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Computing Geomorphologically Salient Networks via Discrete Morse Theory

Authors Tim Ophelders , Anna Schenfisch , Willem Sonke , Bettina Speckmann

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • hydrology
  • network detection
  • intertidal zones
  • braided rivers
  • discrete Morse theory
  • volume persistence

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Abstract

Rivers, estuaries, intertidal zones, and other hydrological systems often give rise to complex networks of interconnected channels. Even today, such networks are typically drawn manually by domain experts. Traditional watershed methods for automating this process, where water flows are assumed to follow steepest descent, fail to capture behavior particular to low-relief terrains. At SoCG 2017, Kleinhans et al. proposed a method to construct a network of source-to-sink paths separated by sufficient sediment volume. However, this method is unstable with respect to minor changes of the input terrain, and constructs only channels that flow from one side of the terrain to the other, thereby failing to detect the dead-end channels ("fingers") that characterize intertidal zones.
We show how to compute geomorphologically salient networks that avoid these issues. After extending elevation data to a discrete Morse function on the terrain, we identify channels that flow through saddles and have sufficient volume of sediment on both sides. We then detect fingers, which follow the boundary of "spurs" that have sufficient volume of sediment above a particular height. The main challenge here lies in meaningfully modeling salient spurs and determining suitable heights to measure volume. We implemented our method and applied it to real-world data. Our expert users have validated the mathematical modeling by confirming that the resulting (finger) channels indeed constitute a geomorphologically salient network.

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Tim Ophelders, Anna Schenfisch, Willem Sonke, and Bettina Speckmann. Computing Geomorphologically Salient Networks via Discrete Morse Theory. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 70:1-70:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SoCG.2025.70

Author Details

Tim Ophelders
  • Utrecht University, The Netherlands
  • TU Eindhoven, The Netherlands
Anna Schenfisch
  • TU Eindhoven, The Netherlands
Willem Sonke
  • TU Eindhoven, The Netherlands
Bettina Speckmann
  • TU Eindhoven, The Netherlands

Funding

This work is part of the WadSED (https://wadsed.nl/) research program financed by the Dutch Research Council (NWO) under grant P21-13.
  • Ophelders, Tim: supported by the Dutch Research Council (NWO) under the project number VI.Veni.212.260.

Supplementary Materials

References

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