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Terrain Prickliness: Theoretical Grounds for High Complexity Viewsheds

Authors Ankush Acharyya, Ramesh K. Jallu, Maarten Löffler, Gert G.T. Meijer, Maria Saumell, Rodrigo I. Silveira, Frank Staals

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  • Theory of computation → Theory and algorithms for application domains
Keywords
  • Digital elevation model
  • Triangulated irregular network
  • Viewshed complexity

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Abstract

An important task in terrain analysis is computing viewsheds. A viewshed is the union of all the parts of the terrain that are visible from a given viewpoint or set of viewpoints. The complexity of a viewshed can vary significantly depending on the terrain topography and the viewpoint position.
In this work we study a new topographic attribute, the prickliness, that measures the number of local maxima in a terrain from all possible angles of view. We show that the prickliness effectively captures the potential of terrains to have high complexity viewsheds. We present near-optimal algorithms to compute it for TIN terrains, and efficient approximate algorithms for raster DEMs. We validate the usefulness of the prickliness attribute with experiments in a large set of real terrains.

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Ankush Acharyya, Ramesh K. Jallu, Maarten Löffler, Gert G.T. Meijer, Maria Saumell, Rodrigo I. Silveira, and Frank Staals. Terrain Prickliness: Theoretical Grounds for High Complexity Viewsheds. In 11th International Conference on Geographic Information Science (GIScience 2021) - Part II. Leibniz International Proceedings in Informatics (LIPIcs), Volume 208, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.GIScience.2021.II.10

Author Details

Ankush Acharyya
  • The Czech Academy of Sciences, Institute of Computer Science, Prague, Czech Republic
Ramesh K. Jallu
  • The Czech Academy of Sciences, Institute of Computer Science, Prague, Czech Republic
Maarten Löffler
  • Deptartment of Information and Computing Sciences, Utrecht University, The Netherlands
Gert G.T. Meijer
  • Academy of ICT and Creative Technologies, NHL Stenden University of Applied Sciences, The Netherlands
Maria Saumell
  • The Czech Academy of Sciences, Institute of Computer Science, Prague, Czech Republic
  • Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
Rodrigo I. Silveira
  • Department of Mathematics, Universitat Politècnica de Catalunya, Barcelona, Spain
Frank Staals
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands

Funding

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 734922. A. A., R. J., and M. S. were supported by the Czech Science Foundation, grant number GJ19-06792Y, and by institutional support RVO: 67985807. M. L. was partially supported by the Netherlands Organization for Scientific Research (NWO) under project no. 614.001.504. R. S. was supported by AEI, project PID2019-104129GB-I00/AEI/10.13039/501100011033, and Gen. Cat. DGR 2017SGR1640.

Acknowledgements

The authors would like to thank Jeff Phillips for a stimulating discussion that, years later, led to the notion of prickliness.

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References

  1. Brent C. Chamberlain and Michael J. Meitner. A route-based visibility analysis for landscape management. Landscape and Urban Planning, 111:13-24, 2013. Google Scholar
  2. Maria Danese, Gabriele Nolè, and Beniamino Murgante. Identifying viewshed: New approaches to visual impact assessment. In Geocomputation, Sustainability and Environmental Planning, pages 73-89. Springer, 2011. Google Scholar
  3. Mark de Berg, Herman Haverkort, and Constantinos P. Tsirogiannis. Visibility maps of realistic terrains have linear smoothed complexity. In Proceedings of the Twenty-Fifth Annual Symposium on Computational Geometry, pages 163-168. ACM, 2009. Google Scholar
  4. D J Dean. Improving the accuracy of forest viewsheds using triangulated networks and the visual permeability method. Canadian Journal of Forest Research, 27(7):969-977, 1997. Google Scholar
  5. Youfu Dong, Guoan Tang, and Ting Zhang. a Systematic Classification Research of Topographic Descriptive Attribute in Digital Terrain Analysis. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 37 B2:357-362, 2008. Google Scholar
  6. Herbert Edelsbrunner and Leonidas J. Guibas. Topologically sweeping an arrangement. Journal of Computer and System Sciences, 38(1):165-194, 1989. Google Scholar
  7. Environmental Systems Research Institute (ESRI). Arcgis pro (2.5.1), May 2020. Google Scholar
  8. Environmental Systems Research Institute (ESRI). Terrain, scale: 10m, February 2020. Google Scholar
  9. W. Randolph Franklin and Christian Vogt. Multiple observer siting on terrain with intervisibility or lo-res data. In XXth Congress, International Society for Photogrammetry and Remote Sensing, pages 12-23, 2004. Google Scholar
  10. Michael T. Goodrich. A polygonal approach to hidden-line and hidden-surface elimination. CVGIP: Graphical Models and Image Processing, 54(1):1-12, January 1992. Google Scholar
  11. Ferran Hurtado, Maarten Löffler, Inês Matos, Vera Sacristán, Maria Saumell, Rodrigo I. Silveira, and Frank Staals. Terrain visibility with multiple viewpoints. International Journal of Computational Geometry & Applications, 24(04):275-306, 2014. Google Scholar
  12. Frank Kammer, Maarten Löffler, Paul Mutser, and Frank Staals. Practical approaches to partially guarding a polyhedral terrain. In Proc. 8th International Conference on Geographic Information Science, LNCS 8728, pages 318-332, 2014. Google Scholar
  13. Young-Hoon Kim, Sanjay Rana, and Steve Wise. Exploring multiple viewshed analysis using terrain features and optimisation techniques. Computers & Geosciences, 30(9):1019-1032, 2004. Google Scholar
  14. Benoit B Mandelbrot. The fractal geometry of nature. W.H. Freeman, New York, 1982. Google Scholar
  15. J. J. Maynard and M. G. Johnson. Scale-dependency of LiDAR derived terrain attributes in quantitative soil-landscape modeling: Effects of grid resolution vs. neighborhood extent. Geoderma, 230-231:29-40, 2014. Google Scholar
  16. W. Henry McNab. Terrain shape index: Quantifying effect of minor landforms on tree height. Forest Science, 35:91-104, 1989. Google Scholar
  17. Gert Meijer. Realistic terrain features and the complexity of joint viewsheds. Master’s thesis, Utrecht University, 2020. Google Scholar
  18. Esther Moet, Marc van Kreveld, and A. Frank van der Stappen. On realistic terrains. Computational Geometry, 41(1):48-67, 2008. Google Scholar
  19. Philip D Riggs and Denis J Dean. An investigation into the causes of errors and inconsistencies in predicted viewsheds. Transactions in GIS, 11(2):175-196, 2007. Google Scholar
  20. Shawn J. Riley, Stephen D. DeGloria, and Robert Elliot. A terrain ruggedness index that quantifies topographic heterogeneity. Journal of Science, 5:23-27, 1999. Google Scholar
  21. Uta Schirpke, Erich Tasser, and Ulrike Tappeiner. Predicting scenic beauty of mountain regions. Landscape Urban Plan., 111:1-12, 2013. Google Scholar
  22. Hind Taud and Jean-François Parrot. Measurement of DEM roughness using the local fractal dimension. Géomorphologie : relief, processus, environnement, 11(4):327-338, 2005. Google Scholar
  23. The CGAL Project. CGAL User and Reference Manual. CGAL Editorial Board, 5.0.2 edition, 2020. Google Scholar
  24. Ron Wein, Eric Berberich, Efi Fogel, Dan Halperin, Michael Hemmer, Oren Salzman, and Baruch Zukerman. 2d arrangements. In CGAL User and Reference Manual. CGAL Editorial Board, 5.0.2 edition, 2020. Google Scholar
  25. Weihua Zhang and David R Montgomery. Digital elevation model grid size, landscape representation, and hydrologic simulations. Water Resources Research, 30(4):1019-1028, 1994. Google Scholar
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