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Topology, Computation and Data Analysis (Dagstuhl Seminar 17292)

Authors: Hamish Carr, Michael Kerber, and Bei Wang

Published in: Dagstuhl Reports, Volume 7, Issue 7 (2018)

Abstract

This report documents the program and the outcomes of Dagstuhl Seminar 17292 "Topology, Computation and Data Analysis". This seminar was the first of its kind in bringing together researchers with mathematical and computational backgrounds in addressing emerging directions within computational topology for data analysis in practice. The seminar connected pure and applied mathematicians, with theoretical and applied computer scientists with an interest in computational topology. It helped to facilitate interactions among data theorist and data practitioners from several communities to address challenges in computational topology, topological data analysis, and topological visualization.

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Hamish Carr, Michael Kerber, and Bei Wang. Topology, Computation and Data Analysis (Dagstuhl Seminar 17292). In Dagstuhl Reports, Volume 7, Issue 7, pp. 88-109, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@Article{carr_et_al:DagRep.7.7.88,
  author =	{Carr, Hamish and Kerber, Michael and Wang, Bei},
  title =	{{Topology, Computation and Data Analysis (Dagstuhl Seminar 17292)}},
  pages =	{88--109},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2018},
  volume =	{7},
  number =	{7},
  editor =	{Carr, Hamish and Kerber, Michael and Wang, Bei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.7.7.88},
  URN =		{urn:nbn:de:0030-drops-84258},
  doi =		{10.4230/DagRep.7.7.88},
  annote =	{Keywords: computational topology, topological data analysis, Topological data visualization}
}

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DOI: 10.4230/DFU.Vol2.SciViz.2011.48

Interpolants Induced by Marching Cases

Authors: Hamish Carr and Eoin Murphy

Published in: Dagstuhl Follow-Ups, Volume 2, Scientific Visualization: Interactions, Features, Metaphors (2011)

Abstract

Visualization depends among other things on the interpolant used in generating images. One way to assess this is to construct case tables for Marching Cubes that represent the chosen interpolant accuracy. Instead, we show how to construct the interpolants induced by Marching Cases for comparison and assessment, how to extend this approach to Marching Squares, Cubes and Hypercubes, and how to construct an interpolant which is computationally equivalent to the digital rules conventionally used in image processing. Furthermore, we demonstrate that unlike tetrahedral meshes, geometric measurements over multi-linear mesh cells are inherently non-linear and cannot be summed as in the Contour Spectrum.

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Hamish Carr and Eoin Murphy. Interpolants Induced by Marching Cases. In Scientific Visualization: Interactions, Features, Metaphors. Dagstuhl Follow-Ups, Volume 2, pp. 48-58, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InCollection{carr_et_al:DFU.Vol2.SciViz.2011.48,
  author =	{Carr, Hamish and Murphy, Eoin},
  title =	{{Interpolants Induced by Marching Cases}},
  booktitle =	{Scientific Visualization: Interactions, Features, Metaphors},
  pages =	{48--58},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-939897-26-2},
  ISSN =	{1868-8977},
  year =	{2011},
  volume =	{2},
  editor =	{Hagen, Hans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DFU.Vol2.SciViz.2011.48},
  URN =		{urn:nbn:de:0030-drops-32837},
  doi =		{10.4230/DFU.Vol2.SciViz.2011.48},
  annote =	{Keywords: Interpolation, Marching Cubes, Isosurfaces}
}

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Documents authored by Carr, Hamish

Topology, Computation and Data Analysis (Dagstuhl Seminar 17292)

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Interpolants Induced by Marching Cases

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