2 Search Results for "Robins, Vanessa"

Document
DOI: 10.4230/LIPIcs.SoCG.2023.60
Slice, Simplify and Stitch: Topology-Preserving Simplification Scheme for Massive Voxel Data

Authors: Hubert Wagner

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
We focus on efficient computations of topological descriptors for voxel data. This type of data includes 2D greyscale images, 3D medical scans, but also higher-dimensional scalar fields arising from physical simulations. In recent years we have seen an increase in applications of topological methods for such data. However, computational issues remain an obstacle. We therefore propose a streaming scheme which simplifies large 3-dimensional voxel data - while provably retaining its persistent homology. We combine this scheme with an efficient boundary matrix reduction implementation, obtaining an end-to-end tool for persistent homology of large data. Computational experiments show its state-of-the-art performance. In particular, we are now able to robustly handle complex datasets with several billions voxels on a regular laptop. A software implementation called Cubicle is available as open-source: https://bitbucket.org/hubwag/cubicle.
Cite as

Hubert Wagner. Slice, Simplify and Stitch: Topology-Preserving Simplification Scheme for Massive Voxel Data. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 60:1-60:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{wagner:LIPIcs.SoCG.2023.60,
  author =	{Wagner, Hubert},
  title =	{{Slice, Simplify and Stitch: Topology-Preserving Simplification Scheme for Massive Voxel Data}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{60:1--60:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.60},
  URN =		{urn:nbn:de:0030-drops-179107},
  doi =		{10.4230/LIPIcs.SoCG.2023.60},
  annote =	{Keywords: Computational topology, topological data analysis, topological image analysis, persistent homology, persistence diagram, discrete Morse theory, algorithm engineering, implementation, voxel data, volume data, image data}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.SoCG.2017.1
The Geometry and Topology of Crystals: From Sphere-Packing to Tiling, Nets, and Knots (Invited Talk)

Authors: Vanessa Robins

Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)

Abstract
Crystal structures have inspired developments in geometry since the Ancient Greeks conceived of Platonic solids after observing tetrahedral, cubical and octahedral mineral forms in their local environment. The internal structure of crystals became accessible with the development of x-ray diffraction techniques just over 100 years ago, and a key step in developing this method was understanding the arrangement of atoms in the simplest crystals as close-packings of spheres. Determining a crystal structure via x-ray diffraction unavoidably requires prior models, and this has led to the intense study of sphere packing, atom-bond networks, and arrangements of polyhedra by crystallographers investigating ever more complex compounds. In the 21st century, chemists are exploring the possibilities of coordination polymers, a wide class of crystalline materials that self-assemble from metal cations and organic ligands into periodic framework materials. Longer organic ligands mean these compounds can form multi-component interwoven network structures where the "edges" are no longer constrained to join nearest-neighbour "nodes" as in simpler atom-bond networks. The challenge for geometers is to devise algorithms for enumerating relevant structures and to devise invariants that will distinguish between different modes of interweaving. This talk will survey various methods from computational geometry and topology that are currently used to describe crystalline structures and outline research directions to address some of the open questions suggested above.
Cite as

Vanessa Robins. The Geometry and Topology of Crystals: From Sphere-Packing to Tiling, Nets, and Knots (Invited Talk). In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{robins:LIPIcs.SoCG.2017.1,
  author =	{Robins, Vanessa},
  title =	{{The Geometry and Topology of Crystals: From Sphere-Packing to Tiling, Nets, and Knots}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Aronov, Boris and Katz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.1},
  URN =		{urn:nbn:de:0030-drops-72374},
  doi =		{10.4230/LIPIcs.SoCG.2017.1},
  annote =	{Keywords: Mathematical crystallography, Combinatorial tiling theory, Graphs and surfaces in the 3-torus}
}
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