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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Martz LW, Garbrecht J (1993) Automated extraction of drainage network and watershed data from digital elevation models. JAWRA 29:901–908
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 240:225–242
Chorowicz J, Ichoku C, Riazanoff S, Kim YJ, Cervelle B (1992) A combined algorithm for automated drainage network extraction. Water Resour Res 28:1293–1302
Martz LW, Garbrecht J (1992) Numerical definition of drainage network and subcatchment areas from digital elevation models. Comput Geosci 18:747–761
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
Tarboton DG (1997) A new method for the determination of flow directions and upslope areas in grid digital elevation models. Water Resour Res 33:309–319
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 20:289–306
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 7:441–459
Nelson EJ et al (1994) Algorithm for precise drainage-basin delineation. J Hydraul Eng 120:298
Mower JE (1994) Data-parallel procedures for drainage basin analysis. Comput Geosci 20:1365–1378
Jones NL, Wright SG et al (1990) Watershed delineation with triangle-based terrain models. J Hydraul Eng 116:1232
Li Z, Zhu Q, Gold C (2005) Digital terrain modeling: principles and methodology. CRC Press, USA
Gold C, Dakowicz M (2005) The crust and skeleton–applications in GIS. Second international symposium on Voronoi diagrams in science and engineering, pp 33–42
Dillabaugh C (2002) Drainage basin delineation from vector drainage networks. Joint international symposium on geospatial theory, processing and applications, Ottawa, Ontario, Canada
McAllister M (1999) The computational geometry of hydrology data in geographic information system. PhD thesis, University of British Columbia
Gold C, Snoeyink J (2001) A one-step crust and skeleton extraction algorithm. Algorithmica 30:144–163
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
Karimipour F, Delavar MR, Frank AU (2010) A simplex-based approach to implement dimension independent spatial analyses. Comput Geosci 36:1123–1134
Blum H et al (1967) A transformation for extracting new descriptors of shape. Models for the perception of speech and visual form 19, 362–380
Amenta N, Bern MW, Eppstein D (1998) The crust and the beta-skeleton: combinatorial curve reconstruction. Graphical Models Image Process 60:125–135
Wenger R (2003) Shape and medial axis approximation from samples. PhD thesis. The Ohio State University
Siddiqi K, Bouix S, Tannenbaum A, Zucker SW (2002) Hamilton-Jacobi Skeletons. Int J Comput Vision 48:215–231
Attali D, Montanvert A (1996) Modeling noise for a better simplification of skeletons. In: IEEE international conference on image processing, vol 3. pp 13–16
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 488–493
Chazal F, Lieutier A (2005) The Lambda Medial Axis. Graph Models 67:304–331
Attali D, Montanvert A (1994) Semicontinuous skeletons of 2D and 3D shapes. In: Proceedings of the second international workshop on visual form, pp 32–41
Giesen J, Miklos B, Pauly M, Wormser C (2009) The scale axis transform. In: Proceedings of the 25th annual symposium on computational geometry, pp 106–115
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, USA
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, Brazil
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 105–108
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Karimipour, F., Ghandehari, M., Ledoux, H. (2013). Medial Axis Approximation of River Networks for Catchment Area Delineation. In: Abdul Rahman, A., Boguslawski, P., Gold, C., Said, M. (eds) Developments in Multidimensional Spatial Data Models. Lecture Notes in Geoinformation and Cartography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36379-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-36379-5_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36378-8
Online ISBN: 978-3-642-36379-5
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)