---
OA_place: repository
_id: '21016'
abstract:
- lang: eng
text: Motivated by applications in chemistry, we give a homlogical definition of
tunnels, or more generally cobordisms, connecting disjoint parts of a cell complex.
For a filtered complex, this defines a persistence module. We give a method for
identifying birth and death times using kernel persistence and a matrix reduction
algorithm for pairing birth and death times.
acknowledgement: "Y. B. B. and L. F. were funded by the Independent Research Fund
Denmark, grant\r\nnumber 1026-00037. T. H. was partially supported by the European
Research Council\r\n(ERC) Horizon 2020, grant number 788183."
article_number: '2505.17858'
article_processing_charge: No
arxiv: 1
author:
- first_name: Yossi
full_name: Bleile, Yossi
id: 920a7385-7995-11ef-9bfd-8c434cd8f3c2
last_name: Bleile
orcid: 0000-0002-4861-9174
- first_name: Lisbeth
full_name: Fajstrup, Lisbeth
last_name: Fajstrup
- first_name: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
- first_name: Anne Marie
full_name: Svane, Anne Marie
last_name: Svane
- first_name: Søren Strandskov
full_name: Sørensen, Søren Strandskov
last_name: Sørensen
citation:
ama: Bokor Bleile Y, Fajstrup L, Heiss T, Svane AM, Sørensen SS. Identifying cobordisms
using kernel persistence. arXiv. doi:10.48550/arXiv.2505.17858
apa: Bokor Bleile, Y., Fajstrup, L., Heiss, T., Svane, A. M., & Sørensen, S.
S. (n.d.). Identifying cobordisms using kernel persistence. arXiv. https://doi.org/10.48550/arXiv.2505.17858
chicago: Bokor Bleile, Yossi, Lisbeth Fajstrup, Teresa Heiss, Anne Marie Svane,
and Søren Strandskov Sørensen. “Identifying Cobordisms Using Kernel Persistence.”
ArXiv, n.d. https://doi.org/10.48550/arXiv.2505.17858.
ieee: Y. Bokor Bleile, L. Fajstrup, T. Heiss, A. M. Svane, and S. S. Sørensen, “Identifying
cobordisms using kernel persistence,” arXiv. .
ista: Bokor Bleile Y, Fajstrup L, Heiss T, Svane AM, Sørensen SS. Identifying cobordisms
using kernel persistence. arXiv, 2505.17858.
mla: Bokor Bleile, Yossi, et al. “Identifying Cobordisms Using Kernel Persistence.”
ArXiv, 2505.17858, doi:10.48550/arXiv.2505.17858.
short: Y. Bokor Bleile, L. Fajstrup, T. Heiss, A.M. Svane, S.S. Sørensen, ArXiv
(n.d.).
date_created: 2026-01-20T10:12:21Z
date_published: 2025-05-23T00:00:00Z
date_updated: 2026-06-11T11:51:13Z
day: '23'
department:
- _id: HeEd
doi: 10.48550/arXiv.2505.17858
ec_funded: 1
external_id:
arxiv:
- '2505.17858'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2505.17858
month: '05'
oa: 1
oa_version: Preprint
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication: arXiv
publication_status: submitted
status: public
title: Identifying cobordisms using kernel persistence
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '20490'
abstract:
- lang: eng
text: "We study flips in hypertriangulations of planar points sets. Here a level-k
hypertriangulation of n\r\n points in the plane is a subdivision induced by the
projection of a k-hypersimplex, which is the convex hull of the barycenters of
the (k-1)-dimensional faces of the standard (n-1)-simplex. In particular, we introduce
four types of flips and prove that the level-2 hypertriangulations are connected
by these flips.\r\n"
acknowledgement: Work by all authors but the second 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 the second author is
partially supported by the Alexander von Humboldt Foundation and by the Simons Foundation
. The second author thanks Jesús A. De Loera for useful discussions on flips and
non-flips and Pavel Galashin and Alexey Balitskiy for useful discussions on plabic
graphs.
article_number: '104248'
article_processing_charge: No
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. Flips in two-dimensional
hypertriangulations. European Journal of Combinatorics. 2025;132. doi:10.1016/j.ejc.2025.104248
apa: Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., & Saghafian, M. (2025).
Flips in two-dimensional hypertriangulations. European Journal of Combinatorics.
Elsevier. https://doi.org/10.1016/j.ejc.2025.104248
chicago: Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and
Morteza Saghafian. “Flips in Two-Dimensional Hypertriangulations.” European
Journal of Combinatorics. Elsevier, 2025. https://doi.org/10.1016/j.ejc.2025.104248.
ieee: H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “Flips
in two-dimensional hypertriangulations,” European Journal of Combinatorics,
vol. 132. Elsevier, 2025.
ista: Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2025. Flips in
two-dimensional hypertriangulations. European Journal of Combinatorics. 132, 104248.
mla: Edelsbrunner, Herbert, et al. “Flips in Two-Dimensional Hypertriangulations.”
European Journal of Combinatorics, vol. 132, 104248, Elsevier, 2025, doi:10.1016/j.ejc.2025.104248.
short: H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, European
Journal of Combinatorics 132 (2025).
corr_author: '1'
date_created: 2025-10-19T22:01:31Z
date_published: 2025-10-10T00:00:00Z
date_updated: 2025-12-01T12:57:29Z
day: '10'
department:
- _id: HeEd
doi: 10.1016/j.ejc.2025.104248
ec_funded: 1
external_id:
arxiv:
- '2212.11380'
isi:
- '001599061500002'
intvolume: ' 132'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2212.11380
month: '10'
oa: 1
oa_version: Preprint
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: Mathematics, Computer Science
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: European Journal of Combinatorics
publication_identifier:
issn:
- 0195-6698
publication_status: epub_ahead
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Flips in two-dimensional hypertriangulations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 132
year: '2025'
...
---
_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. Discrete and
Computational Geometry. 2024;72:29-48. doi:10.1007/s00454-023-00566-1
apa: Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., & Saghafian, M. (2024).
On angles in higher order Brillouin tessellations and related tilings in the plane.
Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00566-1
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.” Discrete and Computational Geometry. Springer Nature,
2024. https://doi.org/10.1007/s00454-023-00566-1.
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,” Discrete
and Computational Geometry, vol. 72. Springer Nature, pp. 29–48, 2024.
ista: Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2024. On angles
in higher order Brillouin tessellations and related tilings in the plane. Discrete
and Computational Geometry. 72, 29–48.
mla: Edelsbrunner, Herbert, et al. “On Angles in Higher Order Brillouin Tessellations
and Related Tilings in the Plane.” Discrete and Computational Geometry,
vol. 72, Springer Nature, 2024, pp. 29–48, doi:10.1007/s00454-023-00566-1.
short: H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete
and Computational Geometry 72 (2024) 29–48.
corr_author: '1'
date_created: 2023-09-17T22:01:10Z
date_published: 2024-07-01T00:00:00Z
date_updated: 2025-04-23T08:41:59Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-023-00566-1
ec_funded: 1
external_id:
arxiv:
- '2204.01076'
isi:
- '001060727600004'
pmid:
- '39610762'
file:
- access_level: open_access
checksum: b207b4e00f904e8ea8a30e24f0251f79
content_type: application/pdf
creator: dernst
date_created: 2024-07-22T09:43:19Z
date_updated: 2024-07-22T09:43:19Z
file_id: '17301'
file_name: 2024_DiscreteComputGeom_Edelsbrunner.pdf
file_size: 892019
relation: main_file
success: 1
file_date_updated: 2024-07-22T09:43:19Z
has_accepted_license: '1'
intvolume: ' 72'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '07'
oa: 1
oa_version: Published Version
page: 29-48
pmid: 1
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: Mathematics, Computer Science
- _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: published
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
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: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 72
year: '2024'
...
---
_id: '17190'
abstract:
- lang: eng
text: "For a locally finite set, \U0001D434⊆ℝ\U0001D451\r\n, the \U0001D458\r\nth
Brillouin zone of \U0001D44E∈\U0001D434\r\n is the region of points \U0001D465∈ℝ\U0001D451\r\n
for which ‖\U0001D465−\U0001D44E‖\r\n is the \U0001D458\r\nth smallest among the
Euclidean distances between \U0001D465\r\n and the points in \U0001D434\r\n. If
\U0001D434\r\n is a lattice, the \U0001D458\r\nth Brillouin zones of the points
in \U0001D434\r\n are translates of each other, and together they tile space.
Depending on the value of \U0001D458\r\n, they express medium- or long-range order
in the set. We study fundamental geometric and combinatorial properties of Brillouin
zones, focusing on the integer lattice and its perturbations. Our results include
the stability of a Brillouin zone under perturbations, a linear upper bound on
the number of chambers in a zone for lattices in ℝ2\r\n, and the convergence of
the maximum volume of a chamber to zero for the integer lattice."
acknowledgement: The second author is partially supported by the Alexander von Humboldt
Foundation. The sixth author is supported by the European Union's Horizon 2020 research
and innovation programme under Marie Sklodowska-Curie grant agreement 754411, and
by Austrian Science Fund(FWF) grant M-3073. All other authors are supported by European
Research Council (ERC) grant 788183, by the Wittgenstein Prize, by Austrian Science
Fund (FWF) grant Z 342-N31, and by the DFG Collaborative Research Center TRR 109,
Austrian Science Fund (FWF) grant I 02979-N35.
article_processing_charge: No
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: Ghafaris, Mohadese
last_name: Ghafaris
- 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: Saghafiant, Morteza
last_name: Saghafiant
- 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, Garber A, Ghafaris M, Heiss T, Saghafiant M, Wintraecken M.
Brillouin zones of integer lattices and their perturbations. SIAM Journal on
Discrete Mathematics. 2024;38(2):1784-1807. doi:10.1137/22M1489071
apa: Edelsbrunner, H., Garber, A., Ghafaris, M., Heiss, T., Saghafiant, M., &
Wintraecken, M. (2024). Brillouin zones of integer lattices and their perturbations.
SIAM Journal on Discrete Mathematics. Society for Industrial and Applied
Mathematics. https://doi.org/10.1137/22M1489071
chicago: Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafaris, Teresa Heiss,
Morteza Saghafiant, and Mathijs Wintraecken. “Brillouin Zones of Integer Lattices
and Their Perturbations.” SIAM Journal on Discrete Mathematics. Society
for Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/22M1489071.
ieee: H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, and M. Wintraecken,
“Brillouin zones of integer lattices and their perturbations,” SIAM Journal
on Discrete Mathematics, vol. 38, no. 2. Society for Industrial and Applied
Mathematics, pp. 1784–1807, 2024.
ista: Edelsbrunner H, Garber A, Ghafaris M, Heiss T, Saghafiant M, Wintraecken M.
2024. Brillouin zones of integer lattices and their perturbations. SIAM Journal
on Discrete Mathematics. 38(2), 1784–1807.
mla: Edelsbrunner, Herbert, et al. “Brillouin Zones of Integer Lattices and Their
Perturbations.” SIAM Journal on Discrete Mathematics, vol. 38, no. 2, Society
for Industrial and Applied Mathematics, 2024, pp. 1784–807, doi:10.1137/22M1489071.
short: H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, M. Wintraecken,
SIAM Journal on Discrete Mathematics 38 (2024) 1784–1807.
corr_author: '1'
date_created: 2024-06-30T22:01:05Z
date_published: 2024-06-07T00:00:00Z
date_updated: 2025-09-08T08:06:04Z
day: '07'
department:
- _id: HeEd
doi: 10.1137/22M1489071
ec_funded: 1
external_id:
arxiv:
- '2204.01077'
isi:
- '001292728600001'
intvolume: ' 38'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2204.01077
month: '06'
oa: 1
oa_version: Preprint
page: 1784-1807
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: fc390959-9c52-11eb-aca3-afa58bd282b2
grant_number: M03073
name: Learning and triangulating manifolds via collapses
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
publication: SIAM Journal on Discrete Mathematics
publication_identifier:
issn:
- 0895-4801
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Brillouin zones of integer lattices and their perturbations
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 38
year: '2024'
...
---
OA_place: repository
_id: '18673'
abstract:
- lang: eng
text: "Motivated by applications to crystalline materials, we generalize the merge
tree and the related barcode of a filtered complex to the periodic setting in
Euclidean space. They are invariant under isometries, changing bases, and indeed
changing lattices. In addition, we prove stability under perturbations and provide
an algorithm that under mild geometric conditions typically satisfied by crystalline
materials takes O((n+m)logn) time, in which n and m are the numbers of vertices
and edges in the quotient complex, respectively.\r\n"
acknowledgement: "Both authors are partially supported by the European Research Council
(ERC) Horizon 2020 project\r\n‘Alpha Shape Theory Extended’, grant no. 788183. The
first author is also partially supported by the DFG\r\nCollaborative Research Center
TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund\r\n(FWF),
grant no. I 02979-N35."
article_processing_charge: No
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: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
citation:
ama: Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. arXiv.
doi:10.48550/arXiv.2408.16575
apa: Edelsbrunner, H., & Heiss, T. (n.d.). Merge trees of periodic filtrations.
arXiv. https://doi.org/10.48550/arXiv.2408.16575
chicago: Edelsbrunner, Herbert, and Teresa Heiss. “Merge Trees of Periodic Filtrations.”
ArXiv, n.d. https://doi.org/10.48550/arXiv.2408.16575.
ieee: H. Edelsbrunner and T. Heiss, “Merge trees of periodic filtrations,” arXiv.
.
ista: Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. arXiv, 10.48550/arXiv.2408.16575.
mla: Edelsbrunner, Herbert, and Teresa Heiss. “Merge Trees of Periodic Filtrations.”
ArXiv, doi:10.48550/arXiv.2408.16575.
short: H. Edelsbrunner, T. Heiss, ArXiv (n.d.).
corr_author: '1'
date_created: 2024-12-18T14:06:57Z
date_published: 2024-08-29T00:00:00Z
date_updated: 2026-04-07T12:54:09Z
day: '29'
department:
- _id: HeEd
doi: 10.48550/arXiv.2408.16575
ec_funded: 1
external_id:
arxiv:
- '2408.16575'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2408.16575
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: arXiv
publication_status: draft
related_material:
record:
- id: '18667'
relation: dissertation_contains
status: public
status: public
title: Merge trees of periodic filtrations
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: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_place: publisher
_id: '18667'
abstract:
- lang: eng
text: "Many chemical and physical properties of materials are determined by the
material’s shape,\r\nfor example the size of its pores and the width of its tunnels.
This makes materials science\r\na prime application area for geometrical and topological
methods. Nevertheless many\r\nmethods in topological data analysis have not been
satisfyingly extended to the needs of\r\nmaterials science. This thesis provides
new methods and new mathematical theorems\r\ntargeted at those specific needs
by answering four different research questions. While the\r\nmotivation for each
of the research questions arises from materials science, the methods\r\nare versatile
and can be applied in different areas as well. \r\n\r\nThe first research question
is concerned with image data, for example a three-dimensional\r\ncomputed tomography
(CT) scan of a material, like sand or stone. There are two commonly\r\nused topologies
for digital images and depending on the application either of them might be\r\nrequired.
However, software for computing the topological data analysis method persistence\r\nhomology,
usually supports only one of the two topologies. We answer the question how to\r\ncompute
persistent homology of an image with respect to one of the two topologies using\r\nsoftware
that is intended for the other topology. \r\n\r\nThe second research question
is concerned with image data as well, and asks how much\r\nof the topological
information of an image is lost when the resolution is coarsened. As\r\ncomputer
tomography scanners are more expensive the higher the resolution, it is an\r\nimportant
question in materials science to know which resolution is enough to get satisfying\r\npersistent
homology. We give theoretical bounds on the information loss based on different\r\ngeometrical
properties of the object to be scanned. In addition, we conduct experiments on\r\nsand
and stone CT image data. \r\n\r\nThe third research question is motivated by comparing
crystalline materials efficiently. As\r\nthe atoms within a crystal repeat periodically,
crystalline materials are either modeled by\r\nunmanageable infinite periodic
point sets, or by one of their fundamental domains, which is\r\nunstable under
perturbation. Therefore a fingerprint of crystalline materials is needed, with\r\nappropriate
properties such that comparing the crystals can be eased by comparing the\r\nfingerprints
instead. We define the density fingerprint and prove the necessary properties.
\r\n\r\nThe fourth research question is motivated by studying the hole-structure
or connectedness,\r\ni.e. persistent homology or merge trees, of crystalline materials.
A common way to deal\r\nwith periodicity is to take a fundamental domain and identify
opposite boundaries to form a\r\ntorus. However, computing persistent homology
or merge trees on that torus loses some\r\nof the information materials scientists
are interested in and is additionally not stable under\r\ncertain noise. We therefore
decorate the merge tree stemming from the torus with additional\r\ninformation
describing the density and growth rate of the periodic copies of a component\r\nwithin
a growing spherical window. We prove all desired properties, like stability and
efficient\r\ncomputability."
acknowledgement: "I was supported by the European Research Council (ERC) Horizon 2020
project\r\n“Alpha Shape Theory Extended” No. 788183 and by the Pöttinger Scholarship.
In addition,\r\nI am very thankful for having been able to attend the second Workshop
for Women in\r\nComputational Topology in July 2019, funded by the Mathematical
Sciences Institute at\r\nANU, the US National Science Foundation through the award
CCF-1841455, the Australian\r\nMathematical Sciences Institute and the Association
for Women in Mathematics. Two of the\r\nprojects presented in this thesis started
there. One of them reached completion thanks to\r\nfunding from the MSRI Summer
Research in Mathematics program awarded to me and my\r\ncollaborators in 2020."
alternative_title:
- ISTA Thesis
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
citation:
ama: Heiss T. New methods for applying topological data analysis to materials science.
2024. doi:10.15479/at:ista:18667
apa: Heiss, T. (2024). New methods for applying topological data analysis to
materials science. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18667
chicago: Heiss, Teresa. “New Methods for Applying Topological Data Analysis to Materials
Science.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18667.
ieee: T. Heiss, “New methods for applying topological data analysis to materials
science,” Institute of Science and Technology Austria, 2024.
ista: Heiss T. 2024. New methods for applying topological data analysis to materials
science. Institute of Science and Technology Austria.
mla: Heiss, Teresa. New Methods for Applying Topological Data Analysis to Materials
Science. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18667.
short: T. Heiss, New Methods for Applying Topological Data Analysis to Materials
Science, Institute of Science and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-12-17T16:17:55Z
date_published: 2024-12-17T00:00:00Z
date_updated: 2026-07-07T13:43:27Z
day: '17'
ddc:
- '514'
- '516'
- '004'
degree_awarded: PhD
department:
- _id: GradSch
- _id: HeEd
doi: 10.15479/at:ista:18667
ec_funded: 1
file:
- access_level: open_access
checksum: 247bb057aed2fba1cd4711917aaa2d77
content_type: application/pdf
creator: theiss
date_created: 2024-12-19T10:24:46Z
date_updated: 2024-12-19T10:24:46Z
file_id: '18686'
file_name: Teresa_Heiss_PhD_Thesis_final.pdf
file_size: 7752253
relation: main_file
success: 1
- access_level: closed
checksum: 9648b45c07a008ee11a07f99856a139d
content_type: application/zip
creator: theiss
date_created: 2024-12-19T10:24:50Z
date_updated: 2024-12-19T10:24:50Z
file_id: '18687'
file_name: PhD_Thesis.zip
file_size: 17197731
relation: source_file
file_date_updated: 2024-12-19T10:24:50Z
has_accepted_license: '1'
keyword:
- persistent homology
- topological data analysis
- periodic
- crystalline materials
- images
- fingerprint
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: '111'
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication_identifier:
isbn:
- 978-3-99078-052-7
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '10828'
relation: part_of_dissertation
status: public
- id: '11440'
relation: part_of_dissertation
status: public
- id: '18673'
relation: part_of_dissertation
status: public
- id: '9345'
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: New methods for applying topological data analysis to materials science
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: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
_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: 2021 IEEE International Conference on
Big Data. IEEE; 2022:3824-3834. doi:10.1109/BigData52589.2021.9671483'
apa: '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. In 2021 IEEE International Conference on Big Data (pp. 3824–3834).
Orlando, FL, United States; Virtuell: IEEE. https://doi.org/10.1109/BigData52589.2021.9671483'
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 2021 IEEE International Conference on Big Data,
3824–34. IEEE, 2022. https://doi.org/10.1109/BigData52589.2021.9671483.
ieee: T. Heiss et al., “The impact of changes in resolution on the persistent
homology of images,” in 2021 IEEE International Conference on Big Data,
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.” 2021 IEEE International Conference on Big Data, IEEE,
2022, pp. 3824–34, doi:10.1109/BigData52589.2021.9671483.
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: 2026-04-07T12:54:09Z
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'
related_material:
record:
- id: '18667'
relation: dissertation_contains
status: public
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. Research
in Computational Topology 2. Vol 30. 1st ed. AWMS. Cham: Springer Nature;
2022:1-26. doi:10.1007/978-3-030-95519-9_1'
apa: 'Bleile, B., Garin, A., Heiss, T., Maggs, K., & Robins, V. (2022). The
persistent homology of dual digital image constructions. In E. Gasparovic, V.
Robins, & K. Turner (Eds.), Research in Computational Topology 2 (1st
ed., Vol. 30, pp. 1–26). Cham: Springer Nature. https://doi.org/10.1007/978-3-030-95519-9_1'
chicago: 'Bleile, Bea, Adélie Garin, Teresa Heiss, Kelly Maggs, and Vanessa Robins.
“The Persistent Homology of Dual Digital Image Constructions.” In Research
in Computational Topology 2, edited by Ellen Gasparovic, Vanessa Robins, and
Katharine Turner, 1st ed., 30:1–26. AWMS. Cham: Springer Nature, 2022. https://doi.org/10.1007/978-3-030-95519-9_1.'
ieee: 'B. Bleile, A. Garin, T. Heiss, K. Maggs, and V. Robins, “The persistent homology
of dual digital image constructions,” in Research in Computational Topology
2, 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.”
Research in Computational Topology 2, edited by Ellen Gasparovic et al.,
1st ed., vol. 30, Springer Nature, 2022, pp. 1–26, doi:10.1007/978-3-030-95519-9_1.
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: 2026-04-07T12:54:09Z
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'
related_material:
record:
- id: '18667'
relation: dissertation_contains
status: public
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: '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
orcid: 0000-0001-7841-0091
- 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.
Notices of the American Mathematical Society. 2021;68(9):1511-1514. doi:10.1090/noti2349
apa: Adams, H., Kourimska, H., Heiss, T., Percival, S., & Ziegelmeier, L. (2021).
How to tutorial-a-thon. Notices of the American Mathematical Society. American
Mathematical Society. https://doi.org/10.1090/noti2349
chicago: Adams, Henry, Hana Kourimska, Teresa Heiss, Sarah Percival, and Lori Ziegelmeier.
“How to Tutorial-a-Thon.” Notices of the American Mathematical Society.
American Mathematical Society, 2021. https://doi.org/10.1090/noti2349.
ieee: H. Adams, H. Kourimska, T. Heiss, S. Percival, and L. Ziegelmeier, “How to
tutorial-a-thon,” Notices of the American Mathematical Society, 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.” Notices of the American Mathematical
Society, vol. 68, no. 9, American Mathematical Society, 2021, pp. 1511–14,
doi:10.1090/noti2349.
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: 2026-06-18T08:36:13Z
day: '01'
ddc:
- '500'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 68
year: '2021'
...
---
_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: 37th International Symposium on Computational
Geometry. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021:32:1-32:16.
doi:10.4230/LIPIcs.SoCG.2021.32'
apa: 'Edelsbrunner, H., Heiss, T., Kurlin , V., Smith, P., & Wintraecken, M.
(2021). The density fingerprint of a periodic point set. In 37th International
Symposium on Computational Geometry (Vol. 189, p. 32:1-32:16). Virtual: Schloss
Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.32'
chicago: Edelsbrunner, Herbert, Teresa Heiss, Vitaliy Kurlin , Philip Smith, and
Mathijs Wintraecken. “The Density Fingerprint of a Periodic Point Set.” In 37th
International Symposium on Computational Geometry, 189:32:1-32:16. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.32.
ieee: H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, and M. Wintraecken, “The
density fingerprint of a periodic point set,” in 37th International Symposium
on Computational Geometry, 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: Symposium on Computational Geometry, LIPIcs, vol. 189, 32:1-32:16.'
mla: Edelsbrunner, Herbert, et al. “The Density Fingerprint of a Periodic Point
Set.” 37th International Symposium on Computational Geometry, vol. 189,
Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16, doi:10.4230/LIPIcs.SoCG.2021.32.
short: H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, M. Wintraecken, in:, 37th
International Symposium on Computational Geometry, 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
das_tickbox: '1'
date_created: 2021-04-22T08:09:58Z
date_published: 2021-06-02T00:00:00Z
date_updated: 2026-07-07T13:43:27Z
day: '02'
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- '516'
department:
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doi: 10.4230/LIPIcs.SoCG.2021.32
ec_funded: 1
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page: 32:1-32:16
project:
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call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
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grant_number: I4887
name: Persistent Homology, Algorithms and Stochastic Geometry
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call_identifier: FWF
grant_number: Z00312
name: Synaptic communication in neuronal microcircuits
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call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 37th International Symposium on Computational Geometry
publication_identifier:
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
record:
- id: '18667'
relation: dissertation_contains
status: public
scopus_import: '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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 189
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
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: 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:10.1007/978-3-319-64689-3_32'
apa: 'Heiss, T., & Wagner, H. (2017). Streaming algorithm for Euler characteristic
curves of multidimensional images. In M. Felsberg, A. Heyden, & N. Krüger
(Eds.) (Vol. 10424, pp. 397–409). Presented at the CAIP: Computer Analysis of
Images and Patterns, Ystad, Sweden: Springer. https://doi.org/10.1007/978-3-319-64689-3_32'
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. https://doi.org/10.1007/978-3-319-64689-3_32.
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. Streaming Algorithm for Euler Characteristic
Curves of Multidimensional Images. Edited by Michael Felsberg et al., vol.
10424, Springer, 2017, pp. 397–409, doi:10.1007/978-3-319-64689-3_32.
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
corr_author: '1'
date_created: 2018-12-11T11:48:45Z
date_published: 2017-07-28T00:00:00Z
date_updated: 2025-06-04T09:54:22Z
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:
arxiv:
- '1705.02045'
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:
- 0302-9743
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 10424
year: '2017'
...