Fuzzy Representation of Special Terrain Features Using a Similarity-based Approach

  • Xun Shi
  • A-Xing Zhu
  • Rongxun Wang


Fuzzy representation of terrain positions can be useful in environmental modeling process, especially in soil-landscape studies. Existing methods for deriving this representation from a digital elevation model (DEM) are often neither effective nor efficient, especially when dealing with some special terrain positions that have only regional or local meanings. This paper presents a similarity-based method for deriving fuzzy representation of special terrain features. This method has two general steps. The first is to find the typical locations (cases) of a specified terrain position and assign full fuzzy membership to these typical locations. The typical locations can be identified in two ways: they can be located by using a set of simple rules based on the geomorphologic definition of the terrain position; or they can be pinpointed or delineated directly by experts using a GIS visualization tool. With the typical locations identified, the next step is to compute the similarities between these typical locations and other landscape locations, and the derived similarity values are then used to approximate the fuzzy memberships of those locations for being the terrain position. This process is applied to some special terrain features in two study areas: one in Wisconsin and the other in Tennessee. In the Wisconsin study area, this method is used to derive the fuzzy representations of broad ridge, narrow ridge, and headwater. In the Tennessee study area, this method is used to derive the fuzzy membership of being a “knob”. The resultant fuzzy representations are realistic and meaningful and the whole process is computationally efficient, which indicates that this similaritybased (cased-based) method can be an effective and flexible approach to deriving fuzzy representations of terrain features.


Digital Elevation Model Typical Location Slope Gradient Fuzzy Membership Test Location 
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.


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  1. Aamodt A, Plaza E (1994) Case-based reasoning: Foundational issues, methodological variations, and system approaches. AI Communications 7:39–52Google Scholar
  2. Aha DW (1997) Editorial. Artificial Intelligence Review 11:7–10CrossRefGoogle Scholar
  3. Burrough PA (1989) Fuzzy mathematical methods for soil survey and land evaluation. J Soil Science 40:477–492Google Scholar
  4. Burrough PA, MacMillan RA, van Deursen W (1992) Fuzzy classification methods for determining land suitability from soil profile observations and topography. J Soil Science 43:193–210Google Scholar
  5. Burt JE (2000) personal communication. Department of Geography, University of Wisconsin-Madison, Madison, WisconsinGoogle Scholar
  6. Conacher AJ, Dalrymple JB (1977) The nine unit landsurface model: an approach to pedogeomorphic research. Geoderma 18:1–54CrossRefGoogle Scholar
  7. Hole FD, Campbell JB (1985) Soil Landscape Analysis. Rowman & Allanheld, Totowa, NJ.Google Scholar
  8. Huggett RJ (1975) Soil landscape systems: a model of soil genesis. Geoderma 13:1–22CrossRefGoogle Scholar
  9. Irvin BJ, Ventura SJ, Slater BK (1996) Fuzzy and isodata classification of landform elements from digital terrain data in Pleasant Valley, Wisconsin. Geoderma 77:137–154Google Scholar
  10. Kandel A (1986) Fuzzy mathematical techniques with applications. Addison-Wesley, Boston, MAGoogle Scholar
  11. Kolodner J (1993) Case-Based Reasoning. Morgan Kaufmann Publishers, San Mateo, CAGoogle Scholar
  12. Lagacherie P, Legros JP, Burrough PA. (1995) A soil survey procedure using the knowledge of soil pattern established on a previously mapped reference area. Geoderma 65:283–301CrossRefGoogle Scholar
  13. Leake DB (1996) CBR in context: the present and future. In D.B. Leake (eds) Case-based reasoning: Experiences, lessons, and future directions. MIT Press, Cambridge, MA, pp 3–30Google Scholar
  14. MacMillan RA, Pettapiece WW, Nolan SC, Goddard TW (2000) A generic procedure for automatically segmenting landforms into landform elements using DEMs, heuristic rules and fuzzy logic. Fuzzy Sets and Systems 113:81–109CrossRefGoogle Scholar
  15. Medin DL, Dewey GI, Murphy TD (1983) Relationships between item and category learning: Evidence that abstraction is not automatic. J. of Experimental Psychology: Learning, Memory, and Cognition 9:607–625Google Scholar
  16. Miline G (1935) Some suggested units of classification and mapping particularly for East African soils. Soil Research 4:183–198Google Scholar
  17. O’Callaghan JF, Mark DM (1984) The extraction of drainage networks from digital elevation data: Computer Vision. Graphics and Image Processing 28:323–344Google Scholar
  18. Peucker TK, Douglas DH (1975) Detection of surface specific points by local parallel processing of discrete terrain elevation data. Computer graphics and Image Processing 4:375–387Google Scholar
  19. Pike RJ (1988) The geometric signature: Quantifying landslide-terrain types from digital elevation models. Mathematical Geology 20:491–510CrossRefGoogle Scholar
  20. Ruhe RV, Walker PH (1968) Hillslope models and soil formation, II: open systems. In: Transactions of the Ninth Congress of the International Soil Science Society, Adelaide, Australia, pp 551–560Google Scholar
  21. Skidmore AK (1990) Terrain position as mapped from a gridded digital elevation model. Int J Geographical Information Systems 4:33–49Google Scholar
  22. Smith JD, Minda JP (1998) Prototypes in the mist: The early epochs of category learning. J. of Experimental Psychology: Learning, Memory, and Cognition 24:1411–1436Google Scholar
  23. Troeh FR (1964) Landform parameters correlated to soil drainage. Soil Science Society of America Proceedings 28:808–812CrossRefGoogle Scholar
  24. Tribe A (1992a) Automated recognition of valley lines and drainage networks from grid digital elevation models: a review and a new method. J Hydrology 139:263–293CrossRefGoogle Scholar
  25. Tribe A (1992b) Problems in automated recognition of valley features from digital elevation models and a new method toward their resolution. Earth Surface Processes & Landforms 17:437–454CrossRefGoogle Scholar
  26. Ventura SJ, Irvin BJ (2000) Automated landform classification methods for soil-landscape studies. In: Wilson JP, Gallant JC (eds) Terrain analysis: Principles and applications. John Wiley & Son, New York, pp 267–294Google Scholar
  27. Watson I (1997) Applying case-based reasoning: Techniques for enterprise systems. Morgan Kaufman Publishers, San Mateo, CAGoogle Scholar
  28. Zhu AX, Band LE (1994) A knowledge-based approach to data integration for soil mapping. Can. J. Remote Sens. 20: 408–418Google Scholar
  29. Zhu AX, Hudson B, Burt JE and Lubich K (2001). Soil mapping using GIS, expert knowledge and fuzzy logic, Soil Science Society of America Journal, Vol. 65, pp. 1463–1472.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Xun Shi
    • 1
  • A-Xing Zhu
    • 2
    • 3
  • Rongxun Wang
    • 3
  1. 1.Geography DepartmentDartmouth CollegeHanoverUSA
  2. 2.State Key Laboratory of Resources and Environmental Information System, Institute of Geographical Sciences and Natural Resources ResearchChinese Academy of SciencesChina
  3. 3.Department of GeographyUniversity of Wisconsin-MadisonMadisonUSA

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