3 Search Results for "Pock, Thomas"

Document
DOI: 10.4230/LIPIcs.SoCG.2023.45
The Localized Union-Of-Balls Bifiltration

Authors: Michael Kerber and Matthias Söls

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

Abstract
We propose an extension of the classical union-of-balls filtration of persistent homology: fixing a point q, we focus our attention to a ball centered at q whose radius is controlled by a second scale parameter. We discuss an absolute variant, where the union is just restricted to the q-ball, and a relative variant where the homology of the q-ball relative to its boundary is considered. Interestingly, these natural constructions lead to bifiltered simplicial complexes which are not k-critical for any finite k. Nevertheless, we demonstrate that these bifiltrations can be computed exactly and efficiently, and we provide a prototypical implementation using the CGAL library. We also argue that some of the recent algorithmic advances for 2-parameter persistence (which usually assume k-criticality for some finite k) carry over to the ∞-critical case.
Cite as

Michael Kerber and Matthias Söls. The Localized Union-Of-Balls Bifiltration. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 45:1-45:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kerber_et_al:LIPIcs.SoCG.2023.45,
  author =	{Kerber, Michael and S\"{o}ls, Matthias},
  title =	{{The Localized Union-Of-Balls Bifiltration}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{45:1--45:19},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.45},
  URN =		{urn:nbn:de:0030-drops-178953},
  doi =		{10.4230/LIPIcs.SoCG.2023.45},
  annote =	{Keywords: Topological Data Analysis, Multi-Parameter Persistence, Persistent Local Homology}
}
Document
DOI: 10.4230/DagRep.6.11.90
Inpainting-Based Image Compression (Dagstuhl Seminar 16462)

Authors: Christine Guillemot, Gerlind Plonka-Hoch, Thomas Pock, and Joachim Weickert

Published in: Dagstuhl Reports, Volume 6, Issue 11 (2017)

Abstract
Inpainting-based image compression is an emerging paradigm for compressing visual data in a completely different way than popular transform-based methods such as JPEG. The underlying idea sounds very simple: One stores only a small, carefully selected subset of the data, which results in a substantial reduction of the file size. In the decoding phase, one interpolates the missing data by means of a suitable inpainting process. It propagates information from the known data into the areas where nothing has been stored, e.g. by solving a partial differential equation or by clever copy-and-paste mechanisms. Inpainting-based codecs (coders and decoders) are more intuitive than transform-based ones, they are closer to biological mechanisms in our brain, and first results show that they may offer promising performance for high compression rates. However, before these ideas become practically viable, a number of difficult fundamental problems must be solved first. They involve e.g. the selection of the data and the inpainting operator, coding strategies, and the search for highly efficient numerical algorithms. This requires a collaborative effort of experts in data compression, inpainting, optimisation, approximation theory, numerical algorithms, and biological vision. In this Dagstuhl seminar we have brought together leading researcher from all these fields for the first time. It enabled a very fruitful and inspiring interaction which will form the basis for future progress.
Cite as

Christine Guillemot, Gerlind Plonka-Hoch, Thomas Pock, and Joachim Weickert. Inpainting-Based Image Compression (Dagstuhl Seminar 16462). In Dagstuhl Reports, Volume 6, Issue 11, pp. 90-107, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@Article{guillemot_et_al:DagRep.6.11.90,
  author =	{Guillemot, Christine and Plonka-Hoch, Gerlind and Pock, Thomas and Weickert, Joachim},
  title =	{{Inpainting-Based Image Compression (Dagstuhl Seminar 16462)}},
  pages =	{90--107},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2017},
  volume =	{6},
  number =	{11},
  editor =	{Guillemot, Christine and Plonka-Hoch, Gerlind and Pock, Thomas and Weickert, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.6.11.90},
  URN =		{urn:nbn:de:0030-drops-70406},
  doi =		{10.4230/DagRep.6.11.90},
  annote =	{Keywords: approximation, inpainting, interpolation, lossy image compression, optimisation, partial differential equations (PDEs), sparsity}
}
Document
DOI: 10.4230/DagRep.1.11.66
Efficient Algorithms for Global Optimisation Methods in Computer Vision (Dagstuhl Seminar 11471)

Authors: Andrés Bruhn, Thomas Pock, and Xue-Cheng Tai

Published in: Dagstuhl Reports, Volume 1, Issue 11 (2012)

Abstract
This report documents the program and the results of Dagstuhl Seminar 11471 Efficient Algorithms for Global Optimisation Methods in Computer Vision, taking place November 20-25 in 2011. The focus of the seminar was to discuss the design of efficient computer vision algorithms based on global optimisation methods in the context of the entire design pipeline. Since there is no such conference that deals with all aspects of the design process -- modelling, mathematical analysis, numerical solvers, and parallelisation -- the seminar aimed at bringing together researchers from computer science and mathematics covering all four fields.
Cite as

Andrés Bruhn, Thomas Pock, and Xue-Cheng Tai. Efficient Algorithms for Global Optimisation Methods in Computer Vision (Dagstuhl Seminar 11471). In Dagstuhl Reports, Volume 1, Issue 11, pp. 66-90, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@Article{bruhn_et_al:DagRep.1.11.66,
  author =	{Bruhn, Andr\'{e}s and Pock, Thomas and Tai, Xue-Cheng},
  title =	{{Efficient Algorithms for Global Optimisation Methods in Computer Vision (Dagstuhl Seminar 11471)}},
  pages =	{66--90},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2012},
  volume =	{1},
  number =	{11},
  editor =	{Bruhn, Andr\'{e}s and Pock, Thomas and Tai, Xue-Cheng},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.1.11.66},
  URN =		{urn:nbn:de:0030-drops-33789},
  doi =		{10.4230/DagRep.1.11.66},
  annote =	{Keywords: Computer Vision, Modelling, Mathematical Foundations, Data Structures, Efficient Algorithms, Parallel Computing}
}
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