A Variational Loop Shrinking Analogy for Handle and Tunnel Detection and Reeb Graph Construction on Surfaces

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dc.contributor.authorWeinrauch, Alexanderen_US
dc.contributor.authorMlakar, Danielen_US
dc.contributor.authorSeidel, Hans-Peteren_US
dc.contributor.authorSteinberger, Markusen_US
dc.contributor.authorZayer, Rhaleben_US
dc.contributor.editorMyszkowski, Karolen_US
dc.contributor.editorNiessner, Matthiasen_US
dc.date.accessioned2023-05-03T06:10:23Z
dc.date.available2023-05-03T06:10:23Z
dc.date.issued2023
dc.description.abstractThe humble loop shrinking property played a central role in the inception of modern topology but it has been eclipsed by more abstract algebraic formalisms. This is particularly true in the context of detecting relevant non-contractible loops on surfaces where elaborate homological and/or graph theoretical constructs are favored in algorithmic solutions. In this work, we devise a variational analogy to the loop shrinking property and show that it yields a simple, intuitive, yet powerful solution allowing a streamlined treatment of the problem of handle and tunnel loop detection. Our formalization tracks the evolution of a diffusion front randomly initiated on a single location on the surface. Capitalizing on a diffuse interface representation combined with a set of rules for concurrent front interactions, we develop a dynamic data structure for tracking the evolution on the surface encoded as a sparse matrix which serves for performing both diffusion numerics and loop detection and acts as the workhorse of our fully parallel implementation. The substantiated results suggest our approach outperforms state of the art and robustly copes with highly detailed geometric models. As a byproduct, our approach can be used to construct Reeb graphs by diffusion thus avoiding commonly encountered issues when using Morse functions.en_US
dc.description.number2
dc.description.sectionheadersTopological and Geometric Shape Understanding
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume42
dc.identifier.doi10.1111/cgf.14763
dc.identifier.issn1467-8659
dc.identifier.pages309-320
dc.identifier.pages12 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.14763
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14763
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectCCS Concepts: Computing methodologies -> Shape analysis; Massively parallel algorithms
dc.subjectComputing methodologies
dc.subjectShape analysis
dc.subjectMassively parallel algorithms
dc.titleA Variational Loop Shrinking Analogy for Handle and Tunnel Detection and Reeb Graph Construction on Surfacesen_US
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