Advertisement

Medial Axis Approximation of River Networks for Catchment Area Delineation

  • Farid Karimipour
  • Mehran Ghandehari
  • Hugo Ledoux
Chapter
Part of the Lecture Notes in Geoinformation and Cartography book series (LNGC)

Abstract

The hydrological catchment areas are commonly extracted from digital elevation models (DEMs). The shortcoming is that computations for large areas are very time consuming and even may be impractical. Furthermore, the DEM may be inaccessible or in a poor quality. This chapter presents an algorithm to approximate the medial axis of river networks, which leads to catchment area delineation. We propose a modification to a Voronoi-based algorithm for medial axis extraction through labeling the sample points in order to automatically avoid appearing extraneous branches in the media axis. The proposed approach is used in a case study and the results are compared with a DEM-based method. The results illustrate that our method is stable, easy to implement and robust, even in the presence of significant noises and perturbations, and guarantees one polygon per catchment.

Keywords

Voronoi diagram Delaunay triangulation Medial axis River network Catchment area delineation 

References

  1. Martz LW, Garbrecht J (1993) Automated extraction of drainage network and watershed data from digital elevation models. JAWRA 29:901–908Google Scholar
  2. Turcotte R, Fortin JP, Rousseau A, Massicotte S, Villeneuve JP (2001) Determination of the drainage structure of a watershed using a digital elevation model and a digital river and lake network. J Hydrol 240:225–242CrossRefGoogle Scholar
  3. Chorowicz J, Ichoku C, Riazanoff S, Kim YJ, Cervelle B (1992) A combined algorithm for automated drainage network extraction. Water Resour Res 28:1293–1302CrossRefGoogle Scholar
  4. Martz LW, Garbrecht J (1992) Numerical definition of drainage network and subcatchment areas from digital elevation models. Comput Geosci 18:747–761CrossRefGoogle Scholar
  5. Mark DM (1984) Part 4: mathematical, algorithmic and data structure issues: automated detection of drainage networks from digital elevation models. cartographica. Int J Geogr Info Geovisualization 21:168–178 Google Scholar
  6. Tarboton DG (1997) A new method for the determination of flow directions and upslope areas in grid digital elevation models. Water Resour Res 33:309–319CrossRefGoogle Scholar
  7. Lin WT, Chou WC, Lin CY, Huang PH, Tsai JS (2006) Automated suitable drainage network extraction from digital elevation models in Taiwan’s upstream watersheds. Hydrol Process 20:289–306CrossRefGoogle Scholar
  8. Yang W, Hou K, Yu F, Liu Z, Sun T (2010) A novel algorithm with heuristic information for extracting drainage networks from Raster DEMs. Hydrol Earth Syst Sci Discuss 7:441–459CrossRefGoogle Scholar
  9. Nelson EJ et al (1994) Algorithm for precise drainage-basin delineation. J Hydraul Eng 120:298CrossRefGoogle Scholar
  10. Mower JE (1994) Data-parallel procedures for drainage basin analysis. Comput Geosci 20:1365–1378CrossRefGoogle Scholar
  11. Jones NL, Wright SG et al (1990) Watershed delineation with triangle-based terrain models. J Hydraul Eng 116:1232CrossRefGoogle Scholar
  12. Li Z, Zhu Q, Gold C (2005) Digital terrain modeling: principles and methodology. CRC Press, USAGoogle Scholar
  13. Gold C, Dakowicz M (2005) The crust and skeleton–applications in GIS. Second international symposium on Voronoi diagrams in science and engineering, pp 33–42Google Scholar
  14. Dillabaugh C (2002) Drainage basin delineation from vector drainage networks. Joint international symposium on geospatial theory, processing and applications, Ottawa, Ontario, CanadaGoogle Scholar
  15. McAllister M (1999) The computational geometry of hydrology data in geographic information system. PhD thesis, University of British Columbia Google Scholar
  16. Gold C, Snoeyink J (2001) A one-step crust and skeleton extraction algorithm. Algorithmica 30:144–163CrossRefGoogle Scholar
  17. Ledoux H (2006) Modelling three-dimensional fields in geo-science with the Voronoi diagram and its dual. PhD Thesis. School of Computing, University of Glamorgan, Pontypridd, Wales, UK Google Scholar
  18. Karimipour F, Delavar MR, Frank AU (2010) A simplex-based approach to implement dimension independent spatial analyses. Comput Geosci 36:1123–1134CrossRefGoogle Scholar
  19. Blum H et al (1967) A transformation for extracting new descriptors of shape. Models for the perception of speech and visual form 19, 362–380Google Scholar
  20. Amenta N, Bern MW, Eppstein D (1998) The crust and the beta-skeleton: combinatorial curve reconstruction. Graphical Models Image Process 60:125–135CrossRefGoogle Scholar
  21. Wenger R (2003) Shape and medial axis approximation from samples. PhD thesis. The Ohio State UniversityGoogle Scholar
  22. Siddiqi K, Bouix S, Tannenbaum A, Zucker SW (2002) Hamilton-Jacobi Skeletons. Int J Comput Vision 48:215–231CrossRefGoogle Scholar
  23. Attali D, Montanvert A (1996) Modeling noise for a better simplification of skeletons. In: IEEE international conference on image processing, vol 3. pp 13–16Google Scholar
  24. Attali D, di Baja G, Thiel E (1995) Pruning discrete and semicontinuous skeletons. In: Proceedings of the 8th international conference on image analysis and processing, vol 974. pp 488–493Google Scholar
  25. Chazal F, Lieutier A (2005) The Lambda Medial Axis. Graph Models 67:304–331CrossRefGoogle Scholar
  26. Attali D, Montanvert A (1994) Semicontinuous skeletons of 2D and 3D shapes. In: Proceedings of the second international workshop on visual form, pp 32–41Google Scholar
  27. Giesen J, Miklos B, Pauly M, Wormser C (2009) The scale axis transform. In: Proceedings of the 25th annual symposium on computational geometry, pp 106–115Google Scholar
  28. Karimipour F, Ghandehari M (2012) A stable Voronoi-based algorithm for medial axis extraction through labeling sample points. In: Proceedings of the 9th international symposium on Voronoi diagrams in science and engineering (ISVD 2012), New Jersey, USAGoogle Scholar
  29. Ghandehari M, Karimipour F (2012) Voronoi-based curve reconstruction: issues and solutions. The international conference on computational science and its applications (ICCSA 2012), Lecture notes in computer science (LNCS), vol 7334. pp 194–207. Springer, BrazilGoogle Scholar
  30. Giesen J, Miklos B, Pauly M (2007) Medial axis approximation of planar shapes from union of balls: a simpler and more robust algorithm. In: Proceedings of the 19th Canadian conference on computational geometry (CCCG), pp 105–108Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Farid Karimipour
    • 1
  • Mehran Ghandehari
    • 1
  • Hugo Ledoux
    • 2
  1. 1.Department of Surveying and Geomatics Engineering, College of EngineeringUniversity of TehranTehranIran
  2. 2.OTB, Section GIS TechnologyDelft University of TechnologyDelftThe Netherlands

Personalised recommendations