skip to main content
10.1145/1811158.1811171acmconferencesArticle/Chapter ViewAbstractPublication PagesafrigraphConference Proceedingsconference-collections
research-article

Minimum spanning trees for valley and ridge characterization in digital elevation maps

Published: 21 June 2010 Publication History

Abstract

Texture synthesis employs neighbourhood matching to generate appropriate new content. Terrain synthesis has the added constraint that new content must be geographically plausible. The profile recognition and polygon breaking algorithm (PPA) [Chang et al. 1998] provides a robust mechanism for characterizing terrain as systems of valley and ridge lines in digital elevation maps. We exploit this to create a terrain characterization metric that is robust, efficient to compute and is sensitive to terrain properties.
Terrain regions are characterized as a minimum spanning tree derived from a graph created from the sample points of the elevation map which are encoded as weights in the edges of the graph. This formulation allows us to provide a single consistent feature definition that is sensitive to the pattern of ridges and valleys in the terrain Alternative formulations of these weights provide richer characteristic measures and we provide examples of alternate definitions based on curvature and contour measures.
We show that the measure is robust, with a significant portion derived directly from information local to the terrain sample. Global terrain characteristics introduce the issue of over- and under-connected valley/ridge lines when working with sub-regions. This is addressed by providing two graph construction strategies, which respectively provide an upper bound on connectivity as a single spanning tree, and a lower bound as a forest of trees.
Efficient minimum spanning tree algorithms are adapted to the context of terrain data and are shown to provide substantially better performance than previous PPA implementations. In particular, these are able to characterize valley and ridge behaviour at every point even in large elevation maps, providing a measure sensitive to terrain features at all scales.
The resulting graph based formulation provides an efficient and elegant algorithm for characterizing terrain features. The measure can be calculated efficiently, is robust under changes of neighbourhood position, size and resolution and the hybrid measure is sensitive to terrain features both locally and globally.

References

[1]
Bangay, S., and Morkel, C. 2006. Graph matching with subdivision surfaces for texture synthesis on surfaces. In AFRIGRAPH 2006: Proceedings of the 4th International Conference on Computer Graphics, Virtual Reality, Visualisation and Interaction in Africa, ACM Press.
[2]
Bazlamaçci, C. F., and Hindi, K. S. 2001. Minimum-weight spanning tree algorithms: A survey and empirical study. Computers & Operations Research 28, 8 (July), 767--785.
[3]
Chang, Y.-C., and Frigeri, A. 2002. Implementing the automatic extraction of ridge and valley axes using the PPA algorithm in Grass GIS. In Proceedings of the Open source GIS - GRASS users conference 2002.
[4]
Chang, Y.-C., and Sinha, G. 2007. A visual basic program for ridge axis picking on DEM data using the profile-recognition and polygon-breaking algorithm. Computers & Geosciences 33, 2, 229--237.
[5]
Chang, Y.-C., Song, G.-S., and Hsu, S.-K. 1998. Automatic extraction of ridge and valley axes using the profile recognition and polygon-breaking algorithm. Computers & Geosciences 24, 1, 83--93.
[6]
Cormen, T. H., Leiserson, C. E., Rivest, R. L., and Stein, C. 2001. Introduction to Algorithms, second ed. The MIT Press, London, UK.
[7]
Efros, A. A., and Leung, T. K. 1999. Texture synthesis by non-parametric sampling. In Proceedings of IEEE International Conference on Computer Vision (ICCV'99), 1033--1038.
[8]
Gulgen, F., and Gokgoz, T. 2004. Automatic extraction of terrain skeleton lines from digital elevation models. In Proceedings of ISPRS 2004: the XXth ISPRS congress: Geo-imagery bridging continents.
[9]
Kruskal, Jr., J. B. 1956. On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical Society 7, 1 (February), 48--50.
[10]
Kweon, I. S., and Kanade, T. 1994. Extracting topographic terrain features from elevation maps. CVGIP: Image Understanding 59, 2 (March), 171--182.
[11]
Lefebvre, S., and Hoppe, H. 2005. Parallel controllable texture synthesis. ACM Transactions on Graphics 24, 3, 777--786.
[12]
Little, J. J., and Shi, P. 2001. Structural lines, TINs, and DEMs. Algorithmica 30, 2 (December), 243--263.
[13]
Ohtake, Y., Belyaev, A., and Seidel, H.-P. 2004. Ridge-valley lines on meshes via implicit surface fitting. ACM Transactions on Graphics 23, 3, 609--612.
[14]
Tribe, A. 1992. Automated recognition of valley lines and drainage networks from grid digital elevation models: a review and a new method. Journal of Hydrology 139, 1--4 (November), 263--293.
[15]
Wei, L.-Y., and Levoy, M. 2000. Fast texture synthesis using tree-structured vector quantization. In Proceedings of ACM SIGGRAPH 2000, ACM Press/Addison-Wesley Publishing Co., 479--488.
[16]
Wei, L.-Y., Lefebvre, S., Kwatra, V., and Turk, G. 2009. State of the art in example-based texture synthesis. In Eurographics 2009, State of the Art Report, EG-STAR, Eurographics Association.
[17]
Zhou, H., Sun, J., Turk, G., and Rehg, J. M. 2007. Terrain synthesis from digital elevation models. IEEE Transactions on Visualization and Computer Graphics 13, 4, 834--848.

Cited By

View all
  • (2020)First Person Sketch-based Terrain EditingGraphics Interface 201410.1201/9781003059325-28(217-224)Online publication date: 30-Oct-2020
  • (2019)Universal features of mountain ridge networks on EarthJournal of Complex Networks10.1093/comnet/cnz017Online publication date: 6-May-2019
  • (2014)First person sketch-based terrain editingProceedings of Graphics Interface 201410.5555/2619648.2619684(217-224)Online publication date: 7-May-2014
  • Show More Cited By

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences
AFRIGRAPH '10: Proceedings of the 7th International Conference on Computer Graphics, Virtual Reality, Visualisation and Interaction in Africa
June 2010
153 pages
ISBN:9781450301183
DOI:10.1145/1811158
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 21 June 2010

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. DEM
  2. graph
  3. line
  4. minimum spanning tree
  5. ridge

Qualifiers

  • Research-article

Conference

AFRIGRAPH '10
Sponsor:

Acceptance Rates

Overall Acceptance Rate 47 of 90 submissions, 52%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)9
  • Downloads (Last 6 weeks)0
Reflects downloads up to 16 Feb 2025

Other Metrics

Citations

Cited By

View all
  • (2020)First Person Sketch-based Terrain EditingGraphics Interface 201410.1201/9781003059325-28(217-224)Online publication date: 30-Oct-2020
  • (2019)Universal features of mountain ridge networks on EarthJournal of Complex Networks10.1093/comnet/cnz017Online publication date: 6-May-2019
  • (2014)First person sketch-based terrain editingProceedings of Graphics Interface 201410.5555/2619648.2619684(217-224)Online publication date: 7-May-2014
  • (2014)Feature-based terrain editing from complex sketchesComputers and Graphics10.1016/j.cag.2014.09.00145:C(101-115)Online publication date: 1-Dec-2014
  • (2012)Enhanced Texture-Based Terrain Synthesis on Graphics HardwareComputer Graphics Forum10.1111/j.1467-8659.2012.03076.x31:6(1959-1972)Online publication date: 1-Sep-2012

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media