---
_id: '1584'
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. Reprint of: Weighted straight
skeletons in the plane. Computational Geometry: Theory and Applications.
2015;48(5):429-442. doi:10.1016/j.comgeo.2015.01.004'
apa: 'Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Reprint
of: Weighted straight skeletons in the plane. Computational Geometry: Theory
and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2015.01.004'
chicago: 'Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader.
“Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry:
Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.01.004.'
ieee: 'T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Reprint of: Weighted
straight skeletons in the plane,” Computational Geometry: Theory and Applications,
vol. 48, no. 5. Elsevier, pp. 429–442, 2015.'
ista: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Reprint of: Weighted
straight skeletons in the plane. Computational Geometry: Theory and Applications.
48(5), 429–442.'
mla: 'Biedl, Therese, et al. “Reprint of: Weighted Straight Skeletons in the Plane.”
Computational Geometry: Theory and Applications, vol. 48, no. 5, Elsevier,
2015, pp. 429–42, doi:10.1016/j.comgeo.2015.01.004.'
short: 'T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry:
Theory and Applications 48 (2015) 429–442.'
date_created: 2018-12-11T11:52:51Z
date_published: 2015-07-01T00:00:00Z
date_updated: 2025-09-29T11:06:25Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2015.01.004
external_id:
isi:
- '000351967400008'
file:
- access_level: open_access
checksum: 5b33719a86f7f4c8e5dc62c1b6893f49
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:17:36Z
date_updated: 2020-07-14T12:45:03Z
file_id: '5292'
file_name: IST-2016-475-v1+1_1-s2.0-S092577211500005X-main.pdf
file_size: 508379
relation: main_file
file_date_updated: 2020-07-14T12:45:03Z
has_accepted_license: '1'
intvolume: ' 48'
isi: 1
issue: '5'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '07'
oa: 1
oa_version: Published Version
page: 429 - 442
publication: 'Computational Geometry: Theory and Applications'
publication_status: published
publisher: Elsevier
publist_id: '5587'
pubrep_id: '475'
quality_controlled: '1'
related_material:
record:
- id: '1582'
relation: other
status: public
scopus_import: '1'
status: public
title: 'Reprint of: Weighted straight skeletons 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 48
year: '2015'
...
---
_id: '1590'
abstract:
- lang: eng
text: 'The straight skeleton of a polygon is the geometric graph obtained by tracing
the vertices during a mitered offsetting process. It is known that the straight
skeleton of a simple polygon is a tree, and one can naturally derive directions
on the edges of the tree from the propagation of the shrinking process. In this
paper, we ask the reverse question: Given a tree with directed edges, can it be
the straight skeleton of a polygon? And if so, can we find a suitable simple polygon?
We answer these questions for all directed trees where the order of edges around
each node is fixed.'
alternative_title:
- LNCS
article_processing_charge: No
arxiv: 1
author:
- first_name: Oswin
full_name: Aichholzer, Oswin
last_name: Aichholzer
- first_name: Therese
full_name: Biedl, Therese
last_name: Biedl
- first_name: Thomas
full_name: Hackl, Thomas
last_name: Hackl
- 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: Peter
full_name: Palfrader, Peter
last_name: Palfrader
- first_name: Birgit
full_name: Vogtenhuber, Birgit
last_name: Vogtenhuber
citation:
ama: 'Aichholzer O, Biedl T, Hackl T, et al. Representing directed trees as straight
skeletons. In: Graph Drawing and Network Visualization. Vol 9411. Springer
Nature; 2015:335-347. doi:10.1007/978-3-319-27261-0_28'
apa: 'Aichholzer, O., Biedl, T., Hackl, T., Held, M., Huber, S., Palfrader, P.,
& Vogtenhuber, B. (2015). Representing directed trees as straight skeletons.
In Graph Drawing and Network Visualization (Vol. 9411, pp. 335–347). Los
Angeles, CA, United States: Springer Nature. https://doi.org/10.1007/978-3-319-27261-0_28'
chicago: Aichholzer, Oswin, Therese Biedl, Thomas Hackl, Martin Held, Stefan Huber,
Peter Palfrader, and Birgit Vogtenhuber. “Representing Directed Trees as Straight
Skeletons.” In Graph Drawing and Network Visualization, 9411:335–47. Springer
Nature, 2015. https://doi.org/10.1007/978-3-319-27261-0_28.
ieee: O. Aichholzer et al., “Representing directed trees as straight skeletons,”
in Graph Drawing and Network Visualization, vol. 9411, Springer Nature,
2015, pp. 335–347.
ista: 'Aichholzer O, Biedl T, Hackl T, Held M, Huber S, Palfrader P, Vogtenhuber
B. 2015.Representing directed trees as straight skeletons. In: Graph Drawing and
Network Visualization. LNCS, vol. 9411, 335–347.'
mla: Aichholzer, Oswin, et al. “Representing Directed Trees as Straight Skeletons.”
Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015,
pp. 335–47, doi:10.1007/978-3-319-27261-0_28.
short: O. Aichholzer, T. Biedl, T. Hackl, M. Held, S. Huber, P. Palfrader, B. Vogtenhuber,
in:, Graph Drawing and Network Visualization, Springer Nature, 2015, pp. 335–347.
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: 2018-12-11T11:52:54Z
date_published: 2015-11-27T00:00:00Z
date_updated: 2025-09-23T10:35:07Z
day: '27'
department:
- _id: HeEd
doi: 10.1007/978-3-319-27261-0_28
external_id:
arxiv:
- '1508.01076'
isi:
- '000373628600028'
intvolume: ' 9411'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1508.01076
month: '11'
oa: 1
oa_version: Preprint
page: 335 - 347
publication: Graph Drawing and Network Visualization
publication_identifier:
eisbn:
- 978-3-319-27261-0
isbn:
- 978-3-319-27260-3
publication_status: published
publisher: Springer Nature
publist_id: '5581'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Representing directed trees as straight skeletons
type: book_chapter
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 9411
year: '2015'
...
---
_id: '1682'
abstract:
- lang: eng
text: 'We study the problem of robust satisfiability of systems of nonlinear equations,
namely, whether for a given continuous function f:K→ ℝn on a finite simplicial
complex K and α > 0, it holds that each function g: K → ℝn such that ||g -
f || ∞ < α, has a root in K. Via a reduction to the extension problem of maps
into a sphere, we particularly show that this problem is decidable in polynomial
time for every fixed n, assuming dimK ≤ 2n - 3. This is a substantial extension
of previous computational applications of topological degree and related concepts
in numerical and interval analysis. Via a reverse reduction, we prove that the
problem is undecidable when dim K > 2n - 2, where the threshold comes from
the stable range in homotopy theory. For the lucidity of our exposition, we focus
on the setting when f is simplexwise linear. Such functions can approximate general
continuous functions, and thus we get approximation schemes and undecidability
of the robust satisfiability in other possible settings.'
article_number: '26'
article_processing_charge: No
arxiv: 1
author:
- first_name: Peter
full_name: Franek, Peter
last_name: Franek
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
citation:
ama: Franek P, Krcál M. Robust satisfiability of systems of equations. Journal
of the ACM. 2015;62(4). doi:10.1145/2751524
apa: Franek, P., & Krcál, M. (2015). Robust satisfiability of systems of equations.
Journal of the ACM. ACM. https://doi.org/10.1145/2751524
chicago: Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.”
Journal of the ACM. ACM, 2015. https://doi.org/10.1145/2751524.
ieee: P. Franek and M. Krcál, “Robust satisfiability of systems of equations,” Journal
of the ACM, vol. 62, no. 4. ACM, 2015.
ista: Franek P, Krcál M. 2015. Robust satisfiability of systems of equations. Journal
of the ACM. 62(4), 26.
mla: Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.”
Journal of the ACM, vol. 62, no. 4, 26, ACM, 2015, doi:10.1145/2751524.
short: P. Franek, M. Krcál, Journal of the ACM 62 (2015).
corr_author: '1'
date_created: 2018-12-11T11:53:27Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2025-09-23T10:38:46Z
day: '01'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1145/2751524
external_id:
arxiv:
- '1402.0858'
isi:
- '000361200500001'
intvolume: ' 62'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1402.0858
month: '08'
oa: 1
oa_version: Preprint
publication: Journal of the ACM
publication_status: published
publisher: ACM
publist_id: '5466'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Robust satisfiability of systems of equations
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 62
year: '2015'
...
---
_id: '1710'
abstract:
- lang: eng
text: 'We consider the hollow on the half-plane {(x, y) : y ≤ 0} ⊂ ℝ2 defined by
a function u : (-1, 1) → ℝ, u(x) < 0, and a vertical flow of point particles
incident on the hollow. It is assumed that u satisfies the so-called single impact
condition (SIC): each incident particle is elastically reflected by graph(u) and
goes away without hitting the graph of u anymore. We solve the problem: find the
function u minimizing the force of resistance created by the flow. We show that
the graph of the minimizer is formed by two arcs of parabolas symmetric to each
other with respect to the y-axis. Assuming that the resistance of u ≡ 0 equals
1, we show that the minimal resistance equals π/2 - 2arctan(1/2) ≈ 0.6435. This
result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014),
pp. 2730-2742] stating in particular that the minimal resistance of a hollow in
higher dimensions equals 0.5. We additionally consider a similar problem of minimal
resistance, where the hollow in the half-space {(x1,...,xd,y) : y ≤ 0} ⊂ ℝd+1
is defined by a radial function U satisfying the SIC, U(x) = u(|x|), with x =
(x1,...,xd), u(ξ) < 0 for 0 ≤ ξ < 1, and u(ξ) = 0 for ξ ≥ 1, and the flow
is parallel to the y-axis. The minimal resistance is greater than 0.5 (and coincides
with 0.6435 when d = 1) and converges to 0.5 as d → ∞.'
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: Alexander
full_name: Plakhov, Alexander
last_name: Plakhov
citation:
ama: Akopyan A, Plakhov A. Minimal resistance of curves under the single impact
assumption. Society for Industrial and Applied Mathematics. 2015;47(4):2754-2769.
doi:10.1137/140993843
apa: Akopyan, A., & Plakhov, A. (2015). Minimal resistance of curves under the
single impact assumption. Society for Industrial and Applied Mathematics.
SIAM. https://doi.org/10.1137/140993843
chicago: Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves
under the Single Impact Assumption.” Society for Industrial and Applied Mathematics.
SIAM, 2015. https://doi.org/10.1137/140993843.
ieee: A. Akopyan and A. Plakhov, “Minimal resistance of curves under the single
impact assumption,” Society for Industrial and Applied Mathematics, vol.
47, no. 4. SIAM, pp. 2754–2769, 2015.
ista: Akopyan A, Plakhov A. 2015. Minimal resistance of curves under the single
impact assumption. Society for Industrial and Applied Mathematics. 47(4), 2754–2769.
mla: Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under
the Single Impact Assumption.” Society for Industrial and Applied Mathematics,
vol. 47, no. 4, SIAM, 2015, pp. 2754–69, doi:10.1137/140993843.
short: A. Akopyan, A. Plakhov, Society for Industrial and Applied Mathematics 47
(2015) 2754–2769.
date_created: 2018-12-11T11:53:36Z
date_published: 2015-07-14T00:00:00Z
date_updated: 2025-09-23T09:35:36Z
day: '14'
department:
- _id: HeEd
doi: 10.1137/140993843
ec_funded: 1
external_id:
arxiv:
- '1410.3736'
isi:
- '000360691500009'
intvolume: ' 47'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1410.3736
month: '07'
oa: 1
oa_version: Preprint
page: 2754 - 2769
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Society for Industrial and Applied Mathematics
publication_status: published
publisher: SIAM
publist_id: '5423'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Minimal resistance of curves under the single impact assumption
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 47
year: '2015'
...
---
_id: '9737'
article_processing_charge: No
author:
- first_name: Olga
full_name: Symonova, Olga
id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87
last_name: Symonova
orcid: 0000-0003-2012-9947
- first_name: Christopher
full_name: Topp, Christopher
last_name: Topp
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Symonova O, Topp C, Edelsbrunner H. Root traits computed by DynamicRoots for
the maize root shown in fig 2. 2015. doi:10.1371/journal.pone.0127657.s001
apa: Symonova, O., Topp, C., & Edelsbrunner, H. (2015). Root traits computed
by DynamicRoots for the maize root shown in fig 2. Public Library of Science.
https://doi.org/10.1371/journal.pone.0127657.s001
chicago: Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “Root Traits
Computed by DynamicRoots for the Maize Root Shown in Fig 2.” Public Library of
Science, 2015. https://doi.org/10.1371/journal.pone.0127657.s001.
ieee: O. Symonova, C. Topp, and H. Edelsbrunner, “Root traits computed by DynamicRoots
for the maize root shown in fig 2.” Public Library of Science, 2015.
ista: Symonova O, Topp C, Edelsbrunner H. 2015. Root traits computed by DynamicRoots
for the maize root shown in fig 2, Public Library of Science, 10.1371/journal.pone.0127657.s001.
mla: Symonova, Olga, et al. Root Traits Computed by DynamicRoots for the Maize
Root Shown in Fig 2. Public Library of Science, 2015, doi:10.1371/journal.pone.0127657.s001.
short: O. Symonova, C. Topp, H. Edelsbrunner, (2015).
date_created: 2021-07-28T06:20:13Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2025-09-23T08:30:43Z
day: '01'
department:
- _id: MaJö
- _id: HeEd
doi: 10.1371/journal.pone.0127657.s001
month: '06'
oa_version: Published Version
publisher: Public Library of Science
related_material:
record:
- id: '1793'
relation: used_in_publication
status: public
status: public
title: Root traits computed by DynamicRoots for the maize root shown in fig 2
type: research_data_reference
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
year: '2015'
...
---
_id: '1792'
abstract:
- lang: eng
text: Motivated by recent ideas of Harman (Unif. Distrib. Theory, 2010) we develop
a new concept of variation of multivariate functions on a compact Hausdorff space
with respect to a collection D of subsets. We prove a general version of the Koksma-Hlawka
theorem that holds for this notion of variation and discrepancy with respect to
D. As special cases, we obtain Koksma-Hlawka inequalities for classical notions,
such as extreme or isotropic discrepancy. For extreme discrepancy, our result
coincides with the usual Koksma-Hlawka theorem. We show that the space of functions
of bounded D-variation contains important discontinuous functions and is closed
under natural algebraic operations. Finally, we illustrate the results on concrete
integration problems from integral geometry and stereology.
acknowledgement: F.P. is supported by the Graduate School of IST Austria, A.M.S is
supported by the Centre for Stochastic Geometry and Advanced Bioimaging funded by
a grant from the Villum Foundation.
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
- first_name: Anne
full_name: Svane, Anne
last_name: Svane
citation:
ama: Pausinger F, Svane A. A Koksma-Hlawka inequality for general discrepancy systems.
Journal of Complexity. 2015;31(6):773-797. doi:10.1016/j.jco.2015.06.002
apa: Pausinger, F., & Svane, A. (2015). A Koksma-Hlawka inequality for general
discrepancy systems. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.06.002
chicago: Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General
Discrepancy Systems.” Journal of Complexity. Academic Press, 2015. https://doi.org/10.1016/j.jco.2015.06.002.
ieee: F. Pausinger and A. Svane, “A Koksma-Hlawka inequality for general discrepancy
systems,” Journal of Complexity, vol. 31, no. 6. Academic Press, pp. 773–797,
2015.
ista: Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy
systems. Journal of Complexity. 31(6), 773–797.
mla: Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General
Discrepancy Systems.” Journal of Complexity, vol. 31, no. 6, Academic Press,
2015, pp. 773–97, doi:10.1016/j.jco.2015.06.002.
short: F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797.
corr_author: '1'
date_created: 2018-12-11T11:54:02Z
date_published: 2015-12-01T00:00:00Z
date_updated: 2026-04-09T14:26:05Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jco.2015.06.002
external_id:
isi:
- '000362926900001'
intvolume: ' 31'
isi: 1
issue: '6'
language:
- iso: eng
month: '12'
oa_version: None
page: 773 - 797
publication: Journal of Complexity
publication_status: published
publisher: Academic Press
publist_id: '5320'
quality_controlled: '1'
related_material:
record:
- id: '1399'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: A Koksma-Hlawka inequality for general discrepancy systems
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 31
year: '2015'
...
---
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: '2905'
abstract:
- lang: eng
text: "Persistent homology is a recent grandchild of homology that has found use
in\r\nscience and engineering as well as in mathematics. This paper surveys the
method as well\r\nas the applications, neglecting completeness in favor of highlighting
ideas and directions."
acknowledgement: This research is partially supported by NSF under grant DBI-0820624,
by ESF under the Research Networking Programme, and by the Russian Government Project
11.G34.31.0053.
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: Dmitriy
full_name: Morozovy, Dmitriy
last_name: Morozovy
citation:
ama: 'Edelsbrunner H, Morozovy D. Persistent homology: Theory and practice. In:
European Mathematical Society; 2014:31-50. doi:10.4171/120-1/3'
apa: 'Edelsbrunner, H., & Morozovy, D. (2014). Persistent homology: Theory and
practice (pp. 31–50). Presented at the ECM: European Congress of Mathematics,
Kraków, Poland: European Mathematical Society. https://doi.org/10.4171/120-1/3'
chicago: 'Edelsbrunner, Herbert, and Dmitriy Morozovy. “Persistent Homology: Theory
and Practice,” 31–50. European Mathematical Society, 2014. https://doi.org/10.4171/120-1/3.'
ieee: 'H. Edelsbrunner and D. Morozovy, “Persistent homology: Theory and practice,”
presented at the ECM: European Congress of Mathematics, Kraków, Poland, 2014,
pp. 31–50.'
ista: 'Edelsbrunner H, Morozovy D. 2014. Persistent homology: Theory and practice.
ECM: European Congress of Mathematics, 31–50.'
mla: 'Edelsbrunner, Herbert, and Dmitriy Morozovy. Persistent Homology: Theory
and Practice. European Mathematical Society, 2014, pp. 31–50, doi:10.4171/120-1/3.'
short: H. Edelsbrunner, D. Morozovy, in:, European Mathematical Society, 2014, pp.
31–50.
conference:
end_date: 2012-07-07
location: Kraków, Poland
name: 'ECM: European Congress of Mathematics'
start_date: 2012-07-02
corr_author: '1'
date_created: 2018-12-11T12:00:16Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2025-06-03T11:46:59Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.4171/120-1/3
file:
- access_level: open_access
checksum: 1d4a046f1af945c407c5c4d411d4c5e4
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:43Z
date_updated: 2020-07-14T12:45:52Z
file_id: '5232'
file_name: IST-2016-544-v1+1_2012-P-11-PHTheoryPractice.pdf
file_size: 435320
relation: main_file
file_date_updated: 2020-07-14T12:45:52Z
has_accepted_license: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Submitted Version
page: 31 - 50
publication_status: published
publisher: European Mathematical Society
publist_id: '3842'
pubrep_id: '544'
quality_controlled: '1'
status: public
title: 'Persistent homology: Theory and practice'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '1816'
abstract:
- lang: eng
text: Watermarking techniques for vector graphics dislocate vertices in order to
embed imperceptible, yet detectable, statistical features into the input data.
The embedding process may result in a change of the topology of the input data,
e.g., by introducing self-intersections, which is undesirable or even disastrous
for many applications. In this paper we present a watermarking framework for two-dimensional
vector graphics that employs conventional watermarking techniques but still provides
the guarantee that the topology of the input data is preserved. The geometric
part of this framework computes so-called maximum perturbation regions (MPR) of
vertices. We propose two efficient algorithms to compute MPRs based on Voronoi
diagrams and constrained triangulations. Furthermore, we present two algorithms
to conditionally correct the watermarked data in order to increase the watermark
embedding capacity and still guarantee topological correctness. While we focus
on the watermarking of input formed by straight-line segments, one of our approaches
can also be extended to circular arcs. We conclude the paper by demonstrating
and analyzing the applicability of our framework in conjunction with two well-known
watermarking techniques.
acknowledgement: 'Work by Martin Held and Stefan Huber was supported by Austrian Science
Fund (FWF): L367-N15 and P25816-N15.'
author:
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Martin
full_name: Held, Martin
last_name: Held
- first_name: Peter
full_name: Meerwald, Peter
last_name: Meerwald
- first_name: Roland
full_name: Kwitt, Roland
last_name: Kwitt
citation:
ama: Huber S, Held M, Meerwald P, Kwitt R. Topology-preserving watermarking of vector
graphics. International Journal of Computational Geometry and Applications.
2014;24(1):61-86. doi:10.1142/S0218195914500034
apa: Huber, S., Held, M., Meerwald, P., & Kwitt, R. (2014). Topology-preserving
watermarking of vector graphics. International Journal of Computational Geometry
and Applications. World Scientific Publishing. https://doi.org/10.1142/S0218195914500034
chicago: Huber, Stefan, Martin Held, Peter Meerwald, and Roland Kwitt. “Topology-Preserving
Watermarking of Vector Graphics.” International Journal of Computational Geometry
and Applications. World Scientific Publishing, 2014. https://doi.org/10.1142/S0218195914500034.
ieee: S. Huber, M. Held, P. Meerwald, and R. Kwitt, “Topology-preserving watermarking
of vector graphics,” International Journal of Computational Geometry and Applications,
vol. 24, no. 1. World Scientific Publishing, pp. 61–86, 2014.
ista: Huber S, Held M, Meerwald P, Kwitt R. 2014. Topology-preserving watermarking
of vector graphics. International Journal of Computational Geometry and Applications.
24(1), 61–86.
mla: Huber, Stefan, et al. “Topology-Preserving Watermarking of Vector Graphics.”
International Journal of Computational Geometry and Applications, vol.
24, no. 1, World Scientific Publishing, 2014, pp. 61–86, doi:10.1142/S0218195914500034.
short: S. Huber, M. Held, P. Meerwald, R. Kwitt, International Journal of Computational
Geometry and Applications 24 (2014) 61–86.
corr_author: '1'
date_created: 2018-12-11T11:54:10Z
date_published: 2014-03-16T00:00:00Z
date_updated: 2024-10-09T20:55:54Z
day: '16'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1142/S0218195914500034
file:
- access_level: open_access
checksum: be45c133ab4d43351260e21beaa8f4b1
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:08:43Z
date_updated: 2020-07-14T12:45:17Z
file_id: '4704'
file_name: IST-2016-443-v1+1_S0218195914500034.pdf
file_size: 991734
relation: main_file
file_date_updated: 2020-07-14T12:45:17Z
has_accepted_license: '1'
intvolume: ' 24'
issue: '1'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 61 - 86
publication: International Journal of Computational Geometry and Applications
publication_status: published
publisher: World Scientific Publishing
publist_id: '5290'
pubrep_id: '443'
quality_controlled: '1'
scopus_import: 1
status: public
title: Topology-preserving watermarking of vector graphics
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2014'
...
---
_id: '1842'
abstract:
- lang: eng
text: We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2
outerplanar triangulations in both convex and general cases. We also prove that
the geometric Ramsey numbers of the ladder graph on 2n vertices are bounded by
O(n3) and O(n10), in the convex and general case, respectively. We then apply
similar methods to prove an (Formula presented.) upper bound on the Ramsey number
of a path with n ordered vertices.
acknowledgement: Marek Krčál was supported by the ERC Advanced Grant No. 267165.
article_processing_charge: No
arxiv: 1
author:
- first_name: Josef
full_name: Cibulka, Josef
last_name: Cibulka
- first_name: Pu
full_name: Gao, Pu
last_name: Gao
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
- first_name: Tomáš
full_name: Valla, Tomáš
last_name: Valla
- first_name: Pavel
full_name: Valtr, Pavel
last_name: Valtr
citation:
ama: Cibulka J, Gao P, Krcál M, Valla T, Valtr P. On the geometric ramsey number
of outerplanar graphs. Discrete & Computational Geometry. 2014;53(1):64-79.
doi:10.1007/s00454-014-9646-x
apa: Cibulka, J., Gao, P., Krcál, M., Valla, T., & Valtr, P. (2014). On the
geometric ramsey number of outerplanar graphs. Discrete & Computational
Geometry. Springer. https://doi.org/10.1007/s00454-014-9646-x
chicago: Cibulka, Josef, Pu Gao, Marek Krcál, Tomáš Valla, and Pavel Valtr. “On
the Geometric Ramsey Number of Outerplanar Graphs.” Discrete & Computational
Geometry. Springer, 2014. https://doi.org/10.1007/s00454-014-9646-x.
ieee: J. Cibulka, P. Gao, M. Krcál, T. Valla, and P. Valtr, “On the geometric ramsey
number of outerplanar graphs,” Discrete & Computational Geometry, vol.
53, no. 1. Springer, pp. 64–79, 2014.
ista: Cibulka J, Gao P, Krcál M, Valla T, Valtr P. 2014. On the geometric ramsey
number of outerplanar graphs. Discrete & Computational Geometry. 53(1), 64–79.
mla: Cibulka, Josef, et al. “On the Geometric Ramsey Number of Outerplanar Graphs.”
Discrete & Computational Geometry, vol. 53, no. 1, Springer, 2014,
pp. 64–79, doi:10.1007/s00454-014-9646-x.
short: J. Cibulka, P. Gao, M. Krcál, T. Valla, P. Valtr, Discrete & Computational
Geometry 53 (2014) 64–79.
date_created: 2018-12-11T11:54:18Z
date_published: 2014-11-14T00:00:00Z
date_updated: 2025-09-29T13:11:56Z
day: '14'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/s00454-014-9646-x
external_id:
arxiv:
- '1310.7004'
isi:
- '000346774600005'
intvolume: ' 53'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1310.7004
month: '11'
oa: 1
oa_version: Submitted Version
page: 64 - 79
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '5260'
scopus_import: '1'
status: public
title: On the geometric ramsey number of outerplanar graphs
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 53
year: '2014'
...
---
OA_place: repository
OA_type: green
_id: '2012'
abstract:
- lang: eng
text: The classical sphere packing problem asks for the best (infinite) arrangement
of non-overlapping unit balls which cover as much space as possible. We define
a generalized version of the problem, where we allow each ball a limited amount
of overlap with other balls. We study two natural choices of overlap measures
and obtain the optimal lattice packings in a parameterized family of lattices
which contains the FCC, BCC, and integer lattice.
acknowledgement: We thank Herbert Edelsbrunner for his valuable discussions and ideas
on the topic of this paper. The second author has been supported by the Max Planck
Center for Visual Computing and Communication
article_processing_charge: No
arxiv: 1
author:
- first_name: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
citation:
ama: 'Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. In:
26th Canadian Conference on Computational Geometry. Canadian Conference
on Computational Geometry; 2014:155-161.'
apa: 'Iglesias Ham, M., Kerber, M., & Uhler, C. (2014). Sphere packing with
limited overlap. In 26th Canadian Conference on Computational Geometry
(pp. 155–161). Halifax, Canada: Canadian Conference on Computational Geometry.'
chicago: Iglesias Ham, Mabel, Michael Kerber, and Caroline Uhler. “Sphere Packing
with Limited Overlap.” In 26th Canadian Conference on Computational Geometry,
155–61. Canadian Conference on Computational Geometry, 2014.
ieee: M. Iglesias Ham, M. Kerber, and C. Uhler, “Sphere packing with limited overlap,”
in 26th Canadian Conference on Computational Geometry, Halifax, Canada,
2014, pp. 155–161.
ista: 'Iglesias Ham M, Kerber M, Uhler C. 2014. Sphere packing with limited overlap.
26th Canadian Conference on Computational Geometry. CCCG: Canadian Conference
on Computational Geometry, 155–161.'
mla: Iglesias Ham, Mabel, et al. “Sphere Packing with Limited Overlap.” 26th
Canadian Conference on Computational Geometry, Canadian Conference on Computational
Geometry, 2014, pp. 155–61.
short: M. Iglesias Ham, M. Kerber, C. Uhler, in:, 26th Canadian Conference on Computational
Geometry, Canadian Conference on Computational Geometry, 2014, pp. 155–161.
conference:
end_date: 2014-08-13
location: Halifax, Canada
name: 'CCCG: Canadian Conference on Computational Geometry'
start_date: 2014-08-11
corr_author: '1'
date_created: 2018-12-11T11:55:12Z
date_published: 2014-09-01T00:00:00Z
date_updated: 2025-01-20T13:57:24Z
day: '01'
department:
- _id: HeEd
- _id: CaUh
external_id:
arxiv:
- '1401.0468'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://cccg.ca/proceedings/2014/papers/paper23.pdf
month: '09'
oa: 1
oa_version: Preprint
page: 155-161
publication: 26th Canadian Conference on Computational Geometry
publication_status: published
publisher: Canadian Conference on Computational Geometry
publist_id: '5064'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sphere packing with limited overlap
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2043'
abstract:
- lang: eng
text: Persistent homology is a popular and powerful tool for capturing topological
features of data. Advances in algorithms for computing persistent homology have
reduced the computation time drastically – as long as the algorithm does not exhaust
the available memory. Following up on a recently presented parallel method for
persistence computation on shared memory systems [1], we demonstrate that a simple
adaption of the standard reduction algorithm leads to a variant for distributed
systems. Our algorithmic design ensures that the data is distributed over the
nodes without redundancy; this permits the computation of much larger instances
than on a single machine. Moreover, we observe that the parallelism at least compensates
for the overhead caused by communication between nodes, and often even speeds
up the computation compared to sequential and even parallel shared memory algorithms.
In our experiments, we were able to compute the persistent homology of filtrations
with more than a billion (109) elements within seconds on a cluster with 32 nodes
using less than 6GB of memory per node.
article_processing_charge: No
arxiv: 1
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
citation:
ama: 'Bauer U, Kerber M, Reininghaus J. Distributed computation of persistent homology.
In: McGeoch C, Meyer U, eds. Proceedings of the Workshop on Algorithm Engineering
and Experiments. Society for Industrial and Applied Mathematics; 2014:31-38.
doi:10.1137/1.9781611973198.4'
apa: 'Bauer, U., Kerber, M., & Reininghaus, J. (2014). Distributed computation
of persistent homology. In C. McGeoch & U. Meyer (Eds.), Proceedings of
the Workshop on Algorithm Engineering and Experiments (pp. 31–38). Portland,
USA: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611973198.4'
chicago: Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Distributed Computation
of Persistent Homology.” In Proceedings of the Workshop on Algorithm Engineering
and Experiments, edited by Catherine McGeoch and Ulrich Meyer, 31–38. Society
for Industrial and Applied Mathematics, 2014. https://doi.org/10.1137/1.9781611973198.4.
ieee: U. Bauer, M. Kerber, and J. Reininghaus, “Distributed computation of persistent
homology,” in Proceedings of the Workshop on Algorithm Engineering and Experiments,
Portland, USA, 2014, pp. 31–38.
ista: 'Bauer U, Kerber M, Reininghaus J. 2014. Distributed computation of persistent
homology. Proceedings of the Workshop on Algorithm Engineering and Experiments.
ALENEX: Algorithm Engineering and Experiments, 31–38.'
mla: Bauer, Ulrich, et al. “Distributed Computation of Persistent Homology.” Proceedings
of the Workshop on Algorithm Engineering and Experiments, edited by Catherine McGeoch
and Ulrich Meyer, Society for Industrial and Applied Mathematics, 2014, pp. 31–38,
doi:10.1137/1.9781611973198.4.
short: U. Bauer, M. Kerber, J. Reininghaus, in:, C. McGeoch, U. Meyer (Eds.), Proceedings
of the Workshop on Algorithm Engineering and Experiments, Society for Industrial
and Applied Mathematics, 2014, pp. 31–38.
conference:
end_date: 2014-01-05
location: Portland, USA
name: 'ALENEX: Algorithm Engineering and Experiments'
start_date: 2014-01-05
date_created: 2018-12-11T11:55:23Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2025-06-11T08:03:07Z
day: '01'
department:
- _id: HeEd
doi: 10.1137/1.9781611973198.4
ec_funded: 1
editor:
- first_name: Catherine
full_name: ' McGeoch, Catherine'
last_name: ' McGeoch'
- first_name: Ulrich
full_name: Meyer, Ulrich
last_name: Meyer
external_id:
arxiv:
- '1310.0710'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1310.0710
month: '01'
oa: 1
oa_version: Submitted Version
page: 31 - 38
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Workshop on Algorithm Engineering and Experiments
publication_status: published
publisher: Society for Industrial and Applied Mathematics
publist_id: '5008'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Distributed computation of persistent homology
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2044'
abstract:
- lang: eng
text: We present a parallel algorithm for computing the persistent homology of a
filtered chain complex. Our approach differs from the commonly used reduction
algorithm by first computing persistence pairs within local chunks, then simplifying
the unpaired columns, and finally applying standard reduction on the simplified
matrix. The approach generalizes a technique by Günther et al., which uses discrete
Morse Theory to compute persistence; we derive the same worst-case complexity
bound in a more general context. The algorithm employs several practical optimization
techniques, which are of independent interest. Our sequential implementation of
the algorithm is competitive with state-of-the-art methods, and we further improve
the performance through parallel computation.
article_processing_charge: No
arxiv: 1
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
citation:
ama: 'Bauer U, Kerber M, Reininghaus J. Clear and Compress: Computing Persistent
Homology in Chunks. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological
Methods in Data Analysis and Visualization III. Mathematics and Visualization.
Springer; 2014:103-117. doi:10.1007/978-3-319-04099-8_7'
apa: 'Bauer, U., Kerber, M., & Reininghaus, J. (2014). Clear and Compress: Computing
Persistent Homology in Chunks. In P.-T. Bremer, I. Hotz, V. Pascucci, & R.
Peikert (Eds.), Topological Methods in Data Analysis and Visualization III
(pp. 103–117). Springer. https://doi.org/10.1007/978-3-319-04099-8_7'
chicago: 'Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Clear and Compress:
Computing Persistent Homology in Chunks.” In Topological Methods in Data Analysis
and Visualization III, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci,
and Ronald Peikert, 103–17. Mathematics and Visualization. Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_7.'
ieee: 'U. Bauer, M. Kerber, and J. Reininghaus, “Clear and Compress: Computing Persistent
Homology in Chunks,” in Topological Methods in Data Analysis and Visualization
III, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Springer, 2014,
pp. 103–117.'
ista: 'Bauer U, Kerber M, Reininghaus J. 2014.Clear and Compress: Computing Persistent
Homology in Chunks. In: Topological Methods in Data Analysis and Visualization
III. , 103–117.'
mla: 'Bauer, Ulrich, et al. “Clear and Compress: Computing Persistent Homology in
Chunks.” Topological Methods in Data Analysis and Visualization III, edited
by Peer-Timo Bremer et al., Springer, 2014, pp. 103–17, doi:10.1007/978-3-319-04099-8_7.'
short: U. Bauer, M. Kerber, J. Reininghaus, in:, P.-T. Bremer, I. Hotz, V. Pascucci,
R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III,
Springer, 2014, pp. 103–117.
corr_author: '1'
date_created: 2018-12-11T11:55:23Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2025-06-11T07:56:57Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-319-04099-8_7
ec_funded: 1
editor:
- first_name: Peer-Timo
full_name: Bremer, Peer-Timo
last_name: Bremer
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
- first_name: Valerio
full_name: Pascucci, Valerio
last_name: Pascucci
- first_name: Ronald
full_name: Peikert, Ronald
last_name: Peikert
external_id:
arxiv:
- '1303.0477'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1303.0477
month: '03'
oa: 1
oa_version: Submitted Version
page: 103 - 117
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Topological Methods in Data Analysis and Visualization III
publication_status: published
publisher: Springer
publist_id: '5007'
quality_controlled: '1'
scopus_import: '1'
series_title: Mathematics and Visualization
status: public
title: 'Clear and Compress: Computing Persistent Homology in Chunks'
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '1876'
abstract:
- lang: eng
text: We study densities of functionals over uniformly bounded triangulations of
a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay
triangulation if this is the case for finite sets.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nikolai
full_name: Dolbilin, Nikolai
last_name: Dolbilin
- 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: Glazyrin, Alexey
last_name: Glazyrin
- first_name: Oleg
full_name: Musin, Oleg
last_name: Musin
citation:
ama: Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. Functionals on triangulations
of delaunay sets. Moscow Mathematical Journal. 2014;14(3):491-504. doi:10.17323/1609-4514-2014-14-3-491-504
apa: Dolbilin, N., Edelsbrunner, H., Glazyrin, A., & Musin, O. (2014). Functionals
on triangulations of delaunay sets. Moscow Mathematical Journal. Independent
University of Moscow. https://doi.org/10.17323/1609-4514-2014-14-3-491-504
chicago: Dolbilin, Nikolai, Herbert Edelsbrunner, Alexey Glazyrin, and Oleg Musin.
“Functionals on Triangulations of Delaunay Sets.” Moscow Mathematical Journal.
Independent University of Moscow, 2014. https://doi.org/10.17323/1609-4514-2014-14-3-491-504.
ieee: N. Dolbilin, H. Edelsbrunner, A. Glazyrin, and O. Musin, “Functionals on triangulations
of delaunay sets,” Moscow Mathematical Journal, vol. 14, no. 3. Independent
University of Moscow, pp. 491–504, 2014.
ista: Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. 2014. Functionals on triangulations
of delaunay sets. Moscow Mathematical Journal. 14(3), 491–504.
mla: Dolbilin, Nikolai, et al. “Functionals on Triangulations of Delaunay Sets.”
Moscow Mathematical Journal, vol. 14, no. 3, Independent University of
Moscow, 2014, pp. 491–504, doi:10.17323/1609-4514-2014-14-3-491-504.
short: N. Dolbilin, H. Edelsbrunner, A. Glazyrin, O. Musin, Moscow Mathematical
Journal 14 (2014) 491–504.
date_created: 2018-12-11T11:54:29Z
date_published: 2014-07-01T00:00:00Z
date_updated: 2025-07-10T11:51:26Z
day: '01'
department:
- _id: HeEd
doi: 10.17323/1609-4514-2014-14-3-491-504
external_id:
arxiv:
- '1211.7053'
intvolume: ' 14'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1211.7053
month: '07'
oa: 1
oa_version: Submitted Version
page: 491 - 504
publication: Moscow Mathematical Journal
publication_identifier:
issn:
- 1609-3321
publication_status: published
publisher: Independent University of Moscow
publist_id: '5220'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Functionals on triangulations of delaunay sets
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14
year: '2014'
...
---
_id: '1929'
abstract:
- lang: eng
text: We propose an algorithm for the generalization of cartographic objects that
can be used to represent maps on different scales.
acknowledgement: We would like to offer our special thanks to students of the Department
of Mathematics of Demidov Yaroslavl State University A. A. Gorokhov and V. N. Knyazev
for participation in developing the program and assistance in preparation of test
data. This work was supported by grant 11.G34.31.0053 from the government of the
Russian Federation.
article_processing_charge: No
article_type: original
author:
- first_name: V V
full_name: Alexeev, V V
last_name: Alexeev
- first_name: V G
full_name: Bogaevskaya, V G
last_name: Bogaevskaya
- first_name: M M
full_name: Preobrazhenskaya, M M
last_name: Preobrazhenskaya
- first_name: A Y
full_name: Ukhalov, A Y
last_name: Ukhalov
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Olga
full_name: Yakimova, Olga
last_name: Yakimova
citation:
ama: Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner H,
Yakimova O. An algorithm for cartographic generalization that preserves global
topology. Journal of Mathematical Sciences. 2014;203(6):754-760. doi:10.1007/s10958-014-2165-8
apa: Alexeev, V. V., Bogaevskaya, V. G., Preobrazhenskaya, M. M., Ukhalov, A. Y.,
Edelsbrunner, H., & Yakimova, O. (2014). An algorithm for cartographic generalization
that preserves global topology. Journal of Mathematical Sciences. Springer.
https://doi.org/10.1007/s10958-014-2165-8
chicago: Alexeev, V V, V G Bogaevskaya, M M Preobrazhenskaya, A Y Ukhalov, Herbert
Edelsbrunner, and Olga Yakimova. “An Algorithm for Cartographic Generalization
That Preserves Global Topology.” Journal of Mathematical Sciences. Springer,
2014. https://doi.org/10.1007/s10958-014-2165-8.
ieee: V. V. Alexeev, V. G. Bogaevskaya, M. M. Preobrazhenskaya, A. Y. Ukhalov, H.
Edelsbrunner, and O. Yakimova, “An algorithm for cartographic generalization that
preserves global topology,” Journal of Mathematical Sciences, vol. 203,
no. 6. Springer, pp. 754–760, 2014.
ista: Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner
H, Yakimova O. 2014. An algorithm for cartographic generalization that preserves
global topology. Journal of Mathematical Sciences. 203(6), 754–760.
mla: Alexeev, V. V., et al. “An Algorithm for Cartographic Generalization That Preserves
Global Topology.” Journal of Mathematical Sciences, vol. 203, no. 6, Springer,
2014, pp. 754–60, doi:10.1007/s10958-014-2165-8.
short: V.V. Alexeev, V.G. Bogaevskaya, M.M. Preobrazhenskaya, A.Y. Ukhalov, H. Edelsbrunner,
O. Yakimova, Journal of Mathematical Sciences 203 (2014) 754–760.
date_created: 2018-12-11T11:54:46Z
date_published: 2014-11-16T00:00:00Z
date_updated: 2022-05-24T10:39:06Z
day: '16'
department:
- _id: HeEd
doi: 10.1007/s10958-014-2165-8
intvolume: ' 203'
issue: '6'
language:
- iso: eng
month: '11'
oa_version: None
page: 754 - 760
publication: Journal of Mathematical Sciences
publication_identifier:
eissn:
- 1573-8795
issn:
- 1072-3374
publication_status: published
publisher: Springer
publist_id: '5165'
quality_controlled: '1'
scopus_import: '1'
status: public
title: An algorithm for cartographic generalization that preserves global topology
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 203
year: '2014'
...
---
_id: '1930'
abstract:
- lang: eng
text: (Figure Presented) Data acquisition, numerical inaccuracies, and sampling
often introduce noise in measurements and simulations. Removing this noise is
often necessary for efficient analysis and visualization of this data, yet many
denoising techniques change the minima and maxima of a scalar field. For example,
the extrema can appear or disappear, spatially move, and change their value. This
can lead to wrong interpretations of the data, e.g., when the maximum temperature
over an area is falsely reported being a few degrees cooler because the denoising
method is unaware of these features. Recently, a topological denoising technique
based on a global energy optimization was proposed, which allows the topology-controlled
denoising of 2D scalar fields. While this method preserves the minima and maxima,
it is constrained by the size of the data. We extend this work to large 2D data
and medium-sized 3D data by introducing a novel domain decomposition approach.
It allows processing small patches of the domain independently while still avoiding
the introduction of new critical points. Furthermore, we propose an iterative
refinement of the solution, which decreases the optimization energy compared to
the previous approach and therefore gives smoother results that are closer to
the input. We illustrate our technique on synthetic and real-world 2D and 3D data
sets that highlight potential applications.
acknowledgement: RTRA Digiteoproject; ERC grant; SNF award; Intel Doctoral Fellowship;
MPC-VCC
article_processing_charge: No
author:
- first_name: David
full_name: Günther, David
last_name: Günther
- first_name: Alec
full_name: Jacobson, Alec
last_name: Jacobson
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Hans
full_name: Seidel, Hans
last_name: Seidel
- first_name: Olga
full_name: Sorkine Hornung, Olga
last_name: Sorkine Hornung
- first_name: Tino
full_name: Weinkauf, Tino
last_name: Weinkauf
citation:
ama: Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf
T. Fast and memory-efficient topological denoising of 2D and 3D scalar fields.
IEEE Transactions on Visualization and Computer Graphics. 2014;20(12):2585-2594.
doi:10.1109/TVCG.2014.2346432
apa: Günther, D., Jacobson, A., Reininghaus, J., Seidel, H., Sorkine Hornung, O.,
& Weinkauf, T. (2014). Fast and memory-efficient topological denoising of
2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics.
IEEE. https://doi.org/10.1109/TVCG.2014.2346432
chicago: Günther, David, Alec Jacobson, Jan Reininghaus, Hans Seidel, Olga Sorkine
Hornung, and Tino Weinkauf. “Fast and Memory-Efficient Topological Denoising of
2D and 3D Scalar Fields.” IEEE Transactions on Visualization and Computer Graphics.
IEEE, 2014. https://doi.org/10.1109/TVCG.2014.2346432.
ieee: D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, and
T. Weinkauf, “Fast and memory-efficient topological denoising of 2D and 3D scalar
fields,” IEEE Transactions on Visualization and Computer Graphics, vol.
20, no. 12. IEEE, pp. 2585–2594, 2014.
ista: Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf
T. 2014. Fast and memory-efficient topological denoising of 2D and 3D scalar fields.
IEEE Transactions on Visualization and Computer Graphics. 20(12), 2585–2594.
mla: Günther, David, et al. “Fast and Memory-Efficient Topological Denoising of
2D and 3D Scalar Fields.” IEEE Transactions on Visualization and Computer Graphics,
vol. 20, no. 12, IEEE, 2014, pp. 2585–94, doi:10.1109/TVCG.2014.2346432.
short: D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, T.
Weinkauf, IEEE Transactions on Visualization and Computer Graphics 20 (2014) 2585–2594.
date_created: 2018-12-11T11:54:46Z
date_published: 2014-12-31T00:00:00Z
date_updated: 2025-09-29T12:11:45Z
day: '31'
department:
- _id: HeEd
doi: 10.1109/TVCG.2014.2346432
external_id:
isi:
- '000344991700104'
intvolume: ' 20'
isi: 1
issue: '12'
language:
- iso: eng
month: '12'
oa_version: None
page: 2585 - 2594
publication: IEEE Transactions on Visualization and Computer Graphics
publication_status: published
publisher: IEEE
publist_id: '5164'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fast and memory-efficient topological denoising of 2D and 3D scalar fields
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 20
year: '2014'
...
---
_id: '10817'
abstract:
- lang: eng
text: The Morse-Smale complex can be either explicitly or implicitly represented.
Depending on the type of representation, the simplification of the Morse-Smale
complex works differently. In the explicit representation, the Morse-Smale complex
is directly simplified by explicitly reconnecting the critical points during the
simplification. In the implicit representation, on the other hand, the Morse-Smale
complex is given by a combinatorial gradient field. In this setting, the simplification
changes the combinatorial flow, which yields an indirect simplification of the
Morse-Smale complex. The topological complexity of the Morse-Smale complex is
reduced in both representations. However, the simplifications generally yield
different results. In this chapter, we emphasize properties of the two representations
that cause these differences. We also provide a complexity analysis of the two
schemes with respect to running time and memory consumption.
acknowledgement: This research is supported and funded by the Digiteo unTopoVis project,
the TOPOSYS project FP7-ICT-318493-STREP, and MPC-VCC.
article_processing_charge: No
author:
- first_name: David
full_name: Günther, David
last_name: Günther
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Hans-Peter
full_name: Seidel, Hans-Peter
last_name: Seidel
- first_name: Tino
full_name: Weinkauf, Tino
last_name: Weinkauf
citation:
ama: 'Günther D, Reininghaus J, Seidel H-P, Weinkauf T. Notes on the simplification
of the Morse-Smale complex. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds.
Topological Methods in Data Analysis and Visualization III. Mathematics
and Visualization. Cham: Springer Nature; 2014:135-150. doi:10.1007/978-3-319-04099-8_9'
apa: 'Günther, D., Reininghaus, J., Seidel, H.-P., & Weinkauf, T. (2014). Notes
on the simplification of the Morse-Smale complex. In P.-T. Bremer, I. Hotz, V.
Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and
Visualization III. (pp. 135–150). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-04099-8_9'
chicago: 'Günther, David, Jan Reininghaus, Hans-Peter Seidel, and Tino Weinkauf.
“Notes on the Simplification of the Morse-Smale Complex.” In Topological Methods
in Data Analysis and Visualization III., edited by Peer-Timo Bremer, Ingrid
Hotz, Valerio Pascucci, and Ronald Peikert, 135–50. Mathematics and Visualization.
Cham: Springer Nature, 2014. https://doi.org/10.1007/978-3-319-04099-8_9.'
ieee: 'D. Günther, J. Reininghaus, H.-P. Seidel, and T. Weinkauf, “Notes on the
simplification of the Morse-Smale complex,” in Topological Methods in Data
Analysis and Visualization III., P.-T. Bremer, I. Hotz, V. Pascucci, and R.
Peikert, Eds. Cham: Springer Nature, 2014, pp. 135–150.'
ista: 'Günther D, Reininghaus J, Seidel H-P, Weinkauf T. 2014.Notes on the simplification
of the Morse-Smale complex. In: Topological Methods in Data Analysis and Visualization
III. , 135–150.'
mla: Günther, David, et al. “Notes on the Simplification of the Morse-Smale Complex.”
Topological Methods in Data Analysis and Visualization III., edited by
Peer-Timo Bremer et al., Springer Nature, 2014, pp. 135–50, doi:10.1007/978-3-319-04099-8_9.
short: D. Günther, J. Reininghaus, H.-P. Seidel, T. Weinkauf, in:, P.-T. Bremer,
I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis
and Visualization III., Springer Nature, Cham, 2014, pp. 135–150.
date_created: 2022-03-04T08:33:57Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2025-04-15T08:37:54Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-319-04099-8_9
ec_funded: 1
editor:
- first_name: Peer-Timo
full_name: Bremer, Peer-Timo
last_name: Bremer
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
- first_name: Valerio
full_name: Pascucci, Valerio
last_name: Pascucci
- first_name: Ronald
full_name: Peikert, Ronald
last_name: Peikert
language:
- iso: eng
month: '03'
oa_version: None
page: 135-150
place: Cham
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Topological Methods in Data Analysis and Visualization III.
publication_identifier:
eisbn:
- '9783319040998'
eissn:
- 2197-666X
isbn:
- '9783319040981'
issn:
- 1612-3786
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: Mathematics and Visualization
status: public
title: Notes on the simplification of the Morse-Smale complex
type: book_chapter
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2014'
...
---
_id: '10886'
abstract:
- lang: eng
text: We propose a method for visualizing two-dimensional symmetric positive definite
tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the
heat kernel and was originally introduced as an isometry invariant shape signature.
Each positive definite tensor field defines a Riemannian manifold by considering
the tensor field as a Riemannian metric. On this Riemmanian manifold we can apply
the definition of the HKS. The resulting scalar quantity is used for the visualization
of tensor fields. The HKS is closely related to the Gaussian curvature of the
Riemannian manifold and the time parameter of the heat kernel allows a multiscale
analysis in a natural way. In this way, the HKS represents field related scale
space properties, enabling a level of detail analysis of tensor fields. This makes
the HKS an interesting new scalar quantity for tensor fields, which differs significantly
from usual tensor invariants like the trace or the determinant. A method for visualization
and a numerical realization of the HKS for tensor fields is proposed in this chapter.
To validate the approach we apply it to some illustrating simple examples as isolated
critical points and to a medical diffusion tensor data set.
acknowledgement: This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP.
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. Visualization of two-dimensional symmetric
positive definite tensor fields using the heat kernel signature. In: Topological
Methods in Data Analysis and Visualization III . Springer; 2014:249-262. doi:10.1007/978-3-319-04099-8_16'
apa: Zobel, V., Reininghaus, J., & Hotz, I. (2014). Visualization of two-dimensional
symmetric positive definite tensor fields using the heat kernel signature. In
Topological Methods in Data Analysis and Visualization III (pp. 249–262).
Springer. https://doi.org/10.1007/978-3-319-04099-8_16
chicago: Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualization of Two-Dimensional
Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” In
Topological Methods in Data Analysis and Visualization III , 249–62. Springer,
2014. https://doi.org/10.1007/978-3-319-04099-8_16.
ieee: V. Zobel, J. Reininghaus, and I. Hotz, “Visualization of two-dimensional symmetric
positive definite tensor fields using the heat kernel signature,” in Topological
Methods in Data Analysis and Visualization III , 2014, pp. 249–262.
ista: Zobel V, Reininghaus J, Hotz I. 2014. Visualization of two-dimensional symmetric
positive definite tensor fields using the heat kernel signature. Topological Methods
in Data Analysis and Visualization III . , Mathematics and Visualization, , 249–262.
mla: Zobel, Valentin, et al. “Visualization of Two-Dimensional Symmetric Positive
Definite Tensor Fields Using the Heat Kernel Signature.” Topological Methods
in Data Analysis and Visualization III , Springer, 2014, pp. 249–62, doi:10.1007/978-3-319-04099-8_16.
short: V. Zobel, J. Reininghaus, I. Hotz, in:, Topological Methods in Data Analysis
and Visualization III , Springer, 2014, pp. 249–262.
date_created: 2022-03-18T13:05:39Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2023-09-05T14:13:16Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-319-04099-8_16
language:
- iso: eng
month: '03'
oa_version: None
page: 249-262
publication: 'Topological Methods in Data Analysis and Visualization III '
publication_identifier:
eisbn:
- '9783319040998'
eissn:
- 2197-666X
isbn:
- '9783319040981'
issn:
- 1612-3786
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Visualization of two-dimensional symmetric positive definite tensor fields
using the heat kernel signature
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2014'
...
---
_id: '10892'
abstract:
- lang: eng
text: "In this paper, we introduce planar matchings on directed pseudo-line arrangements,
which yield a planar set of pseudo-line segments such that only matching-partners
are adjacent. By translating the planar matching problem into a corresponding
stable roommates problem we show that such matchings always exist.\r\nUsing our
new framework, we establish, for the first time, a complete, rigorous definition
of weighted straight skeletons, which are based on a so-called wavefront propagation
process. We present a generalized and unified approach to treat structural changes
in the wavefront that focuses on the restoration of weak planarity by finding
planar matchings."
acknowledgement: 'T. Biedl was supported by NSERC and the Ross and Muriel Cheriton
Fellowship. P. Palfrader was supported by Austrian Science Fund (FWF): P25816-N15.'
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Therese
full_name: Biedl, Therese
last_name: Biedl
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
citation:
ama: 'Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons.
In: 25th International Symposium, ISAAC 2014. Vol 8889. Springer Nature;
2014:117-127. doi:10.1007/978-3-319-13075-0_10'
apa: 'Biedl, T., Huber, S., & Palfrader, P. (2014). Planar matchings for weighted
straight skeletons. In 25th International Symposium, ISAAC 2014 (Vol. 8889,
pp. 117–127). Jeonju, Korea: Springer Nature. https://doi.org/10.1007/978-3-319-13075-0_10'
chicago: Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for
Weighted Straight Skeletons.” In 25th International Symposium, ISAAC 2014,
8889:117–27. Springer Nature, 2014. https://doi.org/10.1007/978-3-319-13075-0_10.
ieee: T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight
skeletons,” in 25th International Symposium, ISAAC 2014, Jeonju, Korea,
2014, vol. 8889, pp. 117–127.
ista: 'Biedl T, Huber S, Palfrader P. 2014. Planar matchings for weighted straight
skeletons. 25th International Symposium, ISAAC 2014. ISAAC: International Symposium
on Algorithms and Computation, LNCS, vol. 8889, 117–127.'
mla: Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.”
25th International Symposium, ISAAC 2014, vol. 8889, Springer Nature, 2014,
pp. 117–27, doi:10.1007/978-3-319-13075-0_10.
short: T. Biedl, S. Huber, P. Palfrader, in:, 25th International Symposium, ISAAC
2014, Springer Nature, 2014, pp. 117–127.
conference:
end_date: 2014-12-17
location: Jeonju, Korea
name: 'ISAAC: International Symposium on Algorithms and Computation'
start_date: 2014-12-15
corr_author: '1'
date_created: 2022-03-21T07:09:03Z
date_published: 2014-11-08T00:00:00Z
date_updated: 2025-09-29T13:22:55Z
day: '08'
department:
- _id: HeEd
doi: 10.1007/978-3-319-13075-0_10
external_id:
isi:
- '000354865900010'
intvolume: ' 8889'
isi: 1
language:
- iso: eng
month: '11'
oa_version: None
page: 117-127
publication: 25th International Symposium, ISAAC 2014
publication_identifier:
eisbn:
- '9783319130750'
eissn:
- 1611-3349
isbn:
- '9783319130743'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '481'
relation: later_version
status: public
scopus_import: '1'
status: public
title: Planar matchings for weighted straight skeletons
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 8889
year: '2014'
...
---
_id: '10893'
abstract:
- lang: eng
text: Saddle periodic orbits are an essential and stable part of the topological
skeleton of a 3D vector field. Nevertheless, there is currently no efficient algorithm
to robustly extract these features. In this chapter, we present a novel technique
to extract saddle periodic orbits. Exploiting the analytic properties of such
an orbit, we propose a scalar measure based on the finite-time Lyapunov exponent
(FTLE) that indicates its presence. Using persistent homology, we can then extract
the robust cycles of this field. These cycles thereby represent the saddle periodic
orbits of the given vector field. We discuss the different existing FTLE approximation
schemes regarding their applicability to this specific problem and propose an
adapted version of FTLE called Normalized Velocity Separation. Finally, we evaluate
our method using simple analytic vector field data.
acknowledgement: First, we thank the reviewers of this paper for their ideas and critical
comments. In addition, we thank Ronny Peikert and Filip Sadlo for a fruitful discussions.
This research is supported by the European Commission under the TOPOSYS project
FP7-ICT-318493-STREP, the European Social Fund (ESF App. No. 100098251), and the
European Science Foundation under the ACAT Research Network Program.
article_processing_charge: No
author:
- first_name: Jens
full_name: Kasten, Jens
last_name: Kasten
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Wieland
full_name: Reich, Wieland
last_name: Reich
- first_name: Gerik
full_name: Scheuermann, Gerik
last_name: Scheuermann
citation:
ama: 'Kasten J, Reininghaus J, Reich W, Scheuermann G. Toward the extraction of
saddle periodic orbits. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological
Methods in Data Analysis and Visualization III . Vol 1. Mathematics and Visualization.
Cham: Springer; 2014:55-69. doi:10.1007/978-3-319-04099-8_4'
apa: 'Kasten, J., Reininghaus, J., Reich, W., & Scheuermann, G. (2014). Toward
the extraction of saddle periodic orbits. In P.-T. Bremer, I. Hotz, V. Pascucci,
& R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization
III (Vol. 1, pp. 55–69). Cham: Springer. https://doi.org/10.1007/978-3-319-04099-8_4'
chicago: 'Kasten, Jens, Jan Reininghaus, Wieland Reich, and Gerik Scheuermann. “Toward
the Extraction of Saddle Periodic Orbits.” In Topological Methods in Data Analysis
and Visualization III , edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci,
and Ronald Peikert, 1:55–69. Mathematics and Visualization. Cham: Springer, 2014.
https://doi.org/10.1007/978-3-319-04099-8_4.'
ieee: 'J. Kasten, J. Reininghaus, W. Reich, and G. Scheuermann, “Toward the extraction
of saddle periodic orbits,” in Topological Methods in Data Analysis and Visualization
III , vol. 1, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham:
Springer, 2014, pp. 55–69.'
ista: 'Kasten J, Reininghaus J, Reich W, Scheuermann G. 2014.Toward the extraction
of saddle periodic orbits. In: Topological Methods in Data Analysis and Visualization
III . vol. 1, 55–69.'
mla: Kasten, Jens, et al. “Toward the Extraction of Saddle Periodic Orbits.” Topological
Methods in Data Analysis and Visualization III , edited by Peer-Timo Bremer
et al., vol. 1, Springer, 2014, pp. 55–69, doi:10.1007/978-3-319-04099-8_4.
short: J. Kasten, J. Reininghaus, W. Reich, G. Scheuermann, in:, P.-T. Bremer, I.
Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and
Visualization III , Springer, Cham, 2014, pp. 55–69.
date_created: 2022-03-21T07:11:23Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2025-04-15T08:37:54Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-319-04099-8_4
ec_funded: 1
editor:
- first_name: Peer-Timo
full_name: Bremer, Peer-Timo
last_name: Bremer
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
- first_name: Valerio
full_name: Pascucci, Valerio
last_name: Pascucci
- first_name: Ronald
full_name: Peikert, Ronald
last_name: Peikert
intvolume: ' 1'
language:
- iso: eng
month: '03'
oa_version: None
page: 55-69
place: Cham
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: 'Topological Methods in Data Analysis and Visualization III '
publication_identifier:
eisbn:
- '9783319040998'
eissn:
- 2197-666X
isbn:
- '9783319040981'
issn:
- 1612-3786
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
series_title: Mathematics and Visualization
status: public
title: Toward the extraction of saddle periodic orbits
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 1
year: '2014'
...