[go: up one dir, main page]
Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Computer Science > Computational Geometry

arXiv:2308.08484 (cs)
[Submitted on 16 Aug 2023]

Title:Taming Horizontal Instability in Merge Trees: On the Computation of a Comprehensive Deformation-based Edit Distance

Authors:Florian Wetzels, Markus Anders, Christoph Garth
View PDF
Abstract:Comparative analysis of scalar fields in scientific visualization often involves distance functions on topological abstractions. This paper focuses on the merge tree abstraction (representing the nesting of sub- or superlevel sets) and proposes the application of the unconstrained deformation-based edit distance. Previous approaches on merge trees often suffer from instability: small perturbations in the data can lead to large distances of the abstractions. While some existing methods can handle so-called vertical instability, the unconstrained deformation-based edit distance addresses both vertical and horizontal instabilities, also called saddle swaps. We establish the computational complexity as NP-complete, and provide an integer linear program formulation for computation. Experimental results on the TOSCA shape matching ensemble provide evidence for the stability of the proposed distance. We thereby showcase the potential of handling saddle swaps for comparison of scalar fields through merge trees.
Subjects: Computational Geometry (cs.CG)
Cite as: arXiv:2308.08484 [cs.CG]
  (or arXiv:2308.08484v1 [cs.CG] for this version)
  https://doi.org/10.48550/arXiv.2308.08484
Related DOI: https://doi.org/10.1109/TopoInVis60193.2023.00015

Submission history

From: Florian Wetzels [view email]
[v1] Wed, 16 Aug 2023 16:40:16 UTC (7,350 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
license icon view license
Current browse context:
cs.CG
< prev   |   next >
new | recent | 2023-08
Change to browse by:
cs

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)