---
_id: '14345'
abstract:
- lang: eng
  text: For a locally finite set in R2, the order-k Brillouin tessellations form an
    infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely
    dense and generic, then the corresponding infinite sequences of minimum and maximum
    angles are both monotonic in k. As an example, a stationary Poisson point process
    in R2  is locally finite, coarsely dense, and generic with probability one. For
    such a set, the distributions of angles in the Voronoi tessellations, Delaunay
    mosaics, and Brillouin tessellations are independent of the order and can be derived
    from the formula for angles in order-1 Delaunay mosaics given by Miles (Math.
    Biosci. 6, 85–127 (1970)).
acknowledgement: Work by all authors but A. Garber is supported by the European Research
  Council (ERC), Grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund
  (FWF), Grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109,
  Austrian Science Fund (FWF), Grant No. I 02979-N35. Work by A. Garber is partially
  supported by the Alexander von Humboldt Foundation.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
- first_name: Alexey
  full_name: Garber, Alexey
  last_name: Garber
- first_name: Mohadese
  full_name: Ghafari, Mohadese
  last_name: Ghafari
- first_name: Teresa
  full_name: Heiss, Teresa
  id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
  last_name: Heiss
  orcid: 0000-0002-1780-2689
- first_name: Morteza
  full_name: Saghafian, Morteza
  id: f86f7148-b140-11ec-9577-95435b8df824
  last_name: Saghafian
citation:
  ama: Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. On angles in higher
    order Brillouin tessellations and related tilings in the plane. <i>Discrete and
    Computational Geometry</i>. 2023. doi:<a href="https://doi.org/10.1007/s00454-023-00566-1">10.1007/s00454-023-00566-1</a>
  apa: Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., &#38; Saghafian, M. (2023).
    On angles in higher order Brillouin tessellations and related tilings in the plane.
    <i>Discrete and Computational Geometry</i>. Springer Nature. <a href="https://doi.org/10.1007/s00454-023-00566-1">https://doi.org/10.1007/s00454-023-00566-1</a>
  chicago: Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and
    Morteza Saghafian. “On Angles in Higher Order Brillouin Tessellations and Related
    Tilings in the Plane.” <i>Discrete and Computational Geometry</i>. Springer Nature,
    2023. <a href="https://doi.org/10.1007/s00454-023-00566-1">https://doi.org/10.1007/s00454-023-00566-1</a>.
  ieee: H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “On angles
    in higher order Brillouin tessellations and related tilings in the plane,” <i>Discrete
    and Computational Geometry</i>. Springer Nature, 2023.
  ista: Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2023. On angles
    in higher order Brillouin tessellations and related tilings in the plane. Discrete
    and Computational Geometry.
  mla: Edelsbrunner, Herbert, et al. “On Angles in Higher Order Brillouin Tessellations
    and Related Tilings in the Plane.” <i>Discrete and Computational Geometry</i>,
    Springer Nature, 2023, doi:<a href="https://doi.org/10.1007/s00454-023-00566-1">10.1007/s00454-023-00566-1</a>.
  short: H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete
    and Computational Geometry (2023).
date_created: 2023-09-17T22:01:10Z
date_published: 2023-09-07T00:00:00Z
date_updated: 2023-12-13T12:25:06Z
day: '07'
department:
- _id: HeEd
doi: 10.1007/s00454-023-00566-1
ec_funded: 1
external_id:
  arxiv:
  - '2204.01076'
  isi:
  - '001060727600004'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1007/s00454-023-00566-1
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '788183'
  name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: Z00342
  name: The Wittgenstein Prize
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I02979-N35
  name: Persistence and stability of geometric complexes
publication: Discrete and Computational Geometry
publication_identifier:
  eissn:
  - 1432-0444
  issn:
  - 0179-5376
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On angles in higher order Brillouin tessellations and related tilings in the
  plane
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '10828'
abstract:
- lang: eng
  text: Digital images enable quantitative analysis of material properties at micro
    and macro length scales, but choosing an appropriate resolution when acquiring
    the image is challenging. A high resolution means longer image acquisition and
    larger data requirements for a given sample, but if the resolution is too low,
    significant information may be lost. This paper studies the impact of changes
    in resolution on persistent homology, a tool from topological data analysis that
    provides a signature of structure in an image across all length scales. Given
    prior information about a function, the geometry of an object, or its density
    distribution at a given resolution, we provide methods to select the coarsest
    resolution yielding results within an acceptable tolerance. We present numerical
    case studies for an illustrative synthetic example and samples from porous materials
    where the theoretical bounds are unknown.
article_processing_charge: No
arxiv: 1
author:
- first_name: Teresa
  full_name: Heiss, Teresa
  id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
  last_name: Heiss
  orcid: 0000-0002-1780-2689
- first_name: Sarah
  full_name: Tymochko, Sarah
  last_name: Tymochko
- first_name: Brittany
  full_name: Story, Brittany
  last_name: Story
- first_name: Adélie
  full_name: Garin, Adélie
  last_name: Garin
- first_name: Hoa
  full_name: Bui, Hoa
  last_name: Bui
- first_name: Bea
  full_name: Bleile, Bea
  last_name: Bleile
- first_name: Vanessa
  full_name: Robins, Vanessa
  last_name: Robins
citation:
  ama: 'Heiss T, Tymochko S, Story B, et al. The impact of changes in resolution on
    the persistent homology of images. In: <i>2021 IEEE International Conference on
    Big Data</i>. IEEE; 2022:3824-3834. doi:<a href="https://doi.org/10.1109/BigData52589.2021.9671483">10.1109/BigData52589.2021.9671483</a>'
  apa: 'Heiss, T., Tymochko, S., Story, B., Garin, A., Bui, H., Bleile, B., &#38;
    Robins, V. (2022). The impact of changes in resolution on the persistent homology
    of images. In <i>2021 IEEE International Conference on Big Data</i> (pp. 3824–3834).
    Orlando, FL, United States; Virtuell: IEEE. <a href="https://doi.org/10.1109/BigData52589.2021.9671483">https://doi.org/10.1109/BigData52589.2021.9671483</a>'
  chicago: Heiss, Teresa, Sarah Tymochko, Brittany Story, Adélie Garin, Hoa Bui, Bea
    Bleile, and Vanessa Robins. “The Impact of Changes in Resolution on the Persistent
    Homology of Images.” In <i>2021 IEEE International Conference on Big Data</i>,
    3824–34. IEEE, 2022. <a href="https://doi.org/10.1109/BigData52589.2021.9671483">https://doi.org/10.1109/BigData52589.2021.9671483</a>.
  ieee: T. Heiss <i>et al.</i>, “The impact of changes in resolution on the persistent
    homology of images,” in <i>2021 IEEE International Conference on Big Data</i>,
    Orlando, FL, United States; Virtuell, 2022, pp. 3824–3834.
  ista: 'Heiss T, Tymochko S, Story B, Garin A, Bui H, Bleile B, Robins V. 2022. The
    impact of changes in resolution on the persistent homology of images. 2021 IEEE
    International Conference on Big Data. Big Data: International Conference on Big
    Data, 3824–3834.'
  mla: Heiss, Teresa, et al. “The Impact of Changes in Resolution on the Persistent
    Homology of Images.” <i>2021 IEEE International Conference on Big Data</i>, IEEE,
    2022, pp. 3824–34, doi:<a href="https://doi.org/10.1109/BigData52589.2021.9671483">10.1109/BigData52589.2021.9671483</a>.
  short: T. Heiss, S. Tymochko, B. Story, A. Garin, H. Bui, B. Bleile, V. Robins,
    in:, 2021 IEEE International Conference on Big Data, IEEE, 2022, pp. 3824–3834.
conference:
  end_date: 2021-12-18
  location: Orlando, FL, United States; Virtuell
  name: 'Big Data: International Conference on Big Data'
  start_date: 2021-12-15
date_created: 2022-03-06T23:01:53Z
date_published: 2022-01-13T00:00:00Z
date_updated: 2023-08-02T14:44:21Z
day: '13'
department:
- _id: HeEd
doi: 10.1109/BigData52589.2021.9671483
external_id:
  arxiv:
  - '2111.05663'
  isi:
  - '000800559503126'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2111.05663
month: '01'
oa: 1
oa_version: Preprint
page: 3824-3834
publication: 2021 IEEE International Conference on Big Data
publication_identifier:
  isbn:
  - '9781665439022'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: The impact of changes in resolution on the persistent homology of images
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2022'
...
---
_id: '11440'
abstract:
- lang: eng
  text: To compute the persistent homology of a grayscale digital image one needs
    to build a simplicial or cubical complex from it. For cubical complexes, the two
    commonly used constructions (corresponding to direct and indirect digital adjacencies)
    can give different results for the same image. The two constructions are almost
    dual to each other, and we use this relationship to extend and modify the cubical
    complexes to become dual filtered cell complexes. We derive a general relationship
    between the persistent homology of two dual filtered cell complexes, and also
    establish how various modifications to a filtered complex change the persistence
    diagram. Applying these results to images, we derive a method to transform the
    persistence diagram computed using one type of cubical complex into a persistence
    diagram for the other construction. This means software for computing persistent
    homology from images can now be easily adapted to produce results for either of
    the two cubical complex constructions without additional low-level code implementation.
acknowledgement: This project started during the Women in Computational Topology workshop
  held in Canberra in July of 2019. All authors are very grateful for its organisation
  and the financial support for the workshop from the Mathematical Sciences Institute
  at ANU, the US National Science Foundation through the award CCF-1841455, the Australian
  Mathematical Sciences Institute and the Association for Women in Mathematics. AG
  is supported by the Swiss National Science Foundation grant CRSII5_177237. TH is
  supported by the European Research Council (ERC) Horizon 2020 project “Alpha Shape
  Theory Extended” No. 788183. KM is supported by the ERC Horizon 2020 research and
  innovation programme under the Marie Sklodowska-Curie grant agreement No. 859860.
  VR was supported by Australian Research Council Future Fellowship FT140100604 during
  the early stages of this project.
alternative_title:
- Association for Women in Mathematics Series
article_processing_charge: No
arxiv: 1
author:
- first_name: Bea
  full_name: Bleile, Bea
  last_name: Bleile
- first_name: Adélie
  full_name: Garin, Adélie
  last_name: Garin
- first_name: Teresa
  full_name: Heiss, Teresa
  id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
  last_name: Heiss
  orcid: 0000-0002-1780-2689
- first_name: Kelly
  full_name: Maggs, Kelly
  last_name: Maggs
- first_name: Vanessa
  full_name: Robins, Vanessa
  last_name: Robins
citation:
  ama: 'Bleile B, Garin A, Heiss T, Maggs K, Robins V. The persistent homology of
    dual digital image constructions. In: Gasparovic E, Robins V, Turner K, eds. <i>Research
    in Computational Topology 2</i>. Vol 30. 1st ed. AWMS. Cham: Springer Nature;
    2022:1-26. doi:<a href="https://doi.org/10.1007/978-3-030-95519-9_1">10.1007/978-3-030-95519-9_1</a>'
  apa: 'Bleile, B., Garin, A., Heiss, T., Maggs, K., &#38; Robins, V. (2022). The
    persistent homology of dual digital image constructions. In E. Gasparovic, V.
    Robins, &#38; K. Turner (Eds.), <i>Research in Computational Topology 2</i> (1st
    ed., Vol. 30, pp. 1–26). Cham: Springer Nature. <a href="https://doi.org/10.1007/978-3-030-95519-9_1">https://doi.org/10.1007/978-3-030-95519-9_1</a>'
  chicago: 'Bleile, Bea, Adélie Garin, Teresa Heiss, Kelly Maggs, and Vanessa Robins.
    “The Persistent Homology of Dual Digital Image Constructions.” In <i>Research
    in Computational Topology 2</i>, edited by Ellen Gasparovic, Vanessa Robins, and
    Katharine Turner, 1st ed., 30:1–26. AWMS. Cham: Springer Nature, 2022. <a href="https://doi.org/10.1007/978-3-030-95519-9_1">https://doi.org/10.1007/978-3-030-95519-9_1</a>.'
  ieee: 'B. Bleile, A. Garin, T. Heiss, K. Maggs, and V. Robins, “The persistent homology
    of dual digital image constructions,” in <i>Research in Computational Topology
    2</i>, 1st ed., vol. 30, E. Gasparovic, V. Robins, and K. Turner, Eds. Cham: Springer
    Nature, 2022, pp. 1–26.'
  ista: 'Bleile B, Garin A, Heiss T, Maggs K, Robins V. 2022.The persistent homology
    of dual digital image constructions. In: Research in Computational Topology 2.
    Association for Women in Mathematics Series, vol. 30, 1–26.'
  mla: Bleile, Bea, et al. “The Persistent Homology of Dual Digital Image Constructions.”
    <i>Research in Computational Topology 2</i>, edited by Ellen Gasparovic et al.,
    1st ed., vol. 30, Springer Nature, 2022, pp. 1–26, doi:<a href="https://doi.org/10.1007/978-3-030-95519-9_1">10.1007/978-3-030-95519-9_1</a>.
  short: B. Bleile, A. Garin, T. Heiss, K. Maggs, V. Robins, in:, E. Gasparovic, V.
    Robins, K. Turner (Eds.), Research in Computational Topology 2, 1st ed., Springer
    Nature, Cham, 2022, pp. 1–26.
date_created: 2022-06-07T08:21:11Z
date_published: 2022-01-27T00:00:00Z
date_updated: 2022-06-07T08:32:42Z
day: '27'
department:
- _id: HeEd
doi: 10.1007/978-3-030-95519-9_1
ec_funded: 1
edition: '1'
editor:
- first_name: Ellen
  full_name: Gasparovic, Ellen
  last_name: Gasparovic
- first_name: Vanessa
  full_name: Robins, Vanessa
  last_name: Robins
- first_name: Katharine
  full_name: Turner, Katharine
  last_name: Turner
external_id:
  arxiv:
  - '2102.11397'
intvolume: '        30'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.48550/arXiv.2102.11397'
month: '01'
oa: 1
oa_version: Preprint
page: 1-26
place: Cham
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '788183'
  name: Alpha Shape Theory Extended
publication: Research in Computational Topology 2
publication_identifier:
  eisbn:
  - '9783030955199'
  isbn:
  - '9783030955182'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: AWMS
status: public
title: The persistent homology of dual digital image constructions
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 30
year: '2022'
...
---
_id: '9345'
abstract:
- lang: eng
  text: Modeling a crystal as a periodic point set, we present a fingerprint consisting
    of density functionsthat facilitates the efficient search for new materials and
    material properties. We prove invarianceunder isometries, continuity, and completeness
    in the generic case, which are necessary featuresfor the reliable comparison of
    crystals. The proof of continuity integrates methods from discretegeometry and
    lattice theory, while the proof of generic completeness combines techniques fromgeometry
    with analysis. The fingerprint has a fast algorithm based on Brillouin zones and
    relatedinclusion-exclusion formulae. We have implemented the algorithm and describe
    its application tocrystal structure prediction.
acknowledgement: The authors thank Janos Pach for insightful discussions on the topic
  of thispaper, Morteza Saghafian for finding the one-dimensional counterexample mentioned
  in Section 5,and Larry Andrews for generously sharing his crystallographic perspective.
alternative_title:
- LIPIcs
article_processing_charge: No
author:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
- first_name: Teresa
  full_name: Heiss, Teresa
  id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
  last_name: Heiss
  orcid: 0000-0002-1780-2689
- first_name: Vitaliy
  full_name: ' Kurlin , Vitaliy'
  last_name: ' Kurlin '
- first_name: Philip
  full_name: Smith, Philip
  last_name: Smith
- first_name: Mathijs
  full_name: Wintraecken, Mathijs
  id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
  last_name: Wintraecken
  orcid: 0000-0002-7472-2220
citation:
  ama: 'Edelsbrunner H, Heiss T,  Kurlin  V, Smith P, Wintraecken M. The density fingerprint
    of a periodic point set. In: <i>37th International Symposium on Computational
    Geometry (SoCG 2021)</i>. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik;
    2021:32:1-32:16. doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2021.32">10.4230/LIPIcs.SoCG.2021.32</a>'
  apa: 'Edelsbrunner, H., Heiss, T.,  Kurlin , V., Smith, P., &#38; Wintraecken, M.
    (2021). The density fingerprint of a periodic point set. In <i>37th International
    Symposium on Computational Geometry (SoCG 2021)</i> (Vol. 189, p. 32:1-32:16).
    Virtual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href="https://doi.org/10.4230/LIPIcs.SoCG.2021.32">https://doi.org/10.4230/LIPIcs.SoCG.2021.32</a>'
  chicago: Edelsbrunner, Herbert, Teresa Heiss, Vitaliy  Kurlin , Philip Smith, and
    Mathijs Wintraecken. “The Density Fingerprint of a Periodic Point Set.” In <i>37th
    International Symposium on Computational Geometry (SoCG 2021)</i>, 189:32:1-32:16.
    Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. <a href="https://doi.org/10.4230/LIPIcs.SoCG.2021.32">https://doi.org/10.4230/LIPIcs.SoCG.2021.32</a>.
  ieee: H. Edelsbrunner, T. Heiss, V.  Kurlin , P. Smith, and M. Wintraecken, “The
    density fingerprint of a periodic point set,” in <i>37th International Symposium
    on Computational Geometry (SoCG 2021)</i>, Virtual, 2021, vol. 189, p. 32:1-32:16.
  ista: 'Edelsbrunner H, Heiss T,  Kurlin  V, Smith P, Wintraecken M. 2021. The density
    fingerprint of a periodic point set. 37th International Symposium on Computational
    Geometry (SoCG 2021). SoCG: Symposium on Computational Geometry, LIPIcs, vol.
    189, 32:1-32:16.'
  mla: Edelsbrunner, Herbert, et al. “The Density Fingerprint of a Periodic Point
    Set.” <i>37th International Symposium on Computational Geometry (SoCG 2021)</i>,
    vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16,
    doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2021.32">10.4230/LIPIcs.SoCG.2021.32</a>.
  short: H. Edelsbrunner, T. Heiss, V.  Kurlin , P. Smith, M. Wintraecken, in:, 37th
    International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl
    - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16.
conference:
  end_date: 2021-06-11
  location: Virtual
  name: 'SoCG: Symposium on Computational Geometry'
  start_date: 2021-06-07
date_created: 2021-04-22T08:09:58Z
date_published: 2021-06-02T00:00:00Z
date_updated: 2023-02-23T13:55:40Z
day: '02'
ddc:
- '004'
- '516'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2021.32
ec_funded: 1
file:
- access_level: open_access
  checksum: 1787baef1523d6d93753b90d0c109a6d
  content_type: application/pdf
  creator: mwintrae
  date_created: 2021-04-22T08:08:14Z
  date_updated: 2021-04-22T08:08:14Z
  file_id: '9346'
  file_name: df_socg_final_version.pdf
  file_size: 3117435
  relation: main_file
  success: 1
file_date_updated: 2021-04-22T08:08:14Z
has_accepted_license: '1'
intvolume: '       189'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 32:1-32:16
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '788183'
  name: Alpha Shape Theory Extended
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
  grant_number: I4887
  name: Discretization in Geometry and Dynamics
- _id: 25C5A090-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: Z00312
  name: The Wittgenstein Prize
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: 37th International Symposium on Computational Geometry (SoCG 2021)
publication_identifier:
  issn:
  - 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
status: public
title: The density fingerprint of a periodic point set
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 189
year: '2021'
...
---
_id: '10071'
alternative_title:
- Early Career
article_processing_charge: No
article_type: letter_note
author:
- first_name: Henry
  full_name: Adams, Henry
  last_name: Adams
- first_name: Hana
  full_name: Kourimska, Hana
  id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E
  last_name: Kourimska
- first_name: Teresa
  full_name: Heiss, Teresa
  id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
  last_name: Heiss
  orcid: 0000-0002-1780-2689
- first_name: Sarah
  full_name: Percival, Sarah
  last_name: Percival
- first_name: Lori
  full_name: Ziegelmeier, Lori
  last_name: Ziegelmeier
citation:
  ama: Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. How to tutorial-a-thon.
    <i>Notices of the American Mathematical Society</i>. 2021;68(9):1511-1514. doi:<a
    href="https://doi.org/10.1090/noti2349">10.1090/noti2349</a>
  apa: Adams, H., Kourimska, H., Heiss, T., Percival, S., &#38; Ziegelmeier, L. (2021).
    How to tutorial-a-thon. <i>Notices of the American Mathematical Society</i>. American
    Mathematical Society. <a href="https://doi.org/10.1090/noti2349">https://doi.org/10.1090/noti2349</a>
  chicago: Adams, Henry, Hana Kourimska, Teresa Heiss, Sarah Percival, and Lori Ziegelmeier.
    “How to Tutorial-a-Thon.” <i>Notices of the American Mathematical Society</i>.
    American Mathematical Society, 2021. <a href="https://doi.org/10.1090/noti2349">https://doi.org/10.1090/noti2349</a>.
  ieee: H. Adams, H. Kourimska, T. Heiss, S. Percival, and L. Ziegelmeier, “How to
    tutorial-a-thon,” <i>Notices of the American Mathematical Society</i>, vol. 68,
    no. 9. American Mathematical Society, pp. 1511–1514, 2021.
  ista: Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. 2021. How to tutorial-a-thon.
    Notices of the American Mathematical Society. 68(9), 1511–1514.
  mla: Adams, Henry, et al. “How to Tutorial-a-Thon.” <i>Notices of the American Mathematical
    Society</i>, vol. 68, no. 9, American Mathematical Society, 2021, pp. 1511–14,
    doi:<a href="https://doi.org/10.1090/noti2349">10.1090/noti2349</a>.
  short: H. Adams, H. Kourimska, T. Heiss, S. Percival, L. Ziegelmeier, Notices of
    the American Mathematical Society 68 (2021) 1511–1514.
date_created: 2021-10-03T22:01:22Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2021-12-03T07:31:26Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/noti2349
intvolume: '        68'
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://www.ams.org/notices/
month: '10'
oa: 1
oa_version: Published Version
page: 1511-1514
publication: Notices of the American Mathematical Society
publication_identifier:
  eissn:
  - 1088-9477
  issn:
  - 0002-9920
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: How to tutorial-a-thon
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 68
year: '2021'
...
---
_id: '833'
abstract:
- lang: eng
  text: We present an efficient algorithm to compute Euler characteristic curves of
    gray scale images of arbitrary dimension. In various applications the Euler characteristic
    curve is used as a descriptor of an image. Our algorithm is the first streaming
    algorithm for Euler characteristic curves. The usage of streaming removes the
    necessity to store the entire image in RAM. Experiments show that our implementation
    handles terabyte scale images on commodity hardware. Due to lock-free parallelism,
    it scales well with the number of processor cores. Additionally, we put the concept
    of the Euler characteristic curve in the wider context of computational topology.
    In particular, we explain the connection with persistence diagrams.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Teresa
  full_name: Heiss, Teresa
  id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
  last_name: Heiss
  orcid: 0000-0002-1780-2689
- first_name: Hubert
  full_name: Wagner, Hubert
  id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
  last_name: Wagner
citation:
  ama: 'Heiss T, Wagner H. Streaming algorithm for Euler characteristic curves of
    multidimensional images. In: Felsberg M, Heyden A, Krüger N, eds. Vol 10424. Springer;
    2017:397-409. doi:<a href="https://doi.org/10.1007/978-3-319-64689-3_32">10.1007/978-3-319-64689-3_32</a>'
  apa: 'Heiss, T., &#38; Wagner, H. (2017). Streaming algorithm for Euler characteristic
    curves of multidimensional images. In M. Felsberg, A. Heyden, &#38; N. Krüger
    (Eds.) (Vol. 10424, pp. 397–409). Presented at the CAIP: Computer Analysis of
    Images and Patterns, Ystad, Sweden: Springer. <a href="https://doi.org/10.1007/978-3-319-64689-3_32">https://doi.org/10.1007/978-3-319-64689-3_32</a>'
  chicago: Heiss, Teresa, and Hubert Wagner. “Streaming Algorithm for Euler Characteristic
    Curves of Multidimensional Images.” edited by Michael Felsberg, Anders Heyden,
    and Norbert Krüger, 10424:397–409. Springer, 2017. <a href="https://doi.org/10.1007/978-3-319-64689-3_32">https://doi.org/10.1007/978-3-319-64689-3_32</a>.
  ieee: 'T. Heiss and H. Wagner, “Streaming algorithm for Euler characteristic curves
    of multidimensional images,” presented at the CAIP: Computer Analysis of Images
    and Patterns, Ystad, Sweden, 2017, vol. 10424, pp. 397–409.'
  ista: 'Heiss T, Wagner H. 2017. Streaming algorithm for Euler characteristic curves
    of multidimensional images. CAIP: Computer Analysis of Images and Patterns, LNCS,
    vol. 10424, 397–409.'
  mla: Heiss, Teresa, and Hubert Wagner. <i>Streaming Algorithm for Euler Characteristic
    Curves of Multidimensional Images</i>. Edited by Michael Felsberg et al., vol.
    10424, Springer, 2017, pp. 397–409, doi:<a href="https://doi.org/10.1007/978-3-319-64689-3_32">10.1007/978-3-319-64689-3_32</a>.
  short: T. Heiss, H. Wagner, in:, M. Felsberg, A. Heyden, N. Krüger (Eds.), Springer,
    2017, pp. 397–409.
conference:
  end_date: 2017-08-24
  location: Ystad, Sweden
  name: 'CAIP: Computer Analysis of Images and Patterns'
  start_date: 2017-08-22
date_created: 2018-12-11T11:48:45Z
date_published: 2017-07-28T00:00:00Z
date_updated: 2023-09-26T16:10:03Z
day: '28'
department:
- _id: HeEd
doi: 10.1007/978-3-319-64689-3_32
editor:
- first_name: Michael
  full_name: Felsberg, Michael
  last_name: Felsberg
- first_name: Anders
  full_name: Heyden, Anders
  last_name: Heyden
- first_name: Norbert
  full_name: Krüger, Norbert
  last_name: Krüger
external_id:
  isi:
  - '000432085900032'
intvolume: '     10424'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1705.02045
month: '07'
oa: 1
oa_version: Submitted Version
page: 397 - 409
publication_identifier:
  issn:
  - '03029743'
publication_status: published
publisher: Springer
publist_id: '6815'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Streaming algorithm for Euler characteristic curves of multidimensional images
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 10424
year: '2017'
...