---
_id: '1360'
abstract:
- lang: eng
text: 'We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard
trajectories in convex bodies, when the length is measured with a (possibly asymmetric)
norm. We prove a lower bound for the length of the shortest closed billiard trajectory,
related to the non-symmetric Mahler problem. With this technique we are able to
give short and elementary proofs to some known results. '
acknowledgement: The first and third authors were supported by the Dynasty Foundation.
The first, second and third authors were supported by the Russian Foundation for
Basic Re- search grant 15-31-20403 (mol a ved).
article_processing_charge: No
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Alexey
full_name: Balitskiy, Alexey
last_name: Balitskiy
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
- first_name: Anastasia
full_name: Sharipova, Anastasia
last_name: Sharipova
citation:
ama: Akopyan A, Balitskiy A, Karasev R, Sharipova A. Elementary approach to closed
billiard trajectories in asymmetric normed spaces. Proceedings of the American
Mathematical Society. 2016;144(10):4501-4513. doi:10.1090/proc/13062
apa: Akopyan, A., Balitskiy, A., Karasev, R., & Sharipova, A. (2016). Elementary
approach to closed billiard trajectories in asymmetric normed spaces. Proceedings
of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/13062
chicago: Akopyan, Arseniy, Alexey Balitskiy, Roman Karasev, and Anastasia Sharipova.
“Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.”
Proceedings of the American Mathematical Society. American Mathematical
Society, 2016. https://doi.org/10.1090/proc/13062.
ieee: A. Akopyan, A. Balitskiy, R. Karasev, and A. Sharipova, “Elementary approach
to closed billiard trajectories in asymmetric normed spaces,” Proceedings of
the American Mathematical Society, vol. 144, no. 10. American Mathematical
Society, pp. 4501–4513, 2016.
ista: Akopyan A, Balitskiy A, Karasev R, Sharipova A. 2016. Elementary approach
to closed billiard trajectories in asymmetric normed spaces. Proceedings of the
American Mathematical Society. 144(10), 4501–4513.
mla: Akopyan, Arseniy, et al. “Elementary Approach to Closed Billiard Trajectories
in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society,
vol. 144, no. 10, American Mathematical Society, 2016, pp. 4501–13, doi:10.1090/proc/13062.
short: A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American
Mathematical Society 144 (2016) 4501–4513.
date_created: 2018-12-11T11:51:34Z
date_published: 2016-10-01T00:00:00Z
date_updated: 2025-09-22T07:44:59Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/13062
ec_funded: 1
external_id:
arxiv:
- '1401.0442'
isi:
- '000383054200034'
intvolume: ' 144'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1401.0442
month: '10'
oa: 1
oa_version: Preprint
page: 4501 - 4513
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Proceedings of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '5885'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Elementary approach to closed billiard trajectories in asymmetric normed spaces
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 144
year: '2016'
...
---
_id: '1408'
abstract:
- lang: eng
text: 'The concept of well group in a special but important case captures homological
properties of the zero set of a continuous map (Formula presented.) on a compact
space K that are invariant with respect to perturbations of f. The perturbations
are arbitrary continuous maps within (Formula presented.) distance r from f for
a given (Formula presented.). The main drawback of the approach is that the computability
of well groups was shown only when (Formula presented.) or (Formula presented.).
Our contribution to the theory of well groups is twofold: on the one hand we improve
on the computability issue, but on the other hand we present a range of examples
where the well groups are incomplete invariants, that is, fail to capture certain
important robust properties of the zero set. For the first part, we identify a
computable subgroup of the well group that is obtained by cap product with the
pullback of the orientation of (Formula presented.) by f. In other words, well
groups can be algorithmically approximated from below. When f is smooth and (Formula
presented.), our approximation of the (Formula presented.)th well group is exact.
For the second part, we find examples of maps (Formula presented.) with all well
groups isomorphic but whose perturbations have different zero sets. We discuss
on a possible replacement of the well groups of vector valued maps by an invariant
of a better descriptive power and computability status.'
acknowledgement: 'Open access funding provided by Institute of Science and Technology
(IST Austria). '
article_processing_charge: Yes (via OA deal)
author:
- first_name: Peter
full_name: Franek, Peter
id: 473294AE-F248-11E8-B48F-1D18A9856A87
last_name: Franek
orcid: 0000-0001-8878-8397
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
citation:
ama: Franek P, Krcál M. On computability and triviality of well groups. Discrete
& Computational Geometry. 2016;56(1):126-164. doi:10.1007/s00454-016-9794-2
apa: Franek, P., & Krcál, M. (2016). On computability and triviality of well
groups. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-016-9794-2
chicago: Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well
Groups.” Discrete & Computational Geometry. Springer, 2016. https://doi.org/10.1007/s00454-016-9794-2.
ieee: P. Franek and M. Krcál, “On computability and triviality of well groups,”
Discrete & Computational Geometry, vol. 56, no. 1. Springer, pp. 126–164,
2016.
ista: Franek P, Krcál M. 2016. On computability and triviality of well groups. Discrete
& Computational Geometry. 56(1), 126–164.
mla: Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.”
Discrete & Computational Geometry, vol. 56, no. 1, Springer, 2016,
pp. 126–64, doi:10.1007/s00454-016-9794-2.
short: P. Franek, M. Krcál, Discrete & Computational Geometry 56 (2016) 126–164.
corr_author: '1'
date_created: 2018-12-11T11:51:51Z
date_published: 2016-07-01T00:00:00Z
date_updated: 2025-09-18T14:30:52Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/s00454-016-9794-2
ec_funded: 1
external_id:
isi:
- '000377722100005'
file:
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checksum: e0da023abf6b72abd8c6a8c76740d53c
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:10:55Z
date_updated: 2020-07-14T12:44:53Z
file_id: '4846'
file_name: IST-2016-614-v1+1_s00454-016-9794-2.pdf
file_size: 905303
relation: main_file
file_date_updated: 2020-07-14T12:44:53Z
has_accepted_license: '1'
intvolume: ' 56'
isi: 1
issue: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '07'
oa: 1
oa_version: Published Version
page: 126 - 164
project:
- _id: 25F8B9BC-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M01980
name: Robust Invariants of Nonlinear Systems
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '5799'
pubrep_id: '614'
quality_controlled: '1'
related_material:
record:
- id: '1510'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: On computability and triviality of well groups
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 56
year: '2016'
...
---
_id: '1617'
abstract:
- lang: eng
text: 'We study the discrepancy of jittered sampling sets: such a set P⊂ [0,1]d
is generated for fixed m∈ℕ by partitioning [0,1]d into md axis aligned cubes of
equal measure and placing a random point inside each of the N=md cubes. We prove
that, for N sufficiently large, 1/10 d/N1/2+1/2d ≤EDN∗(P)≤ √d(log N) 1/2/N1/2+1/2d,
where the upper bound with an unspecified constant Cd was proven earlier by Beck.
Our proof makes crucial use of the sharp Dvoretzky-Kiefer-Wolfowitz inequality
and a suitably taylored Bernstein inequality; we have reasons to believe that
the upper bound has the sharp scaling in N. Additional heuristics suggest that
jittered sampling should be able to improve known bounds on the inverse of the
star-discrepancy in the regime N≳dd. We also prove a partition principle showing
that every partition of [0,1]d combined with a jittered sampling construction
gives rise to a set whose expected squared L2-discrepancy is smaller than that
of purely random points.'
acknowledgement: We are grateful to the referee whose suggestions greatly improved
the quality and clarity of the exposition.
article_processing_charge: No
arxiv: 1
author:
- first_name: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
- first_name: Stefan
full_name: Steinerberger, Stefan
last_name: Steinerberger
citation:
ama: Pausinger F, Steinerberger S. On the discrepancy of jittered sampling. Journal
of Complexity. 2016;33:199-216. doi:10.1016/j.jco.2015.11.003
apa: Pausinger, F., & Steinerberger, S. (2016). On the discrepancy of jittered
sampling. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.11.003
chicago: Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered
Sampling.” Journal of Complexity. Academic Press, 2016. https://doi.org/10.1016/j.jco.2015.11.003.
ieee: F. Pausinger and S. Steinerberger, “On the discrepancy of jittered sampling,”
Journal of Complexity, vol. 33. Academic Press, pp. 199–216, 2016.
ista: Pausinger F, Steinerberger S. 2016. On the discrepancy of jittered sampling.
Journal of Complexity. 33, 199–216.
mla: Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered
Sampling.” Journal of Complexity, vol. 33, Academic Press, 2016, pp. 199–216,
doi:10.1016/j.jco.2015.11.003.
short: F. Pausinger, S. Steinerberger, Journal of Complexity 33 (2016) 199–216.
date_created: 2018-12-11T11:53:03Z
date_published: 2016-04-01T00:00:00Z
date_updated: 2025-09-18T10:57:52Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jco.2015.11.003
external_id:
arxiv:
- '1510.00251'
isi:
- '000370090400011'
intvolume: ' 33'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1510.00251
month: '04'
oa: 1
oa_version: Submitted Version
page: 199 - 216
publication: Journal of Complexity
publication_status: published
publisher: Academic Press
publist_id: '5549'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the discrepancy of jittered sampling
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 33
year: '2016'
...
---
_id: '1662'
abstract:
- lang: eng
text: We introduce a modification of the classic notion of intrinsic volume using
persistence moments of height functions. Evaluating the modified first intrinsic
volume on digital approximations of a compact body with smoothly embedded boundary
in Rn, we prove convergence to the first intrinsic volume of the body as the resolution
of the approximation improves. We have weaker results for the other modified intrinsic
volumes, proving they converge to the corresponding intrinsic volumes of the n-dimensional
unit ball.
acknowledgement: "This research is partially supported by the Toposys project FP7-ICT-318493-STREP,
and by ESF under the ACAT Research Network Programme.\r\nBoth authors thank Anne
Marie Svane for her comments on an early version of this paper. The second author
wishes to thank Eva B. Vedel Jensen and Markus Kiderlen from Aarhus University for
enlightening discussions and their kind hospitality during a visit of their department
in 2014."
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: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
citation:
ama: Edelsbrunner H, Pausinger F. Approximation and convergence of the intrinsic
volume. Advances in Mathematics. 2016;287:674-703. doi:10.1016/j.aim.2015.10.004
apa: Edelsbrunner, H., & Pausinger, F. (2016). Approximation and convergence
of the intrinsic volume. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2015.10.004
chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence
of the Intrinsic Volume.” Advances in Mathematics. Academic Press, 2016.
https://doi.org/10.1016/j.aim.2015.10.004.
ieee: H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic
volume,” Advances in Mathematics, vol. 287. Academic Press, pp. 674–703,
2016.
ista: Edelsbrunner H, Pausinger F. 2016. Approximation and convergence of the intrinsic
volume. Advances in Mathematics. 287, 674–703.
mla: Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence
of the Intrinsic Volume.” Advances in Mathematics, vol. 287, Academic Press,
2016, pp. 674–703, doi:10.1016/j.aim.2015.10.004.
short: H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703.
corr_author: '1'
date_created: 2018-12-11T11:53:20Z
date_published: 2016-01-10T00:00:00Z
date_updated: 2026-04-09T14:26:05Z
day: '10'
ddc:
- '004'
department:
- _id: HeEd
doi: 10.1016/j.aim.2015.10.004
ec_funded: 1
external_id:
isi:
- '000375634100016'
file:
- access_level: open_access
checksum: f8869ec110c35c852ef6a37425374af7
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:12:10Z
date_updated: 2020-07-14T12:45:10Z
file_id: '4928'
file_name: IST-2017-774-v1+1_2016-J-03-FirstIntVolume.pdf
file_size: 248985
relation: main_file
file_date_updated: 2020-07-14T12:45:10Z
has_accepted_license: '1'
intvolume: ' 287'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '01'
oa: 1
oa_version: Published Version
page: 674 - 703
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Advances in Mathematics
publication_status: published
publisher: Academic Press
publist_id: '5488'
pubrep_id: '774'
quality_controlled: '1'
related_material:
record:
- id: '1399'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Approximation and convergence of the intrinsic volume
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 287
year: '2016'
...
---
_id: '5805'
abstract:
- lang: eng
text: Discretization of sphere in the integer space follows a particular discretization
scheme, which, in principle, conforms to some topological model. This eventually
gives rise to interesting topological properties of a discrete spherical surface,
which need to be investigated for its analytical characterization. This paper
presents some novel results on the local topological properties of the naive model
of discrete sphere. They follow from the bijection of each quadraginta octant
of naive sphere with its projection map called f -map on the corresponding functional
plane and from the characterization of certain jumps in the f-map. As an application,
we have shown how these properties can be used in designing an efficient reconstruction
algorithm for a naive spherical surface from an input voxel set when it is sparse
or noisy.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Nabhasmita
full_name: Sen, Nabhasmita
last_name: Sen
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Partha
full_name: Bhowmick, Partha
last_name: Bhowmick
citation:
ama: 'Sen N, Biswas R, Bhowmick P. On some local topological properties of naive
discrete sphere. In: Computational Topology in Image Context. Vol 9667.
Cham: Springer Nature; 2016:253-264. doi:10.1007/978-3-319-39441-1_23'
apa: 'Sen, N., Biswas, R., & Bhowmick, P. (2016). On some local topological
properties of naive discrete sphere. In Computational Topology in Image Context
(Vol. 9667, pp. 253–264). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-39441-1_23'
chicago: 'Sen, Nabhasmita, Ranita Biswas, and Partha Bhowmick. “On Some Local Topological
Properties of Naive Discrete Sphere.” In Computational Topology in Image Context,
9667:253–64. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-39441-1_23.'
ieee: 'N. Sen, R. Biswas, and P. Bhowmick, “On some local topological properties
of naive discrete sphere,” in Computational Topology in Image Context,
vol. 9667, Cham: Springer Nature, 2016, pp. 253–264.'
ista: 'Sen N, Biswas R, Bhowmick P. 2016.On some local topological properties of
naive discrete sphere. In: Computational Topology in Image Context. LNCS, vol.
9667, 253–264.'
mla: Sen, Nabhasmita, et al. “On Some Local Topological Properties of Naive Discrete
Sphere.” Computational Topology in Image Context, vol. 9667, Springer Nature,
2016, pp. 253–64, doi:10.1007/978-3-319-39441-1_23.
short: N. Sen, R. Biswas, P. Bhowmick, in:, Computational Topology in Image Context,
Springer Nature, Cham, 2016, pp. 253–264.
conference:
end_date: 2016-06-17
location: Marseille, France
name: 'CTIC: Computational Topology in Image Context'
start_date: 2016-06-15
date_created: 2019-01-08T20:44:24Z
date_published: 2016-06-02T00:00:00Z
date_updated: 2022-01-28T08:01:22Z
day: '02'
department:
- _id: HeEd
doi: 10.1007/978-3-319-39441-1_23
extern: '1'
intvolume: ' 9667'
language:
- iso: eng
month: '06'
oa_version: None
page: 253-264
place: Cham
publication: Computational Topology in Image Context
publication_identifier:
eisbn:
- 978-3-319-39441-1
eissn:
- 1611-3349
isbn:
- 978-3-319-39440-4
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On some local topological properties of naive discrete sphere
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9667
year: '2016'
...
---
_id: '5806'
abstract:
- lang: eng
text: Although the concept of functional plane for naive plane is studied and reported
in the literature in great detail, no similar study is yet found for naive sphere.
This article exposes the first study in this line, opening up further prospects
of analyzing the topological properties of sphere in the discrete space. We show
that each quadraginta octant Q of a naive sphere forms a bijection with its projected
pixel set on a unique coordinate plane, which thereby serves as the functional
plane of Q, and hence gives rise to merely mono-jumps during back projection.
The other two coordinate planes serve as para-functional and dia-functional planes
for Q, as the former is ‘mono-jumping’ but not bijective, whereas the latter holds
neither of the two. Owing to this, the quadraginta octants form symmetry groups
and subgroups with equivalent jump conditions. We also show a potential application
in generating a special class of discrete 3D circles based on back projection
and jump bridging by Steiner voxels. A circle in this class possesses 4-symmetry,
uniqueness, and bounded distance from the underlying real sphere and real plane.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Partha
full_name: Bhowmick, Partha
last_name: Bhowmick
citation:
ama: 'Biswas R, Bhowmick P. On functionality of quadraginta octants of naive sphere
with application to circle drawing. In: Discrete Geometry for Computer Imagery.
Vol 9647. Cham: Springer Nature; 2016:256-267. doi:10.1007/978-3-319-32360-2_20'
apa: 'Biswas, R., & Bhowmick, P. (2016). On functionality of quadraginta octants
of naive sphere with application to circle drawing. In Discrete Geometry for
Computer Imagery (Vol. 9647, pp. 256–267). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-32360-2_20'
chicago: 'Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta
Octants of Naive Sphere with Application to Circle Drawing.” In Discrete Geometry
for Computer Imagery, 9647:256–67. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-32360-2_20.'
ieee: R. Biswas and P. Bhowmick, “On functionality of quadraginta octants of naive
sphere with application to circle drawing,” in Discrete Geometry for Computer
Imagery, Nantes, France, 2016, vol. 9647, pp. 256–267.
ista: 'Biswas R, Bhowmick P. 2016. On functionality of quadraginta octants of naive
sphere with application to circle drawing. Discrete Geometry for Computer Imagery.
DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS,
vol. 9647, 256–267.'
mla: Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants
of Naive Sphere with Application to Circle Drawing.” Discrete Geometry for
Computer Imagery, vol. 9647, Springer Nature, 2016, pp. 256–67, doi:10.1007/978-3-319-32360-2_20.
short: R. Biswas, P. Bhowmick, in:, Discrete Geometry for Computer Imagery, Springer
Nature, Cham, 2016, pp. 256–267.
conference:
end_date: 2016-04-20
location: Nantes, France
name: 'DGCI: International Conference on Discrete Geometry for Computer Imagery'
start_date: 2016-04-18
date_created: 2019-01-08T20:44:37Z
date_published: 2016-04-09T00:00:00Z
date_updated: 2022-01-28T08:10:11Z
day: '09'
department:
- _id: HeEd
doi: 10.1007/978-3-319-32360-2_20
extern: '1'
intvolume: ' 9647'
language:
- iso: eng
month: '04'
oa_version: None
page: 256-267
place: Cham
publication: Discrete Geometry for Computer Imagery
publication_identifier:
eisbn:
- 978-3-319-32360-2
isbn:
- 978-3-319-32359-6
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On functionality of quadraginta octants of naive sphere with application to
circle drawing
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9647
year: '2016'
...
---
_id: '5809'
abstract:
- lang: eng
text: A discrete spherical circle is a topologically well-connected 3D circle in
the integer space, which belongs to a discrete sphere as well as a discrete plane.
It is one of the most important 3D geometric primitives, but has not possibly
yet been studied up to its merit. This paper is a maiden exposition of some of
its elementary properties, which indicates a sense of its profound theoretical
prospects in the framework of digital geometry. We have shown how different types
of discretization can lead to forbidden and admissible classes, when one attempts
to define the discretization of a spherical circle in terms of intersection between
a discrete sphere and a discrete plane. Several fundamental theoretical results
have been presented, the algorithm for construction of discrete spherical circles
has been discussed, and some test results have been furnished to demonstrate its
practicality and usefulness.
article_processing_charge: No
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Partha
full_name: Bhowmick, Partha
last_name: Bhowmick
- first_name: Valentin E.
full_name: Brimkov, Valentin E.
last_name: Brimkov
citation:
ama: 'Biswas R, Bhowmick P, Brimkov VE. On the connectivity and smoothness of discrete
spherical circles. In: Combinatorial Image Analysis. Vol 9448. Cham: Springer
Nature; 2016:86-100. doi:10.1007/978-3-319-26145-4_7'
apa: 'Biswas, R., Bhowmick, P., & Brimkov, V. E. (2016). On the connectivity
and smoothness of discrete spherical circles. In Combinatorial image analysis
(Vol. 9448, pp. 86–100). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-26145-4_7'
chicago: 'Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Connectivity
and Smoothness of Discrete Spherical Circles.” In Combinatorial Image Analysis,
9448:86–100. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-26145-4_7.'
ieee: 'R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the connectivity and smoothness
of discrete spherical circles,” in Combinatorial image analysis, vol. 9448,
Cham: Springer Nature, 2016, pp. 86–100.'
ista: 'Biswas R, Bhowmick P, Brimkov VE. 2016.On the connectivity and smoothness
of discrete spherical circles. In: Combinatorial image analysis. vol. 9448, 86–100.'
mla: Biswas, Ranita, et al. “On the Connectivity and Smoothness of Discrete Spherical
Circles.” Combinatorial Image Analysis, vol. 9448, Springer Nature, 2016,
pp. 86–100, doi:10.1007/978-3-319-26145-4_7.
short: R. Biswas, P. Bhowmick, V.E. Brimkov, in:, Combinatorial Image Analysis,
Springer Nature, Cham, 2016, pp. 86–100.
conference:
end_date: 2015-11-27
location: Kolkata, India
name: 'IWCIA: International Workshop on Combinatorial Image Analysis'
start_date: 2015-11-24
date_created: 2019-01-08T20:45:19Z
date_published: 2016-01-06T00:00:00Z
date_updated: 2022-01-28T08:13:03Z
day: '06'
department:
- _id: HeEd
doi: 10.1007/978-3-319-26145-4_7
extern: '1'
intvolume: ' 9448'
language:
- iso: eng
month: '01'
oa_version: None
page: 86-100
place: Cham
publication: Combinatorial image analysis
publication_identifier:
eisbn:
- 978-3-319-26145-4
eissn:
- 1611-3349
isbn:
- 978-3-319-26144-7
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On the connectivity and smoothness of discrete spherical circles
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9448
year: '2016'
...
---
OA_place: publisher
_id: '1399'
abstract:
- lang: eng
text: This thesis is concerned with the computation and approximation of intrinsic
volumes. Given a smooth body M and a certain digital approximation of it, we develop
algorithms to approximate various intrinsic volumes of M using only measurements
taken from its digital approximations. The crucial idea behind our novel algorithms
is to link the recent theory of persistent homology to the theory of intrinsic
volumes via the Crofton formula from integral geometry and, in particular, via
Euler characteristic computations. Our main contributions are a multigrid convergent
digital algorithm to compute the first intrinsic volume of a solid body in R^n
as well as an appropriate integration pipeline to approximate integral-geometric
integrals defined over the Grassmannian manifold.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
citation:
ama: Pausinger F. On the approximation of intrinsic volumes. 2015.
apa: Pausinger, F. (2015). On the approximation of intrinsic volumes. Institute
of Science and Technology Austria.
chicago: Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute
of Science and Technology Austria, 2015.
ieee: F. Pausinger, “On the approximation of intrinsic volumes,” Institute of Science
and Technology Austria, 2015.
ista: Pausinger F. 2015. On the approximation of intrinsic volumes. Institute of
Science and Technology Austria.
mla: Pausinger, Florian. On the Approximation of Intrinsic Volumes. Institute
of Science and Technology Austria, 2015.
short: F. Pausinger, On the Approximation of Intrinsic Volumes, Institute of Science
and Technology Austria, 2015.
corr_author: '1'
date_created: 2018-12-11T11:51:48Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2026-04-16T10:09:04Z
day: '01'
degree_awarded: PhD
department:
- _id: HeEd
language:
- iso: eng
month: '06'
oa_version: None
page: '144'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
publist_id: '5808'
related_material:
record:
- id: '1662'
relation: part_of_dissertation
status: public
- id: '1792'
relation: part_of_dissertation
status: public
- id: '2255'
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: On the approximation of intrinsic volumes
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2015'
...
---
_id: '1424'
abstract:
- lang: eng
text: We consider the problem of statistical computations with persistence diagrams,
a summary representation of topological features in data. These diagrams encode
persistent homology, a widely used invariant in topological data analysis. While
several avenues towards a statistical treatment of the diagrams have been explored
recently, we follow an alternative route that is motivated by the success of methods
based on the embedding of probability measures into reproducing kernel Hilbert
spaces. In fact, a positive definite kernel on persistence diagrams has recently
been proposed, connecting persistent homology to popular kernel-based learning
techniques such as support vector machines. However, important properties of that
kernel enabling a principled use in the context of probability measure embeddings
remain to be explored. Our contribution is to close this gap by proving universality
of a variant of the original kernel, and to demonstrate its effective use in twosample
hypothesis testing on synthetic as well as real-world data.
acknowledgement: This work was partially supported by the Austrian Science FUnd, project
no. KLI 00012.
alternative_title:
- Advances in Neural Information Processing Systems
article_processing_charge: No
author:
- first_name: Roland
full_name: Kwitt, Roland
last_name: Kwitt
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Marc
full_name: Niethammer, Marc
last_name: Niethammer
- first_name: Weili
full_name: Lin, Weili
last_name: Lin
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
citation:
ama: 'Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. Statistical topological data
analysis-A kernel perspective. In: Vol 28. Neural Information Processing Systems
Foundation; 2015:3070-3078.'
apa: 'Kwitt, R., Huber, S., Niethammer, M., Lin, W., & Bauer, U. (2015). Statistical
topological data analysis-A kernel perspective (Vol. 28, pp. 3070–3078). Presented
at the NIPS: Neural Information Processing Systems, Montreal, Canada: Neural Information
Processing Systems Foundation.'
chicago: Kwitt, Roland, Stefan Huber, Marc Niethammer, Weili Lin, and Ulrich Bauer.
“Statistical Topological Data Analysis-A Kernel Perspective,” 28:3070–78. Neural
Information Processing Systems Foundation, 2015.
ieee: 'R. Kwitt, S. Huber, M. Niethammer, W. Lin, and U. Bauer, “Statistical topological
data analysis-A kernel perspective,” presented at the NIPS: Neural Information
Processing Systems, Montreal, Canada, 2015, vol. 28, pp. 3070–3078.'
ista: 'Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. 2015. Statistical topological
data analysis-A kernel perspective. NIPS: Neural Information Processing Systems,
Advances in Neural Information Processing Systems, vol. 28, 3070–3078.'
mla: Kwitt, Roland, et al. Statistical Topological Data Analysis-A Kernel Perspective.
Vol. 28, Neural Information Processing Systems Foundation, 2015, pp. 3070–78.
short: R. Kwitt, S. Huber, M. Niethammer, W. Lin, U. Bauer, in:, Neural Information
Processing Systems Foundation, 2015, pp. 3070–3078.
conference:
end_date: 2015-12-12
location: Montreal, Canada
name: 'NIPS: Neural Information Processing Systems'
start_date: 2015-12-07
date_created: 2018-12-11T11:51:56Z
date_published: 2015-12-01T00:00:00Z
date_updated: 2025-06-03T11:41:36Z
day: '01'
department:
- _id: HeEd
intvolume: ' 28'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://papers.nips.cc/paper/5887-statistical-topological-data-analysis-a-kernel-perspective
month: '12'
oa: 1
oa_version: Submitted Version
page: 3070 - 3078
publication_status: published
publisher: Neural Information Processing Systems Foundation
publist_id: '5782'
quality_controlled: '1'
status: public
title: Statistical topological data analysis-A kernel perspective
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2015'
...
---
_id: '1483'
abstract:
- lang: eng
text: Topological data analysis offers a rich source of valuable information to
study vision problems. Yet, so far we lack a theoretically sound connection to
popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In
this work, we establish such a connection by designing a multi-scale kernel for
persistence diagrams, a stable summary representation of topological features
in data. We show that this kernel is positive definite and prove its stability
with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets
for 3D shape classification/retrieval and texture recognition show considerable
performance gains of the proposed method compared to an alternative approach that
is based on the recently introduced persistence landscapes.
article_processing_charge: No
arxiv: 1
author:
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Roland
full_name: Kwitt, Roland
last_name: Kwitt
citation:
ama: 'Reininghaus J, Huber S, Bauer U, Kwitt R. A stable multi-scale kernel for
topological machine learning. In: IEEE; 2015:4741-4748. doi:10.1109/CVPR.2015.7299106'
apa: 'Reininghaus, J., Huber, S., Bauer, U., & Kwitt, R. (2015). A stable multi-scale
kernel for topological machine learning (pp. 4741–4748). Presented at the CVPR:
Computer Vision and Pattern Recognition, Boston, MA, USA: IEEE. https://doi.org/10.1109/CVPR.2015.7299106'
chicago: Reininghaus, Jan, Stefan Huber, Ulrich Bauer, and Roland Kwitt. “A Stable
Multi-Scale Kernel for Topological Machine Learning,” 4741–48. IEEE, 2015. https://doi.org/10.1109/CVPR.2015.7299106.
ieee: 'J. Reininghaus, S. Huber, U. Bauer, and R. Kwitt, “A stable multi-scale kernel
for topological machine learning,” presented at the CVPR: Computer Vision and
Pattern Recognition, Boston, MA, USA, 2015, pp. 4741–4748.'
ista: 'Reininghaus J, Huber S, Bauer U, Kwitt R. 2015. A stable multi-scale kernel
for topological machine learning. CVPR: Computer Vision and Pattern Recognition,
4741–4748.'
mla: Reininghaus, Jan, et al. A Stable Multi-Scale Kernel for Topological Machine
Learning. IEEE, 2015, pp. 4741–48, doi:10.1109/CVPR.2015.7299106.
short: J. Reininghaus, S. Huber, U. Bauer, R. Kwitt, in:, IEEE, 2015, pp. 4741–4748.
conference:
end_date: 2015-06-12
location: Boston, MA, USA
name: 'CVPR: Computer Vision and Pattern Recognition'
start_date: 2015-06-07
date_created: 2018-12-11T11:52:17Z
date_published: 2015-10-14T00:00:00Z
date_updated: 2025-06-11T06:37:43Z
day: '14'
department:
- _id: HeEd
doi: 10.1109/CVPR.2015.7299106
external_id:
arxiv:
- '1412.6821'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1412.6821
month: '10'
oa: 1
oa_version: Preprint
page: 4741 - 4748
publication_identifier:
eisbn:
- '978-1-4673-6964-0 '
publication_status: published
publisher: IEEE
publist_id: '5709'
scopus_import: '1'
status: public
title: A stable multi-scale kernel for topological machine learning
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2015'
...
---
_id: '1495'
abstract:
- lang: eng
text: 'Motivated by biological questions, we study configurations of equal-sized
disks in the Euclidean plane that neither pack nor cover. Measuring the quality
by the probability that a random point lies in exactly one disk, we show that
the regular hexagonal grid gives the maximum among lattice configurations. '
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: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
- first_name: Vitaliy
full_name: Kurlin, Vitaliy
last_name: Kurlin
citation:
ama: 'Edelsbrunner H, Iglesias Ham M, Kurlin V. Relaxed disk packing. In: Proceedings
of the 27th Canadian Conference on Computational Geometry. Vol 2015-August.
Queen’s University; 2015:128-135.'
apa: 'Edelsbrunner, H., Iglesias Ham, M., & Kurlin, V. (2015). Relaxed disk
packing. In Proceedings of the 27th Canadian Conference on Computational Geometry
(Vol. 2015–August, pp. 128–135). Ontario, Canada: Queen’s University.'
chicago: Edelsbrunner, Herbert, Mabel Iglesias Ham, and Vitaliy Kurlin. “Relaxed
Disk Packing.” In Proceedings of the 27th Canadian Conference on Computational
Geometry, 2015–August:128–35. Queen’s University, 2015.
ieee: H. Edelsbrunner, M. Iglesias Ham, and V. Kurlin, “Relaxed disk packing,” in
Proceedings of the 27th Canadian Conference on Computational Geometry,
Ontario, Canada, 2015, vol. 2015–August, pp. 128–135.
ista: 'Edelsbrunner H, Iglesias Ham M, Kurlin V. 2015. Relaxed disk packing. Proceedings
of the 27th Canadian Conference on Computational Geometry. CCCG: Canadian Conference
on Computational Geometry vol. 2015–August, 128–135.'
mla: Edelsbrunner, Herbert, et al. “Relaxed Disk Packing.” Proceedings of the
27th Canadian Conference on Computational Geometry, vol. 2015–August, Queen’s
University, 2015, pp. 128–35.
short: H. Edelsbrunner, M. Iglesias Ham, V. Kurlin, in:, Proceedings of the 27th
Canadian Conference on Computational Geometry, Queen’s University, 2015, pp. 128–135.
conference:
end_date: 2015-08-12
location: Ontario, Canada
name: 'CCCG: Canadian Conference on Computational Geometry'
start_date: 2015-08-10
date_created: 2018-12-11T11:52:21Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2025-06-11T06:38:01Z
day: '01'
department:
- _id: HeEd
ec_funded: 1
external_id:
arxiv:
- '1505.03402'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1505.03402
month: '08'
oa: 1
oa_version: Submitted Version
page: 128-135
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the 27th Canadian Conference on Computational Geometry
publication_status: published
publisher: Queen's University
publist_id: '5684'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Relaxed disk packing
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2015-August
year: '2015'
...
---
_id: '1510'
abstract:
- lang: eng
text: 'The concept of well group in a special but important case captures homological
properties of the zero set of a continuous map f from K to R^n on a compact space
K that are invariant with respect to perturbations of f. The perturbations are
arbitrary continuous maps within L_infty distance r from f for a given r >
0. The main drawback of the approach is that the computability of well groups
was shown only when dim K = n or n = 1. Our contribution to the theory of well
groups is twofold: on the one hand we improve on the computability issue, but
on the other hand we present a range of examples where the well groups are incomplete
invariants, that is, fail to capture certain important robust properties of the
zero set. For the first part, we identify a computable subgroup of the well group
that is obtained by cap product with the pullback of the orientation of R^n by
f. In other words, well groups can be algorithmically approximated from below.
When f is smooth and dim K < 2n-2, our approximation of the (dim K-n)th well
group is exact. For the second part, we find examples of maps f, f'' from K to
R^n with all well groups isomorphic but whose perturbations have different zero
sets. We discuss on a possible replacement of the well groups of vector valued
maps by an invariant of a better descriptive power and computability status. '
alternative_title:
- LIPIcs
author:
- first_name: Peter
full_name: Franek, Peter
id: 473294AE-F248-11E8-B48F-1D18A9856A87
last_name: Franek
orcid: 0000-0001-8878-8397
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
citation:
ama: 'Franek P, Krcál M. On computability and triviality of well groups. In: Vol
34. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2015:842-856. doi:10.4230/LIPIcs.SOCG.2015.842'
apa: 'Franek, P., & Krcál, M. (2015). On computability and triviality of well
groups (Vol. 34, pp. 842–856). Presented at the SoCG: Symposium on Computational
Geometry, Eindhoven, Netherlands: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.SOCG.2015.842'
chicago: Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well
Groups,” 34:842–56. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. https://doi.org/10.4230/LIPIcs.SOCG.2015.842.
ieee: 'P. Franek and M. Krcál, “On computability and triviality of well groups,”
presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands,
2015, vol. 34, pp. 842–856.'
ista: 'Franek P, Krcál M. 2015. On computability and triviality of well groups.
SoCG: Symposium on Computational Geometry, LIPIcs, vol. 34, 842–856.'
mla: Franek, Peter, and Marek Krcál. On Computability and Triviality of Well
Groups. Vol. 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015,
pp. 842–56, doi:10.4230/LIPIcs.SOCG.2015.842.
short: P. Franek, M. Krcál, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2015, pp. 842–856.
conference:
end_date: 2015-06-25
location: Eindhoven, Netherlands
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2015-06-22
date_created: 2018-12-11T11:52:26Z
date_published: 2015-06-11T00:00:00Z
date_updated: 2025-09-18T14:30:52Z
day: '11'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
doi: 10.4230/LIPIcs.SOCG.2015.842
ec_funded: 1
file:
- access_level: open_access
checksum: 49eb5021caafaabe5356c65b9c5f8c9c
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:13:19Z
date_updated: 2020-07-14T12:44:59Z
file_id: '5001'
file_name: IST-2016-503-v1+1_32.pdf
file_size: 623563
relation: main_file
file_date_updated: 2020-07-14T12:44:59Z
has_accepted_license: '1'
intvolume: ' 34'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 842 - 856
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '5667'
pubrep_id: '503'
quality_controlled: '1'
related_material:
record:
- id: '1408'
relation: later_version
status: public
scopus_import: 1
status: public
title: On computability and triviality of well groups
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: 34
year: '2015'
...
---
_id: '1531'
abstract:
- lang: eng
text: The Heat Kernel Signature (HKS) is a scalar quantity which is derived from
the heat kernel of a given shape. Due to its robustness, isometry invariance,
and multiscale nature, it has been successfully applied in many geometric applications.
From a more general point of view, the HKS can be considered as a descriptor of
the metric of a Riemannian manifold. Given a symmetric positive definite tensor
field we may interpret it as the metric of some Riemannian manifold and thereby
apply the HKS to visualize and analyze the given tensor data. In this paper, we
propose a generalization of this approach that enables the treatment of indefinite
tensor fields, like the stress tensor, by interpreting them as a generator of
a positive definite tensor field. To investigate the usefulness of this approach
we consider the stress tensor from the two-point-load model example and from a
mechanical work piece.
alternative_title:
- Mathematics and Visualization
article_processing_charge: No
author:
- first_name: Valentin
full_name: Zobel, Valentin
last_name: Zobel
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
citation:
ama: 'Zobel V, Reininghaus J, Hotz I. Visualizing symmetric indefinite 2D tensor
fields using The Heat Kernel Signature. In: Hotz I, Schultz T, eds. Visualization
and Processing of Higher Order Descriptors for Multi-Valued Data. Vol 40.
1st ed. Springer; 2015:257-267. doi:10.1007/978-3-319-15090-1_13'
apa: Zobel, V., Reininghaus, J., & Hotz, I. (2015). Visualizing symmetric indefinite
2D tensor fields using The Heat Kernel Signature. In I. Hotz & T. Schultz
(Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued
Data (1st ed., Vol. 40, pp. 257–267). Springer. https://doi.org/10.1007/978-3-319-15090-1_13
chicago: Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualizing Symmetric
Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” In Visualization
and Processing of Higher Order Descriptors for Multi-Valued Data, edited by
Ingrid Hotz and Thomas Schultz, 1st ed., 40:257–67. Springer, 2015. https://doi.org/10.1007/978-3-319-15090-1_13.
ieee: V. Zobel, J. Reininghaus, and I. Hotz, “Visualizing symmetric indefinite 2D
tensor fields using The Heat Kernel Signature,” in Visualization and Processing
of Higher Order Descriptors for Multi-Valued Data, 1st ed., vol. 40, I. Hotz
and T. Schultz, Eds. Springer, 2015, pp. 257–267.
ista: 'Zobel V, Reininghaus J, Hotz I. 2015.Visualizing symmetric indefinite 2D
tensor fields using The Heat Kernel Signature. In: Visualization and Processing
of Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization,
vol. 40, 257–267.'
mla: Zobel, Valentin, et al. “Visualizing Symmetric Indefinite 2D Tensor Fields
Using The Heat Kernel Signature.” Visualization and Processing of Higher Order
Descriptors for Multi-Valued Data, edited by Ingrid Hotz and Thomas Schultz,
1st ed., vol. 40, Springer, 2015, pp. 257–67, doi:10.1007/978-3-319-15090-1_13.
short: V. Zobel, J. Reininghaus, I. Hotz, in:, I. Hotz, T. Schultz (Eds.), Visualization
and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., Springer,
2015, pp. 257–267.
date_created: 2018-12-11T11:52:33Z
date_published: 2015-01-01T00:00:00Z
date_updated: 2022-06-10T09:50:14Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-319-15090-1_13
edition: '1'
editor:
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
- first_name: Thomas
full_name: Schultz, Thomas
last_name: Schultz
intvolume: ' 40'
language:
- iso: eng
month: '01'
oa_version: None
page: 257 - 267
publication: Visualization and Processing of Higher Order Descriptors for Multi-Valued
Data
publication_identifier:
isbn:
- 978-3-319-15089-5
publication_status: published
publisher: Springer
publist_id: '5640'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 40
year: '2015'
...
---
_id: '1555'
abstract:
- lang: eng
text: We show that incorporating spatial dispersal of individuals into a simple
vaccination epidemic model may give rise to a model that exhibits rich dynamical
behavior. Using an SIVS (susceptible-infected-vaccinated-susceptible) model as
a basis, we describe the spread of an infectious disease in a population split
into two regions. In each subpopulation, both forward and backward bifurcations
can occur. This implies that for disconnected regions the two-patch system may
admit several steady states. We consider traveling between the regions and investigate
the impact of spatial dispersal of individuals on the model dynamics. We establish
conditions for the existence of multiple nontrivial steady states in the system,
and we study the structure of the equilibria. The mathematical analysis reveals
an unusually rich dynamical behavior, not normally found in the simple epidemic
models. In addition to the disease-free equilibrium, eight endemic equilibria
emerge from backward transcritical and saddle-node bifurcation points, forming
an interesting bifurcation diagram. Stability of steady states, their bifurcations,
and the global dynamics are investigated with analytical tools, numerical simulations,
and rigorous set-oriented numerical computations.
acknowledgement: Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg,
Austria (pawel.pilarczyk@ist.ac.at). This author’s work was partially supported
by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework
Programme (FP7/2007-2013) under REA grant agreement 622033, by Fundo Europeu de
Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de
Competitividade (POFC), by the Portuguese national funds through Funda ̧caoparaaCiˆencia
e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645
(ref. FCT PTDC/MAT/098871/2008), and by European Research Council through StG 259559
in the framework of the EPIDELAY project.
article_processing_charge: No
article_type: original
author:
- first_name: Diána
full_name: Knipl, Diána
last_name: Knipl
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
- first_name: Gergely
full_name: Röst, Gergely
last_name: Röst
citation:
ama: Knipl D, Pilarczyk P, Röst G. Rich bifurcation structure in a two patch vaccination
model. SIAM Journal on Applied Dynamical Systems. 2015;14(2):980-1017.
doi:10.1137/140993934
apa: Knipl, D., Pilarczyk, P., & Röst, G. (2015). Rich bifurcation structure
in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems.
Society for Industrial and Applied Mathematics . https://doi.org/10.1137/140993934
chicago: Knipl, Diána, Pawel Pilarczyk, and Gergely Röst. “Rich Bifurcation Structure
in a Two Patch Vaccination Model.” SIAM Journal on Applied Dynamical Systems.
Society for Industrial and Applied Mathematics , 2015. https://doi.org/10.1137/140993934.
ieee: D. Knipl, P. Pilarczyk, and G. Röst, “Rich bifurcation structure in a two
patch vaccination model,” SIAM Journal on Applied Dynamical Systems, vol.
14, no. 2. Society for Industrial and Applied Mathematics , pp. 980–1017, 2015.
ista: Knipl D, Pilarczyk P, Röst G. 2015. Rich bifurcation structure in a two patch
vaccination model. SIAM Journal on Applied Dynamical Systems. 14(2), 980–1017.
mla: Knipl, Diána, et al. “Rich Bifurcation Structure in a Two Patch Vaccination
Model.” SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2, Society
for Industrial and Applied Mathematics , 2015, pp. 980–1017, doi:10.1137/140993934.
short: D. Knipl, P. Pilarczyk, G. Röst, SIAM Journal on Applied Dynamical Systems
14 (2015) 980–1017.
date_created: 2018-12-11T11:52:42Z
date_published: 2015-01-01T00:00:00Z
date_updated: 2025-09-23T10:37:17Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1137/140993934
ec_funded: 1
external_id:
isi:
- '000357310400015'
intvolume: ' 14'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://discovery.ucl.ac.uk/1473750/1/99393.pdf
month: '01'
oa: 1
oa_version: Published Version
page: 980 - 1017
project:
- _id: 255F06BE-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '622033'
name: Persistent Homology - Images, Data and Maps
publication: SIAM Journal on Applied Dynamical Systems
publication_identifier:
eissn:
- 1536-0040
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '5616'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Rich bifurcation structure in a two patch vaccination model
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 14
year: '2015'
...
---
_id: '1563'
abstract:
- lang: eng
text: For a given self-map $f$ of $M$, a closed smooth connected and simply-connected
manifold of dimension $m\geq 4$, we provide an algorithm for estimating the values
of the topological invariant $D^m_r[f]$, which equals the minimal number of $r$-periodic
points in the smooth homotopy class of $f$. Our results are based on the combinatorial
scheme for computing $D^m_r[f]$ introduced by G. Graff and J. Jezierski [J. Fixed
Point Theory Appl. 13 (2013), 63-84]. An open-source implementation of the algorithm
programmed in C++ is publicly available at {\tt http://www.pawelpilarczyk.com/combtop/}.
author:
- first_name: Grzegorz
full_name: Graff, Grzegorz
last_name: Graff
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
citation:
ama: Graff G, Pilarczyk P. An algorithmic approach to estimating the minimal number
of periodic points for smooth self-maps of simply-connected manifolds. Topological
Methods in Nonlinear Analysis. 2015;45(1):273-286. doi:10.12775/TMNA.2015.014
apa: Graff, G., & Pilarczyk, P. (2015). An algorithmic approach to estimating
the minimal number of periodic points for smooth self-maps of simply-connected
manifolds. Topological Methods in Nonlinear Analysis. Juliusz Schauder
Center for Nonlinear Studies. https://doi.org/10.12775/TMNA.2015.014
chicago: Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating
the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected
Manifolds.” Topological Methods in Nonlinear Analysis. Juliusz Schauder
Center for Nonlinear Studies, 2015. https://doi.org/10.12775/TMNA.2015.014.
ieee: G. Graff and P. Pilarczyk, “An algorithmic approach to estimating the minimal
number of periodic points for smooth self-maps of simply-connected manifolds,”
Topological Methods in Nonlinear Analysis, vol. 45, no. 1. Juliusz Schauder
Center for Nonlinear Studies, pp. 273–286, 2015.
ista: Graff G, Pilarczyk P. 2015. An algorithmic approach to estimating the minimal
number of periodic points for smooth self-maps of simply-connected manifolds.
Topological Methods in Nonlinear Analysis. 45(1), 273–286.
mla: Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating
the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected
Manifolds.” Topological Methods in Nonlinear Analysis, vol. 45, no. 1,
Juliusz Schauder Center for Nonlinear Studies, 2015, pp. 273–86, doi:10.12775/TMNA.2015.014.
short: G. Graff, P. Pilarczyk, Topological Methods in Nonlinear Analysis 45 (2015)
273–286.
date_created: 2018-12-11T11:52:44Z
date_published: 2015-03-01T00:00:00Z
date_updated: 2021-01-12T06:51:37Z
day: '01'
department:
- _id: HeEd
doi: 10.12775/TMNA.2015.014
intvolume: ' 45'
issue: '1'
language:
- iso: eng
month: '03'
oa_version: None
page: 273 - 286
publication: Topological Methods in Nonlinear Analysis
publication_status: published
publisher: Juliusz Schauder Center for Nonlinear Studies
publist_id: '5608'
quality_controlled: '1'
scopus_import: 1
status: public
title: An algorithmic approach to estimating the minimal number of periodic points
for smooth self-maps of simply-connected manifolds
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 45
year: '2015'
...
---
_id: '1567'
abstract:
- lang: eng
text: My personal journey to the fascinating world of geometric forms started more
than 30 years ago with the invention of alpha shapes in the plane. It took about
10 years before we generalized the concept to higher dimensions, we produced working
software with a graphics interface for the three-dimensional case. At the same
time, we added homology to the computations. Needless to say that this foreshadowed
the inception of persistent homology, because it suggested the study of filtrations
to capture the scale of a shape or data set. Importantly, this method has fast
algorithms. The arguably most useful result on persistent homology is the stability
of its diagrams under perturbations.
alternative_title:
- LNCS
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
citation:
ama: 'Edelsbrunner H. Shape, homology, persistence, and stability. In: 23rd International
Symposium. Vol 9411. Springer Nature; 2015.'
apa: 'Edelsbrunner, H. (2015). Shape, homology, persistence, and stability. In 23rd
International Symposium (Vol. 9411). Los Angeles, CA, United States: Springer
Nature.'
chicago: Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” In
23rd International Symposium, Vol. 9411. Springer Nature, 2015.
ieee: H. Edelsbrunner, “Shape, homology, persistence, and stability,” in 23rd
International Symposium, Los Angeles, CA, United States, 2015, vol. 9411.
ista: 'Edelsbrunner H. 2015. Shape, homology, persistence, and stability. 23rd International
Symposium. GD: Graph Drawing and Network Visualization, LNCS, vol. 9411.'
mla: Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” 23rd
International Symposium, vol. 9411, Springer Nature, 2015.
short: H. Edelsbrunner, in:, 23rd International Symposium, Springer Nature, 2015.
conference:
end_date: 2015-09-26
location: Los Angeles, CA, United States
name: 'GD: Graph Drawing and Network Visualization'
start_date: 2015-09-24
date_created: 2018-12-11T11:52:46Z
date_published: 2015-01-01T00:00:00Z
date_updated: 2022-01-28T08:25:00Z
day: '01'
department:
- _id: HeEd
intvolume: ' 9411'
language:
- iso: eng
month: '01'
oa_version: None
publication: 23rd International Symposium
publication_status: published
publisher: Springer Nature
publist_id: '5604'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Shape, homology, persistence, and stability
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9411
year: '2015'
...
---
_id: '1568'
abstract:
- lang: eng
text: Aiming at the automatic diagnosis of tumors from narrow band imaging (NBI)
magnifying endoscopy (ME) images of the stomach, we combine methods from image
processing, computational topology, and machine learning to classify patterns
into normal, tubular, vessel. Training the algorithm on a small number of images
of each type, we achieve a high rate of correct classifications. The analysis
of the learning algorithm reveals that a handful of geometric and topological
features are responsible for the overwhelming majority of decisions.
acknowledgement: This research is supported by the project No. 477 of P.G. Demidov
Yaroslavl State University within State Assignment for Research.
article_processing_charge: No
author:
- first_name: Olga
full_name: Dunaeva, Olga
last_name: Dunaeva
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Anton
full_name: Lukyanov, Anton
last_name: Lukyanov
- first_name: Michael
full_name: Machin, Michael
last_name: Machin
- first_name: Daria
full_name: Malkova, Daria
last_name: Malkova
citation:
ama: 'Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. The classification
of endoscopy images with persistent homology. In: Proceedings - 16th International
Symposium on Symbolic and Numeric Algorithms for Scientific Computing. IEEE;
2015:7034731. doi:10.1109/SYNASC.2014.81'
apa: 'Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., & Malkova, D.
(2015). The classification of endoscopy images with persistent homology. In Proceedings
- 16th International Symposium on Symbolic and Numeric Algorithms for Scientific
Computing (p. 7034731). Timisoara, Romania: IEEE. https://doi.org/10.1109/SYNASC.2014.81'
chicago: Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, and
Daria Malkova. “The Classification of Endoscopy Images with Persistent Homology.”
In Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms
for Scientific Computing, 7034731. IEEE, 2015. https://doi.org/10.1109/SYNASC.2014.81.
ieee: O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, and D. Malkova, “The
classification of endoscopy images with persistent homology,” in Proceedings
- 16th International Symposium on Symbolic and Numeric Algorithms for Scientific
Computing, Timisoara, Romania, 2015, p. 7034731.
ista: 'Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. 2015. The classification
of endoscopy images with persistent homology. Proceedings - 16th International
Symposium on Symbolic and Numeric Algorithms for Scientific Computing. SYNASC:
Symbolic and Numeric Algorithms for Scientific Computing, 7034731.'
mla: Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent
Homology.” Proceedings - 16th International Symposium on Symbolic and Numeric
Algorithms for Scientific Computing, IEEE, 2015, p. 7034731, doi:10.1109/SYNASC.2014.81.
short: O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, in:, Proceedings
- 16th International Symposium on Symbolic and Numeric Algorithms for Scientific
Computing, IEEE, 2015, p. 7034731.
conference:
end_date: 2014-09-25
location: Timisoara, Romania
name: 'SYNASC: Symbolic and Numeric Algorithms for Scientific Computing'
start_date: 2014-09-22
date_created: 2018-12-11T11:52:46Z
date_published: 2015-02-05T00:00:00Z
date_updated: 2025-09-23T13:44:17Z
day: '05'
department:
- _id: HeEd
doi: 10.1109/SYNASC.2014.81
external_id:
isi:
- '000366596600074'
isi: 1
language:
- iso: eng
month: '02'
oa_version: None
page: '7034731'
publication: Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms
for Scientific Computing
publication_status: published
publisher: IEEE
publist_id: '5603'
quality_controlled: '1'
related_material:
record:
- id: '1289'
relation: later_version
status: public
scopus_import: '1'
status: public
title: The classification of endoscopy images with persistent homology
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2015'
...
---
_id: '1578'
abstract:
- lang: eng
text: We prove that the dual of the digital Voronoi diagram constructed by flooding
the plane from the data points gives a geometrically and topologically correct
dual triangulation. This provides the proof of correctness for recently developed
GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional
Delaunay triangulations.
acknowledgement: "The research of the second author is partially supported by NSF
under grant DBI-0820624 and by DARPA under grants HR011-05-1-0057 and HR0011-09-006\r\n"
article_processing_charge: No
author:
- first_name: Thanhtung
full_name: Cao, Thanhtung
last_name: Cao
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Tiowseng
full_name: Tan, Tiowseng
last_name: Tan
citation:
ama: Cao T, Edelsbrunner H, Tan T. Triangulations from topologically correct digital
Voronoi diagrams. Computational Geometry. 2015;48(7):507-519. doi:10.1016/j.comgeo.2015.04.001
apa: Cao, T., Edelsbrunner, H., & Tan, T. (2015). Triangulations from topologically
correct digital Voronoi diagrams. Computational Geometry. Elsevier. https://doi.org/10.1016/j.comgeo.2015.04.001
chicago: Cao, Thanhtung, Herbert Edelsbrunner, and Tiowseng Tan. “Triangulations
from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry.
Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.04.001.
ieee: T. Cao, H. Edelsbrunner, and T. Tan, “Triangulations from topologically correct
digital Voronoi diagrams,” Computational Geometry, vol. 48, no. 7. Elsevier,
pp. 507–519, 2015.
ista: Cao T, Edelsbrunner H, Tan T. 2015. Triangulations from topologically correct
digital Voronoi diagrams. Computational Geometry. 48(7), 507–519.
mla: Cao, Thanhtung, et al. “Triangulations from Topologically Correct Digital Voronoi
Diagrams.” Computational Geometry, vol. 48, no. 7, Elsevier, 2015, pp.
507–19, doi:10.1016/j.comgeo.2015.04.001.
short: T. Cao, H. Edelsbrunner, T. Tan, Computational Geometry 48 (2015) 507–519.
date_created: 2018-12-11T11:52:49Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2025-09-29T10:58:50Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2015.04.001
external_id:
isi:
- '000355887700001'
intvolume: ' 48'
isi: 1
issue: '7'
language:
- iso: eng
month: '08'
oa_version: None
page: 507 - 519
publication: Computational Geometry
publication_status: published
publisher: Elsevier
publist_id: '5593'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Triangulations from topologically correct digital Voronoi diagrams
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 48
year: '2015'
...
---
_id: '1582'
abstract:
- lang: eng
text: We investigate weighted straight skeletons from a geometric, graph-theoretical,
and combinatorial point of view. We start with a thorough definition and shed
light on some ambiguity issues in the procedural definition. We investigate the
geometry, combinatorics, and topology of faces and the roof model, and we discuss
in which cases a weighted straight skeleton is connected. Finally, we show that
the weighted straight skeleton of even a simple polygon may be non-planar and
may contain cycles, and we discuss under which restrictions on the weights and/or
the input polygon the weighted straight skeleton still behaves similar to its
unweighted counterpart. In particular, we obtain a non-procedural description
and a linear-time construction algorithm for the straight skeleton of strictly
convex polygons with arbitrary weights.
article_processing_charge: No
author:
- first_name: Therese
full_name: Biedl, Therese
last_name: Biedl
- first_name: Martin
full_name: Held, Martin
last_name: Held
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Dominik
full_name: Kaaser, Dominik
last_name: Kaaser
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
citation:
ama: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Weighted straight skeletons
in the plane. Computational Geometry: Theory and Applications. 2015;48(2):120-133.
doi:10.1016/j.comgeo.2014.08.006'
apa: 'Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Weighted
straight skeletons in the plane. Computational Geometry: Theory and Applications.
Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.006'
chicago: 'Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader.
“Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory
and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.006.'
ieee: 'T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Weighted straight
skeletons in the plane,” Computational Geometry: Theory and Applications,
vol. 48, no. 2. Elsevier, pp. 120–133, 2015.'
ista: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Weighted straight
skeletons in the plane. Computational Geometry: Theory and Applications. 48(2),
120–133.'
mla: 'Biedl, Therese, et al. “Weighted Straight Skeletons in the Plane.” Computational
Geometry: Theory and Applications, vol. 48, no. 2, Elsevier, 2015, pp. 120–33,
doi:10.1016/j.comgeo.2014.08.006.'
short: 'T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry:
Theory and Applications 48 (2015) 120–133.'
date_created: 2018-12-11T11:52:51Z
date_published: 2015-02-01T00:00:00Z
date_updated: 2025-09-29T11:06:26Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2014.08.006
external_id:
isi:
- '000345056700007'
file:
- access_level: open_access
checksum: c1ef67f6ec925e12f73a96b8fe285ab4
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:28Z
date_updated: 2020-07-14T12:45:02Z
file_id: '5215'
file_name: IST-2016-474-v1+1_1-s2.0-S0925772114000807-main.pdf
file_size: 505987
relation: main_file
file_date_updated: 2020-07-14T12:45:02Z
has_accepted_license: '1'
intvolume: ' 48'
isi: 1
issue: '2'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 120 - 133
publication: 'Computational Geometry: Theory and Applications'
publication_status: published
publisher: Elsevier
publist_id: '5589'
pubrep_id: '474'
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record:
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relation: other
status: public
scopus_import: '1'
status: public
title: Weighted straight skeletons in the plane
tmp:
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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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 48
year: '2015'
...
---
_id: '1583'
abstract:
- lang: eng
text: We study the characteristics of straight skeletons of monotone polygonal chains
and use them to devise an algorithm for computing positively weighted straight
skeletons of monotone polygons. Our algorithm runs in O(nlogn) time and O(n) space,
where n denotes the number of vertices of the polygon.
article_processing_charge: No
author:
- first_name: Therese
full_name: Biedl, Therese
last_name: Biedl
- first_name: Martin
full_name: Held, Martin
last_name: Held
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Dominik
full_name: Kaaser, Dominik
last_name: Kaaser
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
citation:
ama: Biedl T, Held M, Huber S, Kaaser D, Palfrader P. A simple algorithm for computing
positively weighted straight skeletons of monotone polygons. Information Processing
Letters. 2015;115(2):243-247. doi:10.1016/j.ipl.2014.09.021
apa: Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). A simple
algorithm for computing positively weighted straight skeletons of monotone polygons.
Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2014.09.021
chicago: Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader.
“A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone
Polygons.” Information Processing Letters. Elsevier, 2015. https://doi.org/10.1016/j.ipl.2014.09.021.
ieee: T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “A simple algorithm
for computing positively weighted straight skeletons of monotone polygons,” Information
Processing Letters, vol. 115, no. 2. Elsevier, pp. 243–247, 2015.
ista: Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. A simple algorithm
for computing positively weighted straight skeletons of monotone polygons. Information
Processing Letters. 115(2), 243–247.
mla: Biedl, Therese, et al. “A Simple Algorithm for Computing Positively Weighted
Straight Skeletons of Monotone Polygons.” Information Processing Letters,
vol. 115, no. 2, Elsevier, 2015, pp. 243–47, doi:10.1016/j.ipl.2014.09.021.
short: T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Information Processing
Letters 115 (2015) 243–247.
date_created: 2018-12-11T11:52:51Z
date_published: 2015-02-01T00:00:00Z
date_updated: 2025-09-22T14:35:14Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.ipl.2014.09.021
external_id:
isi:
- '000346225300034'
file:
- access_level: open_access
checksum: 2779a648610c9b5c86d0b51a62816d23
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:18:45Z
date_updated: 2020-07-14T12:45:03Z
file_id: '5367'
file_name: IST-2016-473-v1+1_1-s2.0-S0020019014001987-main.pdf
file_size: 270137
relation: main_file
file_date_updated: 2020-07-14T12:45:03Z
has_accepted_license: '1'
intvolume: ' 115'
isi: 1
issue: '2'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 243 - 247
publication: Information Processing Letters
publication_status: published
publisher: Elsevier
publist_id: '5588'
pubrep_id: '473'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A simple algorithm for computing positively weighted straight skeletons of
monotone polygons
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 115
year: '2015'
...