---
_id: '7460'
abstract:
- lang: eng
  text: "Many methods for the reconstruction of shapes from sets of points produce
    ordered simplicial complexes, which are collections of vertices, edges, triangles,
    and their higher-dimensional analogues, called simplices, in which every simplex
    gets assigned a real value measuring its size. This thesis studies ordered simplicial
    complexes, with a focus on their topology, which reflects the connectedness of
    the represented shapes and the presence of holes. We are interested both in understanding
    better the structure of these complexes, as well as in developing algorithms for
    applications.\r\n\r\nFor the Delaunay triangulation, the most popular measure
    for a simplex is the radius of the smallest empty circumsphere. Based on it, we
    revisit Alpha and Wrap complexes and experimentally determine their probabilistic
    properties for random data. Also, we prove the existence of tri-partitions, propose
    algorithms to open and close holes, and extend the concepts from Euclidean to
    Bregman geometries."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Katharina
  full_name: Ölsböck, Katharina
  id: 4D4AA390-F248-11E8-B48F-1D18A9856A87
  last_name: Ölsböck
  orcid: 0000-0002-4672-8297
citation:
  ama: Ölsböck K. The hole system of triangulated shapes. 2020. doi:<a href="https://doi.org/10.15479/AT:ISTA:7460">10.15479/AT:ISTA:7460</a>
  apa: Ölsböck, K. (2020). <i>The hole system of triangulated shapes</i>. Institute
    of Science and Technology Austria. <a href="https://doi.org/10.15479/AT:ISTA:7460">https://doi.org/10.15479/AT:ISTA:7460</a>
  chicago: Ölsböck, Katharina. “The Hole System of Triangulated Shapes.” Institute
    of Science and Technology Austria, 2020. <a href="https://doi.org/10.15479/AT:ISTA:7460">https://doi.org/10.15479/AT:ISTA:7460</a>.
  ieee: K. Ölsböck, “The hole system of triangulated shapes,” Institute of Science
    and Technology Austria, 2020.
  ista: Ölsböck K. 2020. The hole system of triangulated shapes. Institute of Science
    and Technology Austria.
  mla: Ölsböck, Katharina. <i>The Hole System of Triangulated Shapes</i>. Institute
    of Science and Technology Austria, 2020, doi:<a href="https://doi.org/10.15479/AT:ISTA:7460">10.15479/AT:ISTA:7460</a>.
  short: K. Ölsböck, The Hole System of Triangulated Shapes, Institute of Science
    and Technology Austria, 2020.
date_created: 2020-02-06T14:56:53Z
date_published: 2020-02-10T00:00:00Z
date_updated: 2023-09-07T13:15:30Z
day: '10'
ddc:
- '514'
degree_awarded: PhD
department:
- _id: HeEd
- _id: GradSch
doi: 10.15479/AT:ISTA:7460
file:
- access_level: open_access
  checksum: 1df9f8c530b443c0e63a3f2e4fde412e
  content_type: application/pdf
  creator: koelsboe
  date_created: 2020-02-06T14:43:54Z
  date_updated: 2020-07-14T12:47:58Z
  file_id: '7461'
  file_name: thesis_ist-final_noack.pdf
  file_size: 76195184
  relation: main_file
- access_level: closed
  checksum: 7a52383c812b0be64d3826546509e5a4
  content_type: application/x-zip-compressed
  creator: koelsboe
  date_created: 2020-02-06T14:52:45Z
  date_updated: 2020-07-14T12:47:58Z
  description: latex source files, figures
  file_id: '7462'
  file_name: latex-files.zip
  file_size: 122103715
  relation: source_file
file_date_updated: 2020-07-14T12:47:58Z
has_accepted_license: '1'
keyword:
- shape reconstruction
- hole manipulation
- ordered complexes
- Alpha complex
- Wrap complex
- computational topology
- Bregman geometry
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: '155'
publication_identifier:
  issn:
  - 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
  record:
  - id: '6608'
    relation: part_of_dissertation
    status: public
status: public
supervisor:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
title: The hole system of triangulated shapes
tmp:
  image: /images/cc_by_nc_sa.png
  legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
  name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
    BY-NC-SA 4.0)
  short: CC BY-NC-SA (4.0)
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2020'
...