---
res:
bibo_abstract:
- "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.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Katharina
foaf_name: Ölsböck, Katharina
foaf_surname: Ölsböck
foaf_workInfoHomepage: http://www.librecat.org/personId=4D4AA390-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-4672-8297
bibo_doi: 10.15479/AT:ISTA:7460
dct_date: 2020^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/2663-337X
dct_language: eng
dct_publisher: Institute of Science and Technology Austria@
dct_subject:
- shape reconstruction
- hole manipulation
- ordered complexes
- Alpha complex
- Wrap complex
- computational topology
- Bregman geometry
dct_title: The hole system of triangulated shapes@
...