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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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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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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

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.

Subject Classification

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

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