Abstract
In many applications of terrain analysis, pits or local minima are considered artifacts that must be removed before the terrain can be used. Most of the existing methods for local minima removal work only for raster terrains. In this paper we consider algorithms to remove local minima from polyhedral terrains, by modifying the heights of the vertices. To limit the changes introduced to the terrain, we try to minimize the total displacement of the vertices. Two approaches to remove local minima are analyzed: lifting vertices and lowering vertices. For the former we show that all local minima in a terrain with n vertices can be removed in the optimal way in 
time. For the latter we prove that the problem is NP-hard, and present an approximation algorithm with factor 2 ln k, where k is the number of local minima in the terrain.
This research has been partially funded by the Netherlands Organisation for Scientific Research (NWO) under the project GOGO.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Carr, H., Snoeyink, J., Axen, U.: Computing contour trees in all dimensions. Comput. Geom. Theory Appl. 24, 75–94 (2003)
Charleux-Demargne, J., Puech, C.: Quality assessment for drainage networks and watershed boundaries extraction from a digital elevation model. In: Proc. 8th ACM Symp. on Advances in GIS, pp. 89–94. ACM Press, New York (2000)
de Kok, T., van Kreveld, M., Löffler, M.: Generating realistic terrains with higher-order Delaunay triangulations. Comput. Geom. Th. Appl. 36, 52–65 (2007)
Freeman, H., Morse, S.P.: On searching a contour map for a given terrain profile. J. of the Franklin Institute 248, 1–25 (1967)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)
Gold, C., Cormack, S.: Spatially ordered networks and topographic reconstructions. In: Proc. 2nd Internat. Sympos. Spatial Data Handling, pp. 74–85 (1986)
Gudmundsson, J., Hammar, M., van Kreveld, M.: Higher order Delaunay triangulations. Comput. Geom. Theory Appl. 23, 85–98 (2002)
Guha, S., Khuller, S.: Improved methods for approximating node weighted steiner trees and connected dominating sets. Inform. Comput. 150, 57–74 (1999)
Klein, P., Ravi, R.: A nearly best-possible approximation algorithm for node-weighted steiner trees. J. Algorithms 19, 104–115 (1995)
Lindsay, J.B., Creed, I.F.: Removal of artifact depressions from digital elevation models: towards a minimum impact approach. Hydr. Proc. 19, 3113–3126 (2005)
Liu, Y., Snoeyink, J.: Flooding triangulated terrain. In: Proc. 11th Int. Symp. on Spatial Data Handling, pp. 137–148 (2004)
Mark, D.: Network models in geomorphology. In: Anderson, M.G. (ed.) Modelling Geomorphological Systems, ch. 4, pp. 73–97. John Wiley & Sons, West Sussex (1988)
Martz, L.W., Garbrecht, J.: An outlet breaching algorithm for the treatment of closed depressions in a raster dem. Comp. & Geosciences 25, 835–844 (1999)
Rieger, W.: A phenomenon-based approach to upslope contributing area and depressions in DEMs. Hydrological Processes 12, 857–872 (1998)
Shinagawa, Y., Kunii, T.L.: Constructing a Reeb graph automatically from cross sections. IEEE Comput. Graph. Appl. 11, 44–51 (1991)
Sircar, J.K., Cerbrian, J.A.: Application of image processing techniques to the automated labelling of raster digitized contours. In: Proc. 2nd Internat. Sympos. Spatial Data Handling, pp. 171–184 (1986)
Takahashi, S., Ikeda, T., Shinagawa, Y., Kunii, T.L., Ueda, M.: Algorithms for extracting correct critical points and constructing topological graphs from discrete geographical elevation data. In: Eurographics 1995, vol. 14, pp. C–181–C–192 (1995)
Temme, A., Schoorl, J., Veldkamp, A.: Algorithm for dealing with depressions in dynamic landscape evolution models. Comp. & Geosciences 32, 452–461 (2006)
Theobald, D., Goodchild, M.: Artifacts of tin-based surface flow modeling. In: Proc. GIS/LIS 1990, pp. 955–964 (1990)
van Kreveld, M., van Oostrum, R., Bajaj, C., Pascucci, V., Schikore, D.: Contour trees and small seed sets for isosurface generation. In: Rana, S. (ed.) Topological Data Structures for Surfaces, ch. 5, pp. 71–85. Wiley, New York (2004)
Zhu, Q., Tian, Y., Zhao, J.: An efficient depression processing algorithm for hydrologic analysis. Comp. & Geosciences 32, 615–623 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Silveira, R.I., van Oostrum, R. (2007). Flooding Countries and Destroying Dams. In: Dehne, F., Sack, JR., Zeh, N. (eds) Algorithms and Data Structures. WADS 2007. Lecture Notes in Computer Science, vol 4619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73951-7_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-73951-7_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73948-7
Online ISBN: 978-3-540-73951-7
eBook Packages: Computer ScienceComputer Science (R0)