Objects with Indeterminate Boundaries, pp. 71–85. Taylor & Francis, London (1996)

    Google Scholar 

  29. Varzi, A.C.: Vagueness in geography. Philosophy & Geography 4(1), 49–65 (2001)

    Article  Google Scholar 

  30. Walter, H., Harnickell, E., Mueller-Dombois, D.: Climate-diagram maps of the individual continents and the ecological climatic regions of the earth. Text volume (Vegetation Monographs; 36 pp.) and 9 folded maps issued together in a case. Springer, Berlin (1975)

    Google Scholar 

  31. Zadeh, I.: Fuzzy Sets. Information and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  32. Zhang, J., Stuart, N.: Fuzzy methods for categorical mapping with image-based land cover data. International Journal of Geographical Information Science 15(2), 175–195 (2001)

    Article  Google Scholar 

  33. Zhang, L., Liu, C., Davis, C.J., Solomon, D.S., Brann, T.B., Caldwell, L.E.: Fuzzy classification of ecological habitats from FIA data. Forest Science 50(1), 117–127 (2004)

    Google Scholar 

  34. Zhu, A.: A similarity model for representing soil spatial information. Geoderma 77, 217–242 (1997)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geography, George Mason University, 4400 University Drive, MS 1E2, Fairfax, VA, USA

    Barry J. Kronenfeld

Authors
  1. Barry J. Kronenfeld
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Stephan Winter Matt Duckham Lars Kulik Ben Kuipers

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kronenfeld, B.J. (2007). Triangulation of Gradient Polygons: A Spatial Data Model for Categorical Fields. In: Winter, S., Duckham, M., Kulik, L., Kuipers, B. (eds) Spatial Information Theory. COSIT 2007. Lecture Notes in Computer Science, vol 4736. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74788-8_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-74788-8_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74786-4

  • Online ISBN: 978-3-540-74788-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation