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Contour trees of uncertain terrains

Authors:

Pankaj K. Agarwal,

Sayan MukherjeeAuthors Info & Claims

SIGSPATIAL '15: Proceedings of the 23rd SIGSPATIAL International Conference on Advances in Geographic Information Systems

Article No.: 43, Pages 1 - 10

https://doi.org/10.1145/2820783.2820823

Published: 03 November 2015 Publication History

Abstract

We study contour trees of terrains, which encode the topological changes of the level set of the height value ℓ as we raise ℓ from -∞ to +∞ on the terrains, in the presence of uncertainty in data. We assume that the terrain is represented by a piecewise-linear height function over a planar triangulation M, by specifying the height of each vertex. We study the case when M is fixed and the uncertainty lies in the height of each vertex in the triangulation, which is described by a probability distribution. We present efficient sampling-based Monte Carlo methods for estimating, with high probability, (i) the probability that two points lie on the same edge of the contour tree, within additive error; (ii) the expected distance of two points p, q and the probability that the distance of p, q is at least ℓ on the contour tree, within additive error, where the distance of p, q on a contour tree is defined to be the difference between the maximum height and the minimum height on the unique path from p to q on the contour tree. The main technical contribution of the paper is to prove that a small number of samples are sufficient to estimate these quantities. We present two applications of these algorithms, and also some experimental results to demonstrate the effectiveness of our approach.

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Cited By

Vietinghoff DBöttinger MScheuermann GHeine C(2023)A Mathematical Foundation for the Spatial Uncertainty of Critical Points in Probabilistic Scalar Fields2023 Topological Data Analysis and Visualization (TopoInVis)10.1109/TopoInVis60193.2023.00010(30-40)Online publication date: 22-Oct-2023
https://doi.org/10.1109/TopoInVis60193.2023.00010
Athawale TMaljovec DYan LJohnson CPascucci VWang B(2022)Uncertainty Visualization of 2D Morse Complex Ensembles Using Statistical Summary MapsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2020.302235928:4(1955-1966)Online publication date: 1-Apr-2022
https://doi.org/10.1109/TVCG.2020.3022359
Bujack RYan LHotz IGarth CWang B(2020)State of the Art in Time‐Dependent Flow Topology: Interpreting Physical Meaningfulness Through Mathematical PropertiesComputer Graphics Forum10.1111/cgf.1403739:3(811-835)Online publication date: 18-Jul-2020
https://doi.org/10.1111/cgf.14037
Show More Cited By

Index Terms

Contour trees of uncertain terrains
1. Information systems
  1. Information retrieval
    1. Document representation
    2. Search engine architectures and scalability
      1. Search engine indexing
2. Theory of computation
  1. Design and analysis of algorithms

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Published In

cover image ACM Conferences

SIGSPATIAL '15: Proceedings of the 23rd SIGSPATIAL International Conference on Advances in Geographic Information Systems

November 2015

646 pages

ISBN:9781450339674

DOI:10.1145/2820783

General Chairs:
Mohamed Ali
University of Washington, Tacoma
,
Yan Huang
University of North Texas
,
Program Chairs:
Michael Gertz
Heidelberg University, Germany
,
Matthias Renz
LMU Munich, Germany
,
Jagan Sankaranarayanan
NEC Labs

Copyright © 2015 ACM.

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]

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SIGSPATIAL: ACM Special Interest Group on Spatial Information

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SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 03 November 2015

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SIGSPATIAL'15: 23rd SIGSPATIAL International Conference on Advances in Geographic Information Systems

November 3 - 6, 2015

Washington, Seattle

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SIGSPATIAL '15 Paper Acceptance Rate 38 of 212 submissions, 18%;

Overall Acceptance Rate 220 of 1,116 submissions, 20%

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Cited By

Vietinghoff DBöttinger MScheuermann GHeine C(2023)A Mathematical Foundation for the Spatial Uncertainty of Critical Points in Probabilistic Scalar Fields2023 Topological Data Analysis and Visualization (TopoInVis)10.1109/TopoInVis60193.2023.00010(30-40)Online publication date: 22-Oct-2023
https://doi.org/10.1109/TopoInVis60193.2023.00010
Athawale TMaljovec DYan LJohnson CPascucci VWang B(2022)Uncertainty Visualization of 2D Morse Complex Ensembles Using Statistical Summary MapsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2020.302235928:4(1955-1966)Online publication date: 1-Apr-2022
https://doi.org/10.1109/TVCG.2020.3022359
Bujack RYan LHotz IGarth CWang B(2020)State of the Art in Time‐Dependent Flow Topology: Interpreting Physical Meaningfulness Through Mathematical PropertiesComputer Graphics Forum10.1111/cgf.1403739:3(811-835)Online publication date: 18-Jul-2020
https://doi.org/10.1111/cgf.14037
Rav MLowe AAgarwal P(2019)Flood Risk Analysis on TerrainsACM Transactions on Spatial Algorithms and Systems10.1145/32954595:1(1-31)Online publication date: 5-Jun-2019
https://dl.acm.org/doi/10.1145/3295459
Yan LWang YMunch EGasparovic EWang B(2019)A Structural Average of Labeled Merge Trees for Uncertainty VisualizationIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2019.2934242(1-1)Online publication date: 2019
https://doi.org/10.1109/TVCG.2019.2934242
Rav MLowe AAgarwal P(2017)Flood Risk Analysis on TerrainsProceedings of the 25th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems10.1145/3139958.3139985(1-10)Online publication date: 7-Nov-2017
https://dl.acm.org/doi/10.1145/3139958.3139985
Heine CLeitte HHlawitschka MIuricich FDe Floriani LScheuermann GHagen HGarth C(2016)A Survey of Topology-based Methods in VisualizationComputer Graphics Forum10.5555/3071534.307159335:3(643-667)Online publication date: 1-Jun-2016
https://dl.acm.org/doi/10.5555/3071534.3071593
Heine CLeitte HHlawitschka MIuricich FDe Floriani LScheuermann GHagen HGarth C(2016)A Survey of Topology‐based Methods in VisualizationComputer Graphics Forum10.1111/cgf.1293335:3(643-667)Online publication date: 4-Jul-2016
https://doi.org/10.1111/cgf.12933

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