---
_id: '1805'
abstract:
- lang: eng
text: 'We consider the problem of deciding whether the persistent homology group
of a simplicial pair (K,L) can be realized as the homology H∗(X) of some complex
X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded
in double-struck R3. As a consequence, we show that it is NP-hard to simplify
level and sublevel sets of scalar functions on double-struck S3 within a given
tolerance constraint. This problem has relevance to the visualization of medical
images by isosurfaces. We also show an implication to the theory of well groups
of scalar functions: not every well group can be realized by some level set, and
deciding whether a well group can be realized is NP-hard.'
author:
- first_name: Dominique
full_name: Attali, Dominique
last_name: Attali
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Olivier
full_name: Devillers, Olivier
last_name: Devillers
- first_name: Marc
full_name: Glisse, Marc
last_name: Glisse
- first_name: André
full_name: Lieutier, André
last_name: Lieutier
citation:
ama: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction
and simplification in R3. Computational Geometry: Theory and Applications.
2015;48(8):606-621. doi:10.1016/j.comgeo.2014.08.010'
apa: 'Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2015).
Homological reconstruction and simplification in R3. Computational Geometry:
Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.010'
chicago: 'Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André
Lieutier. “Homological Reconstruction and Simplification in R3.” Computational
Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.010.'
ieee: 'D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological
reconstruction and simplification in R3,” Computational Geometry: Theory and
Applications, vol. 48, no. 8. Elsevier, pp. 606–621, 2015.'
ista: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2015. Homological reconstruction
and simplification in R3. Computational Geometry: Theory and Applications. 48(8),
606–621.'
mla: 'Attali, Dominique, et al. “Homological Reconstruction and Simplification in
R3.” Computational Geometry: Theory and Applications, vol. 48, no. 8, Elsevier,
2015, pp. 606–21, doi:10.1016/j.comgeo.2014.08.010.'
short: 'D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, Computational
Geometry: Theory and Applications 48 (2015) 606–621.'
date_created: 2018-12-11T11:54:06Z
date_published: 2015-06-03T00:00:00Z
date_updated: 2023-02-23T10:59:19Z
day: '03'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2014.08.010
ec_funded: 1
intvolume: ' 48'
issue: '8'
language:
- iso: eng
month: '06'
oa_version: None
page: 606 - 621
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: 'Computational Geometry: Theory and Applications'
publication_status: published
publisher: Elsevier
publist_id: '5305'
quality_controlled: '1'
related_material:
record:
- id: '2812'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: Homological reconstruction and simplification in R3
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 48
year: '2015'
...
---
_id: '1793'
abstract:
- lang: eng
text: We present a software platform for reconstructing and analyzing the growth
of a plant root system from a time-series of 3D voxelized shapes. It aligns the
shapes with each other, constructs a geometric graph representation together with
the function that records the time of growth, and organizes the branches into
a hierarchy that reflects the order of creation. The software includes the automatic
computation of structural and dynamic traits for each root in the system enabling
the quantification of growth on fine-scale. These are important advances in plant
phenotyping with applications to the study of genetic and environmental influences
on growth.
article_number: e0127657
author:
- first_name: Olga
full_name: Symonova, Olga
id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87
last_name: Symonova
- 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. DynamicRoots: A software platform for
the reconstruction and analysis of growing plant roots. PLoS One. 2015;10(6).
doi:10.1371/journal.pone.0127657'
apa: 'Symonova, O., Topp, C., & Edelsbrunner, H. (2015). DynamicRoots: A software
platform for the reconstruction and analysis of growing plant roots. PLoS One.
Public Library of Science. https://doi.org/10.1371/journal.pone.0127657'
chicago: 'Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “DynamicRoots:
A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.”
PLoS One. Public Library of Science, 2015. https://doi.org/10.1371/journal.pone.0127657.'
ieee: 'O. Symonova, C. Topp, and H. Edelsbrunner, “DynamicRoots: A software platform
for the reconstruction and analysis of growing plant roots,” PLoS One,
vol. 10, no. 6. Public Library of Science, 2015.'
ista: 'Symonova O, Topp C, Edelsbrunner H. 2015. DynamicRoots: A software platform
for the reconstruction and analysis of growing plant roots. PLoS One. 10(6), e0127657.'
mla: 'Symonova, Olga, et al. “DynamicRoots: A Software Platform for the Reconstruction
and Analysis of Growing Plant Roots.” PLoS One, vol. 10, no. 6, e0127657,
Public Library of Science, 2015, doi:10.1371/journal.pone.0127657.'
short: O. Symonova, C. Topp, H. Edelsbrunner, PLoS One 10 (2015).
date_created: 2018-12-11T11:54:02Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2023-02-23T14:06:33Z
day: '01'
ddc:
- '000'
department:
- _id: MaJö
- _id: HeEd
doi: 10.1371/journal.pone.0127657
file:
- access_level: open_access
checksum: d20f26461ca575276ad3ed9ce4bfc787
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:15:30Z
date_updated: 2020-07-14T12:45:16Z
file_id: '5150'
file_name: IST-2016-454-v1+1_journal.pone.0127657.pdf
file_size: 1850825
relation: main_file
file_date_updated: 2020-07-14T12:45:16Z
has_accepted_license: '1'
intvolume: ' 10'
issue: '6'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
publication: PLoS One
publication_status: published
publisher: Public Library of Science
publist_id: '5318'
pubrep_id: '454'
quality_controlled: '1'
related_material:
record:
- id: '9737'
relation: research_data
status: public
scopus_import: 1
status: public
title: 'DynamicRoots: A software platform for the reconstruction and analysis of growing
plant roots'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 10
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
- 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: 2023-02-23T10:14:42Z
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.
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.
date_created: 2018-12-11T11:54:02Z
date_published: 2015-12-01T00:00:00Z
date_updated: 2023-09-07T11:41:25Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jco.2015.06.002
intvolume: ' 31'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 31
year: '2015'
...
---
_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.
date_created: 2018-12-11T11:51:48Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2023-09-07T11:41:25Z
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2015'
...
---
_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: 2022-06-21T12:01:47Z
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'
...
---
_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.
date_created: 2018-12-11T11:54:10Z
date_published: 2014-03-16T00:00:00Z
date_updated: 2021-01-12T06:53:23Z
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.
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: 2021-01-12T06:53:33Z
day: '14'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/s00454-014-9646-x
intvolume: ' 53'
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: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 53
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
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: 2022-03-03T11:47:09Z
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:
- '16093321'
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
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: 2021-01-12T06:54:09Z
day: '31'
department:
- _id: HeEd
doi: 10.1109/TVCG.2014.2346432
intvolume: ' 20'
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: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 20
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.
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 of 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 of 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
of 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 of 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 of 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: 2021-01-12T06:54:56Z
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
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 of 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: 4435EBFC-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.
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.
date_created: 2018-12-11T11:55:23Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2021-01-12T06:54:56Z
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
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: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2153'
abstract:
- lang: eng
text: 'We define a simple, explicit map sending a morphism f : M → N of pointwise
finite dimensional persistence modules to a matching between the barcodes of M
and N. Our main result is that, in a precise sense, the quality of this matching
is tightly controlled by the lengths of the longest intervals in the barcodes
of ker f and coker f . As an immediate corollary, we obtain a new proof of the
algebraic stability theorem for persistence barcodes [5, 9], a fundamental result
in the theory of persistent homology. In contrast to previous proofs, ours shows
explicitly how a δ-interleaving morphism between two persistence modules induces
a δ-matching between the barcodes of the two modules. Our main result also specializes
to a structure theorem for submodules and quotients of persistence modules. Copyright
is held by the owner/author(s).'
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: Lesnick, Michael
last_name: Lesnick
citation:
ama: 'Bauer U, Lesnick M. Induced matchings of barcodes and the algebraic stability
of persistence. In: Proceedings of the Annual Symposium on Computational Geometry.
ACM; 2014:355-364. doi:10.1145/2582112.2582168'
apa: 'Bauer, U., & Lesnick, M. (2014). Induced matchings of barcodes and the
algebraic stability of persistence. In Proceedings of the Annual Symposium
on Computational Geometry (pp. 355–364). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582168'
chicago: Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and
the Algebraic Stability of Persistence.” In Proceedings of the Annual Symposium
on Computational Geometry, 355–64. ACM, 2014. https://doi.org/10.1145/2582112.2582168.
ieee: U. Bauer and M. Lesnick, “Induced matchings of barcodes and the algebraic
stability of persistence,” in Proceedings of the Annual Symposium on Computational
Geometry, Kyoto, Japan, 2014, pp. 355–364.
ista: 'Bauer U, Lesnick M. 2014. Induced matchings of barcodes and the algebraic
stability of persistence. Proceedings of the Annual Symposium on Computational
Geometry. SoCG: Symposium on Computational Geometry, 355–364.'
mla: Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the
Algebraic Stability of Persistence.” Proceedings of the Annual Symposium on
Computational Geometry, ACM, 2014, pp. 355–64, doi:10.1145/2582112.2582168.
short: U. Bauer, M. Lesnick, in:, Proceedings of the Annual Symposium on Computational
Geometry, ACM, 2014, pp. 355–364.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
date_created: 2018-12-11T11:56:01Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2021-01-12T06:55:38Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582168
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1311.3681
month: '06'
oa: 1
oa_version: Submitted Version
page: 355 - 364
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Annual Symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4853'
quality_controlled: '1'
scopus_import: 1
status: public
title: Induced matchings of barcodes and the algebraic stability of persistence
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2156'
abstract:
- lang: eng
text: We propose a metric for Reeb graphs, called the functional distortion distance.
Under this distance, the Reeb graph is stable against small changes of input functions.
At the same time, it remains discriminative at differentiating input functions.
In particular, the main result is that the functional distortion distance between
two Reeb graphs is bounded from below by the bottleneck distance between both
the ordinary and extended persistence diagrams for appropriate dimensions. As
an application of our results, we analyze a natural simplification scheme for
Reeb graphs, and show that persistent features in Reeb graph remains persistent
under simplification. Understanding the stability of important features of the
Reeb graph under simplification is an interesting problem on its own right, and
critical to the practical usage of Reeb graphs. Copyright is held by the owner/author(s).
acknowledgement: National Science Foundation under grants CCF-1319406, CCF-1116258.
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Xiaoyin
full_name: Ge, Xiaoyin
last_name: Ge
- first_name: Yusu
full_name: Wang, Yusu
last_name: Wang
citation:
ama: 'Bauer U, Ge X, Wang Y. Measuring distance between Reeb graphs. In: Proceedings
of the Annual Symposium on Computational Geometry. ACM; 2014:464-473. doi:10.1145/2582112.2582169'
apa: 'Bauer, U., Ge, X., & Wang, Y. (2014). Measuring distance between Reeb
graphs. In Proceedings of the Annual Symposium on Computational Geometry
(pp. 464–473). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582169'
chicago: Bauer, Ulrich, Xiaoyin Ge, and Yusu Wang. “Measuring Distance between Reeb
Graphs.” In Proceedings of the Annual Symposium on Computational Geometry,
464–73. ACM, 2014. https://doi.org/10.1145/2582112.2582169.
ieee: U. Bauer, X. Ge, and Y. Wang, “Measuring distance between Reeb graphs,” in
Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan,
2014, pp. 464–473.
ista: 'Bauer U, Ge X, Wang Y. 2014. Measuring distance between Reeb graphs. Proceedings
of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational
Geometry, 464–473.'
mla: Bauer, Ulrich, et al. “Measuring Distance between Reeb Graphs.” Proceedings
of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–73,
doi:10.1145/2582112.2582169.
short: U. Bauer, X. Ge, Y. Wang, in:, Proceedings of the Annual Symposium on Computational
Geometry, ACM, 2014, pp. 464–473.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
date_created: 2018-12-11T11:56:02Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2021-01-12T06:55:39Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582169
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1307.2839
month: '06'
oa: 1
oa_version: Submitted Version
page: 464 - 473
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Annual Symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4850'
quality_controlled: '1'
scopus_import: 1
status: public
title: Measuring distance between Reeb graphs
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2155'
abstract:
- lang: eng
text: Given a finite set of points in Rn and a positive radius, we study the Čech,
Delaunay-Čech, alpha, and wrap complexes as instances of a generalized discrete
Morse theory. We prove that the latter three complexes are simple-homotopy equivalent.
Our results have applications in topological data analysis and in the reconstruction
of shapes from sampled data. Copyright is held by the owner/author(s).
acknowledgement: This research is partially supported by ESF under the ACAT Research
Network Programme, and by the Russian Government under mega project 11.G34.31.0053
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: 'Bauer U, Edelsbrunner H. The morse theory of Čech and Delaunay filtrations.
In: Proceedings of the Annual Symposium on Computational Geometry. ACM;
2014:484-490. doi:10.1145/2582112.2582167'
apa: 'Bauer, U., & Edelsbrunner, H. (2014). The morse theory of Čech and Delaunay
filtrations. In Proceedings of the Annual Symposium on Computational Geometry
(pp. 484–490). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582167'
chicago: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and
Delaunay Filtrations.” In Proceedings of the Annual Symposium on Computational
Geometry, 484–90. ACM, 2014. https://doi.org/10.1145/2582112.2582167.
ieee: U. Bauer and H. Edelsbrunner, “The morse theory of Čech and Delaunay filtrations,”
in Proceedings of the Annual Symposium on Computational Geometry, Kyoto,
Japan, 2014, pp. 484–490.
ista: 'Bauer U, Edelsbrunner H. 2014. The morse theory of Čech and Delaunay filtrations.
Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium
on Computational Geometry, 484–490.'
mla: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay
Filtrations.” Proceedings of the Annual Symposium on Computational Geometry,
ACM, 2014, pp. 484–90, doi:10.1145/2582112.2582167.
short: U. Bauer, H. Edelsbrunner, in:, Proceedings of the Annual Symposium on Computational
Geometry, ACM, 2014, pp. 484–490.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
date_created: 2018-12-11T11:56:01Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2021-01-12T06:55:38Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582167
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1312.1231
month: '06'
oa: 1
oa_version: Submitted Version
page: 484 - 490
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Annual Symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4851'
quality_controlled: '1'
scopus_import: 1
status: public
title: The morse theory of Čech and Delaunay filtrations
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2177'
abstract:
- lang: eng
text: We give evidence for the difficulty of computing Betti numbers of simplicial
complexes over a finite field. We do this by reducing the rank computation for
sparse matrices with to non-zero entries to computing Betti numbers of simplicial
complexes consisting of at most a constant times to simplices. Together with the
known reduction in the other direction, this implies that the two problems have
the same computational complexity.
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Salman
full_name: Parsa, Salman
id: 4BDBD4F2-F248-11E8-B48F-1D18A9856A87
last_name: Parsa
citation:
ama: 'Edelsbrunner H, Parsa S. On the computational complexity of betti numbers
reductions from matrix rank. In: Proceedings of the Annual ACM-SIAM Symposium
on Discrete Algorithms. SIAM; 2014:152-160. doi:10.1137/1.9781611973402.11'
apa: 'Edelsbrunner, H., & Parsa, S. (2014). On the computational complexity
of betti numbers reductions from matrix rank. In Proceedings of the Annual
ACM-SIAM Symposium on Discrete Algorithms (pp. 152–160). Portland, USA: SIAM.
https://doi.org/10.1137/1.9781611973402.11'
chicago: Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity
of Betti Numbers Reductions from Matrix Rank.” In Proceedings of the Annual
ACM-SIAM Symposium on Discrete Algorithms, 152–60. SIAM, 2014. https://doi.org/10.1137/1.9781611973402.11.
ieee: H. Edelsbrunner and S. Parsa, “On the computational complexity of betti numbers
reductions from matrix rank,” in Proceedings of the Annual ACM-SIAM Symposium
on Discrete Algorithms, Portland, USA, 2014, pp. 152–160.
ista: 'Edelsbrunner H, Parsa S. 2014. On the computational complexity of betti numbers
reductions from matrix rank. Proceedings of the Annual ACM-SIAM Symposium on Discrete
Algorithms. SODA: Symposium on Discrete Algorithms, 152–160.'
mla: Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of
Betti Numbers Reductions from Matrix Rank.” Proceedings of the Annual ACM-SIAM
Symposium on Discrete Algorithms, SIAM, 2014, pp. 152–60, doi:10.1137/1.9781611973402.11.
short: H. Edelsbrunner, S. Parsa, in:, Proceedings of the Annual ACM-SIAM Symposium
on Discrete Algorithms, SIAM, 2014, pp. 152–160.
conference:
end_date: 2014-01-07
location: Portland, USA
name: 'SODA: Symposium on Discrete Algorithms'
start_date: 2014-01-05
date_created: 2018-12-11T11:56:09Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2021-01-12T06:55:48Z
day: '01'
department:
- _id: HeEd
doi: 10.1137/1.9781611973402.11
language:
- iso: eng
month: '01'
oa_version: None
page: 152 - 160
publication: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
publication_status: published
publisher: SIAM
publist_id: '4805'
quality_controlled: '1'
scopus_import: 1
status: public
title: On the computational complexity of betti numbers reductions from matrix rank
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2184'
abstract:
- lang: eng
text: 'Given topological spaces X,Y, a fundamental problem of algebraic topology
is understanding the structure of all continuous maps X→ Y. We consider a computational
version, where X,Y are given as finite simplicial complexes, and the goal is to
compute [X,Y], that is, all homotopy classes of suchmaps.We solve this problem
in the stable range, where for some d ≥ 2, we have dim X ≤ 2d-2 and Y is (d-1)-connected;
in particular, Y can be the d-dimensional sphere Sd. The algorithm combines classical
tools and ideas from homotopy theory (obstruction theory, Postnikov systems, and
simplicial sets) with algorithmic tools from effective algebraic topology (locally
effective simplicial sets and objects with effective homology). In contrast, [X,Y]
is known to be uncomputable for general X,Y, since for X = S1 it includes a well
known undecidable problem: testing triviality of the fundamental group of Y. In
follow-up papers, the algorithm is shown to run in polynomial time for d fixed,
and extended to other problems, such as the extension problem, where we are given
a subspace A ⊂ X and a map A→ Y and ask whether it extends to a map X → Y, or
computing the Z2-index-everything in the stable range. Outside the stable range,
the extension problem is undecidable.'
acknowledgement: The research by M. K. was supported by project GAUK 49209. The research
by M. K. was also supported by project 1M0545 by the Ministry of Education of the
Czech Republic and by Center of Excellence { Inst. for Theor. Comput. Sci., Prague
(project P202/12/G061 of GACR). The research by U. W. was supported by the Swiss
National Science Foundation (SNF Projects 200021-125309, 200020-138230, and PP00P2-138948).
article_number: '17 '
author:
- first_name: Martin
full_name: Čadek, Martin
last_name: Čadek
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Francis
full_name: Sergeraert, Francis
last_name: Sergeraert
- first_name: Lukáš
full_name: Vokřínek, Lukáš
last_name: Vokřínek
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. Computing
all maps into a sphere. Journal of the ACM. 2014;61(3). doi:10.1145/2597629
apa: Čadek, M., Krcál, M., Matoušek, J., Sergeraert, F., Vokřínek, L., & Wagner,
U. (2014). Computing all maps into a sphere. Journal of the ACM. ACM. https://doi.org/10.1145/2597629
chicago: Čadek, Martin, Marek Krcál, Jiří Matoušek, Francis Sergeraert, Lukáš Vokřínek,
and Uli Wagner. “Computing All Maps into a Sphere.” Journal of the ACM.
ACM, 2014. https://doi.org/10.1145/2597629.
ieee: M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, and U. Wagner,
“Computing all maps into a sphere,” Journal of the ACM, vol. 61, no. 3.
ACM, 2014.
ista: Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. 2014. Computing
all maps into a sphere. Journal of the ACM. 61(3), 17.
mla: Čadek, Martin, et al. “Computing All Maps into a Sphere.” Journal of the
ACM, vol. 61, no. 3, 17, ACM, 2014, doi:10.1145/2597629.
short: M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, U. Wagner, Journal
of the ACM 61 (2014).
date_created: 2018-12-11T11:56:12Z
date_published: 2014-05-01T00:00:00Z
date_updated: 2021-01-12T06:55:50Z
day: '01'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1145/2597629
intvolume: ' 61'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1105.6257
month: '05'
oa: 1
oa_version: Preprint
publication: Journal of the ACM
publication_status: published
publisher: ACM
publist_id: '4797'
quality_controlled: '1'
scopus_import: 1
status: public
title: Computing all maps into a sphere
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 61
year: '2014'
...
---
_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 Publishing House; 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 Publishing House. https://doi.org/10.4171/120-1/3'
chicago: 'Edelsbrunner, Herbert, and Dmitriy Morozovy. “Persistent Homology: Theory
and Practice,” 31–50. European Mathematical Society Publishing House, 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 Publishing House, 2014, pp. 31–50,
doi:10.4171/120-1/3.'
short: H. Edelsbrunner, D. Morozovy, in:, European Mathematical Society Publishing
House, 2014, pp. 31–50.
conference:
end_date: 2012-07-07
location: Kraków, Poland
name: 'ECM: European Congress of Mathematics'
start_date: 2012-07-02
date_created: 2018-12-11T12:00:16Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2021-01-12T07:00:36Z
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 Publishing House
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: '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
date_created: 2022-03-21T07:09:03Z
date_published: 2014-11-08T00:00:00Z
date_updated: 2023-02-23T12:20:55Z
day: '08'
department:
- _id: HeEd
doi: 10.1007/978-3-319-13075-0_10
intvolume: ' 8889'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8889
year: '2014'
...
---
_id: '6853'
abstract:
- lang: eng
text: This monograph presents a short course in computational geometry and topology.
In the first part the book covers Voronoi diagrams and Delaunay triangulations,
then it presents the theory of alpha complexes which play a crucial role in biology.
The central part of the book is the homology theory and their computation, including
the theory of persistence which is indispensable for applications, e.g. shape
reconstruction. The target audience comprises researchers and practitioners in
mathematics, biology, neuroscience and computer science, but the book may also
be beneficial to graduate students of these fields.
alternative_title:
- SpringerBriefs in Applied Sciences and Technology
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. A Short Course in Computational Geometry and Topology.
1st ed. Cham: Springer Nature; 2014. doi:10.1007/978-3-319-05957-0'
apa: 'Edelsbrunner, H. (2014). A Short Course in Computational Geometry and Topology
(1st ed.). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-05957-0'
chicago: 'Edelsbrunner, Herbert. A Short Course in Computational Geometry and
Topology. 1st ed. SpringerBriefs in Applied Sciences and Technology. Cham:
Springer Nature, 2014. https://doi.org/10.1007/978-3-319-05957-0.'
ieee: 'H. Edelsbrunner, A Short Course in Computational Geometry and Topology,
1st ed. Cham: Springer Nature, 2014.'
ista: 'Edelsbrunner H. 2014. A Short Course in Computational Geometry and Topology
1st ed., Cham: Springer Nature, IX, 110p.'
mla: Edelsbrunner, Herbert. A Short Course in Computational Geometry and Topology.
1st ed., Springer Nature, 2014, doi:10.1007/978-3-319-05957-0.
short: H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st
ed., Springer Nature, Cham, 2014.
date_created: 2019-09-06T09:22:33Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2022-03-04T07:47:54Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-319-05957-0
edition: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: IX, 110
place: Cham
publication_identifier:
eisbn:
- 9-783-3190-5957-0
eissn:
- 2191-5318
isbn:
- 9-783-3190-5956-3
issn:
- 2191-530X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
link:
- description: available as eBook via catalog IST BookList
relation: other
url: https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=356106
- description: available via catalog IST BookList
relation: other
url: https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=373842
scopus_import: '1'
series_title: SpringerBriefs in Applied Sciences and Technology
status: public
title: A Short Course in Computational Geometry and Topology
type: book
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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: '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: 2023-09-05T15:33:45Z
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: '2255'
abstract:
- lang: eng
text: Motivated by applications in biology, we present an algorithm for estimating
the length of tube-like shapes in 3-dimensional Euclidean space. In a first step,
we combine the tube formula of Weyl with integral geometric methods to obtain
an integral representation of the length, which we approximate using a variant
of the Koksma-Hlawka Theorem. In a second step, we use tools from computational
topology to decrease the dependence on small perturbations of the shape. We present
computational experiments that shed light on the stability and the convergence
rate of our algorithm.
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. Stable length estimates of tube-like shapes. Journal
of Mathematical Imaging and Vision. 2014;50(1):164-177. doi:10.1007/s10851-013-0468-x
apa: Edelsbrunner, H., & Pausinger, F. (2014). Stable length estimates of tube-like
shapes. Journal of Mathematical Imaging and Vision. Springer. https://doi.org/10.1007/s10851-013-0468-x
chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates
of Tube-like Shapes.” Journal of Mathematical Imaging and Vision. Springer,
2014. https://doi.org/10.1007/s10851-013-0468-x.
ieee: H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,”
Journal of Mathematical Imaging and Vision, vol. 50, no. 1. Springer, pp.
164–177, 2014.
ista: Edelsbrunner H, Pausinger F. 2014. Stable length estimates of tube-like shapes.
Journal of Mathematical Imaging and Vision. 50(1), 164–177.
mla: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like
Shapes.” Journal of Mathematical Imaging and Vision, vol. 50, no. 1, Springer,
2014, pp. 164–77, doi:10.1007/s10851-013-0468-x.
short: H. Edelsbrunner, F. Pausinger, Journal of Mathematical Imaging and Vision
50 (2014) 164–177.
date_created: 2018-12-11T11:56:36Z
date_published: 2014-09-01T00:00:00Z
date_updated: 2023-09-07T11:41:25Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s10851-013-0468-x
ec_funded: 1
file:
- access_level: open_access
checksum: 2f93f3e63a38a85cd4404d7953913b14
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:18Z
date_updated: 2020-07-14T12:45:35Z
file_id: '5204'
file_name: IST-2016-549-v1+1_2014-J-06-LengthEstimate.pdf
file_size: 3941391
relation: main_file
file_date_updated: 2020-07-14T12:45:35Z
has_accepted_license: '1'
intvolume: ' 50'
issue: '1'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Submitted Version
page: 164 - 177
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Journal of Mathematical Imaging and Vision
publication_identifier:
issn:
- '09249907'
publication_status: published
publisher: Springer
publist_id: '4691'
pubrep_id: '549'
quality_controlled: '1'
related_material:
record:
- id: '2843'
relation: earlier_version
status: public
- id: '1399'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: Stable length estimates of tube-like shapes
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 50
year: '2014'
...
---
_id: '10894'
abstract:
- lang: eng
text: PHAT is a C++ library for the computation of persistent homology by matrix
reduction. We aim for a simple generic design that decouples algorithms from data
structures without sacrificing efficiency or user-friendliness. This makes PHAT
a versatile platform for experimenting with algorithmic ideas and comparing them
to state of the art implementations.
article_processing_charge: No
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
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Hubert
full_name: Wagner, Hubert
last_name: Wagner
citation:
ama: 'Bauer U, Kerber M, Reininghaus J, Wagner H. PHAT – Persistent Homology Algorithms
Toolbox. In: ICMS 2014: International Congress on Mathematical Software.
Vol 8592. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg; 2014:137-143.
doi:10.1007/978-3-662-44199-2_24'
apa: 'Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2014). PHAT – Persistent
Homology Algorithms Toolbox. In ICMS 2014: International Congress on Mathematical
Software (Vol. 8592, pp. 137–143). Berlin, Heidelberg: Springer Berlin Heidelberg.
https://doi.org/10.1007/978-3-662-44199-2_24'
chicago: 'Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “PHAT
– Persistent Homology Algorithms Toolbox.” In ICMS 2014: International Congress
on Mathematical Software, 8592:137–43. LNCS. Berlin, Heidelberg: Springer
Berlin Heidelberg, 2014. https://doi.org/10.1007/978-3-662-44199-2_24.'
ieee: 'U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “PHAT – Persistent Homology
Algorithms Toolbox,” in ICMS 2014: International Congress on Mathematical Software,
Seoul, South Korea, 2014, vol. 8592, pp. 137–143.'
ista: 'Bauer U, Kerber M, Reininghaus J, Wagner H. 2014. PHAT – Persistent Homology
Algorithms Toolbox. ICMS 2014: International Congress on Mathematical Software.
ICMS: International Congress on Mathematical SoftwareLNCS vol. 8592, 137–143.'
mla: 'Bauer, Ulrich, et al. “PHAT – Persistent Homology Algorithms Toolbox.” ICMS
2014: International Congress on Mathematical Software, vol. 8592, Springer
Berlin Heidelberg, 2014, pp. 137–43, doi:10.1007/978-3-662-44199-2_24.'
short: 'U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, in:, ICMS 2014: International
Congress on Mathematical Software, Springer Berlin Heidelberg, Berlin, Heidelberg,
2014, pp. 137–143.'
conference:
end_date: 2014-08-09
location: Seoul, South Korea
name: 'ICMS: International Congress on Mathematical Software'
start_date: 2014-08-05
date_created: 2022-03-21T07:12:16Z
date_published: 2014-09-01T00:00:00Z
date_updated: 2023-09-20T09:42:40Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-662-44199-2_24
intvolume: ' 8592'
language:
- iso: eng
month: '09'
oa_version: None
page: 137-143
place: Berlin, Heidelberg
publication: 'ICMS 2014: International Congress on Mathematical Software'
publication_identifier:
eisbn:
- '9783662441992'
eissn:
- 1611-3349
isbn:
- '9783662441985'
issn:
- 0302-9743
publication_status: published
publisher: Springer Berlin Heidelberg
quality_controlled: '1'
related_material:
record:
- id: '1433'
relation: later_version
status: public
scopus_import: '1'
series_title: LNCS
status: public
title: PHAT – Persistent Homology Algorithms Toolbox
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 8592
year: '2014'
...
---
_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_number: '1401.0468'
article_processing_charge: No
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. arXiv.
doi:10.48550/arXiv.1401.0468
apa: Iglesias Ham, M., Kerber, M., & Uhler, C. (n.d.). Sphere packing with limited
overlap. arXiv. https://doi.org/10.48550/arXiv.1401.0468
chicago: Iglesias Ham, Mabel, Michael Kerber, and Caroline Uhler. “Sphere Packing
with Limited Overlap.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1401.0468.
ieee: M. Iglesias Ham, M. Kerber, and C. Uhler, “Sphere packing with limited overlap,”
arXiv. .
ista: Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv,
1401.0468.
mla: Iglesias Ham, Mabel, et al. “Sphere Packing with Limited Overlap.” ArXiv,
1401.0468, doi:10.48550/arXiv.1401.0468.
short: M. Iglesias Ham, M. Kerber, C. Uhler, ArXiv (n.d.).
date_created: 2018-12-11T11:55:12Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2023-10-18T08:06:45Z
day: '01'
department:
- _id: HeEd
- _id: CaUh
doi: 10.48550/arXiv.1401.0468
external_id:
arxiv:
- '1401.0468'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://cccg.ca/proceedings/2014/papers/paper23.pdf
month: '01'
oa: 1
oa_version: Submitted Version
publication: arXiv
publication_status: submitted
publist_id: '5064'
status: public
title: Sphere packing with limited overlap
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2209'
abstract:
- lang: eng
text: "A straight skeleton is a well-known geometric structure, and several algorithms
exist to construct the straight skeleton for a given polygon or planar straight-line
graph. In this paper, we ask the reverse question: Given the straight skeleton
(in form of a planar straight-line graph, with some rays to infinity), can we
reconstruct a planar straight-line graph for which this was the straight skeleton?
We show how to reduce this problem to the problem of finding a line that intersects
a set of convex polygons. We can find these convex polygons and all such lines
in $O(nlog n)$ time in the Real RAM computer model, where $n$ denotes the number
of edges of the input graph. We also explain how our approach can be used for
recognizing Voronoi diagrams of points, thereby completing a partial solution
provided by Ash and Bolker in 1985.\r\n"
alternative_title:
- '2013 10th International Symposium on Voronoi Diagrams in Science and Engineering
(ISVD 2013) '
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
citation:
ama: 'Biedl T, Held M, Huber S. Recognizing straight skeletons and Voronoi diagrams
and reconstructing their input. In: IEEE; 2013:37-46. doi:10.1109/ISVD.2013.11'
apa: 'Biedl, T., Held, M., & Huber, S. (2013). Recognizing straight skeletons
and Voronoi diagrams and reconstructing their input (pp. 37–46). Presented at
the ISVD: Voronoi Diagrams in Science and Engineering, St. Petersburg, Russia:
IEEE. https://doi.org/10.1109/ISVD.2013.11'
chicago: Biedl, Therese, Martin Held, and Stefan Huber. “Recognizing Straight Skeletons
and Voronoi Diagrams and Reconstructing Their Input,” 37–46. IEEE, 2013. https://doi.org/10.1109/ISVD.2013.11.
ieee: 'T. Biedl, M. Held, and S. Huber, “Recognizing straight skeletons and Voronoi
diagrams and reconstructing their input,” presented at the ISVD: Voronoi Diagrams
in Science and Engineering, St. Petersburg, Russia, 2013, pp. 37–46.'
ista: 'Biedl T, Held M, Huber S. 2013. Recognizing straight skeletons and Voronoi
diagrams and reconstructing their input. ISVD: Voronoi Diagrams in Science and
Engineering, 2013 10th International Symposium on Voronoi Diagrams in Science
and Engineering (ISVD 2013) , , 37–46.'
mla: Biedl, Therese, et al. Recognizing Straight Skeletons and Voronoi Diagrams
and Reconstructing Their Input. IEEE, 2013, pp. 37–46, doi:10.1109/ISVD.2013.11.
short: T. Biedl, M. Held, S. Huber, in:, IEEE, 2013, pp. 37–46.
conference:
end_date: 2013-07-10
location: St. Petersburg, Russia
name: 'ISVD: Voronoi Diagrams in Science and Engineering'
start_date: 2013-07-08
date_created: 2018-12-11T11:56:20Z
date_published: 2013-12-01T00:00:00Z
date_updated: 2021-01-12T06:56:00Z
day: '01'
department:
- _id: HeEd
doi: 10.1109/ISVD.2013.11
language:
- iso: eng
month: '12'
oa_version: None
page: 37 - 46
publication_identifier:
eisbn:
- '978-0-7695-5037-4 '
publication_status: published
publisher: IEEE
publist_id: '4763'
quality_controlled: '1'
scopus_import: 1
status: public
title: Recognizing straight skeletons and Voronoi diagrams and reconstructing their
input
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2013'
...
---
_id: '2210'
abstract:
- lang: eng
text: 'A straight skeleton is a well-known geometric structure, and several algorithms
exist to construct the straight skeleton for a given polygon. In this paper, we
ask the reverse question: Given the straight skeleton (in form of a tree with
a drawing in the plane, but with the exact position of the leaves unspecified),
can we reconstruct the polygon? We show that in most cases there exists at most
one polygon; in the remaining case there is an infinite number of polygons determined
by one angle that can range in an interval. We can find this (set of) polygon(s)
in linear time in the Real RAM computer model.'
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
citation:
ama: 'Biedl T, Held M, Huber S. Reconstructing polygons from embedded straight skeletons.
In: 29th European Workshop on Computational Geometry. TU Braunschweig;
2013:95-98.'
apa: 'Biedl, T., Held, M., & Huber, S. (2013). Reconstructing polygons from
embedded straight skeletons. In 29th European Workshop on Computational Geometry
(pp. 95–98). Braunschweig, Germany: TU Braunschweig.'
chicago: Biedl, Therese, Martin Held, and Stefan Huber. “Reconstructing Polygons
from Embedded Straight Skeletons.” In 29th European Workshop on Computational
Geometry, 95–98. TU Braunschweig, 2013.
ieee: T. Biedl, M. Held, and S. Huber, “Reconstructing polygons from embedded straight
skeletons,” in 29th European Workshop on Computational Geometry, Braunschweig,
Germany, 2013, pp. 95–98.
ista: 'Biedl T, Held M, Huber S. 2013. Reconstructing polygons from embedded straight
skeletons. 29th European Workshop on Computational Geometry. EuroCG: European
Workshop on Computational Geometry, 95–98.'
mla: Biedl, Therese, et al. “Reconstructing Polygons from Embedded Straight Skeletons.”
29th European Workshop on Computational Geometry, TU Braunschweig, 2013,
pp. 95–98.
short: T. Biedl, M. Held, S. Huber, in:, 29th European Workshop on Computational
Geometry, TU Braunschweig, 2013, pp. 95–98.
conference:
end_date: 2013-03-20
location: Braunschweig, Germany
name: 'EuroCG: European Workshop on Computational Geometry'
start_date: 2013-03-17
date_created: 2018-12-11T11:56:21Z
date_published: 2013-03-01T00:00:00Z
date_updated: 2021-01-12T06:56:00Z
day: '01'
department:
- _id: HeEd
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.ibr.cs.tu-bs.de/alg/eurocg13/booklet_eurocg13.pdf
month: '03'
oa: 1
oa_version: Submitted Version
page: 95 - 98
publication: 29th European Workshop on Computational Geometry
publication_status: published
publisher: TU Braunschweig
publist_id: '4762'
status: public
title: Reconstructing polygons from embedded straight skeletons
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2013'
...
---
_id: '2304'
abstract:
- lang: eng
text: This extended abstract is concerned with the irregularities of distribution
of one-dimensional permuted van der Corput sequences that are generated from linear
permutations. We show how to obtain upper bounds for the discrepancy and diaphony
of these sequences, by relating them to Kronecker sequences and applying earlier
results of Faure and Niederreiter.
acknowledgement: This research is supported by the Graduate school of IST Austria
(Institute of Science and Technology Austria).
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. Van der Corput sequences and linear permutations. Electronic
Notes in Discrete Mathematics. 2013;43:43-50. doi:10.1016/j.endm.2013.07.008
apa: Pausinger, F. (2013). Van der Corput sequences and linear permutations. Electronic
Notes in Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.endm.2013.07.008
chicago: Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.”
Electronic Notes in Discrete Mathematics. Elsevier, 2013. https://doi.org/10.1016/j.endm.2013.07.008.
ieee: F. Pausinger, “Van der Corput sequences and linear permutations,” Electronic
Notes in Discrete Mathematics, vol. 43. Elsevier, pp. 43–50, 2013.
ista: Pausinger F. 2013. Van der Corput sequences and linear permutations. Electronic
Notes in Discrete Mathematics. 43, 43–50.
mla: Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” Electronic
Notes in Discrete Mathematics, vol. 43, Elsevier, 2013, pp. 43–50, doi:10.1016/j.endm.2013.07.008.
short: F. Pausinger, Electronic Notes in Discrete Mathematics 43 (2013) 43–50.
date_created: 2018-12-11T11:56:53Z
date_published: 2013-09-05T00:00:00Z
date_updated: 2021-01-12T06:56:39Z
day: '05'
department:
- _id: HeEd
doi: 10.1016/j.endm.2013.07.008
intvolume: ' 43'
language:
- iso: eng
month: '09'
oa_version: None
page: 43 - 50
publication: Electronic Notes in Discrete Mathematics
publication_status: published
publisher: Elsevier
publist_id: '4623'
quality_controlled: '1'
scopus_import: 1
status: public
title: Van der Corput sequences and linear permutations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 43
year: '2013'
...
---
_id: '2807'
abstract:
- lang: eng
text: 'We consider several basic problems of algebraic topology, with connections
to combinatorial and geometric questions, from the point of view of computational
complexity. The extension problem asks, given topological spaces X; Y , a subspace
A ⊆ X, and a (continuous) map f : A → Y , whether f can be extended to a map X
→ Y . For computational purposes, we assume that X and Y are represented as finite
simplicial complexes, A is a subcomplex of X, and f is given as a simplicial map.
In this generality the problem is undecidable, as follows from Novikov''s result
from the 1950s on uncomputability of the fundamental group π1(Y ). We thus study
the problem under the assumption that, for some k ≥ 2, Y is (k - 1)-connected;
informally, this means that Y has \no holes up to dimension k-1" (a basic
example of such a Y is the sphere Sk). We prove that, on the one hand, this problem
is still undecidable for dimX = 2k. On the other hand, for every fixed k ≥ 2,
we obtain an algorithm that solves the extension problem in polynomial time assuming
Y (k - 1)-connected and dimX ≤ 2k - 1. For dimX ≤ 2k - 2, the algorithm also provides
a classification of all extensions up to homotopy (continuous deformation). This
relies on results of our SODA 2012 paper, and the main new ingredient is a machinery
of objects with polynomial-time homology, which is a polynomial-time analog of
objects with effective homology developed earlier by Sergeraert et al. We also
consider the computation of the higher homotopy groups πk(Y ), k ≥ 2, for a 1-connected
Y . Their computability was established by Brown in 1957; we show that πk(Y )
can be computed in polynomial time for every fixed k ≥ 2. On the other hand, Anick
proved in 1989 that computing πk(Y ) is #P-hard if k is a part of input, where
Y is a cell complex with certain rather compact encoding. We strengthen his result
to #P-hardness for Y given as a simplicial complex. '
author:
- first_name: Martin
full_name: Čadek, Martin
last_name: Čadek
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Lukáš
full_name: Vokřínek, Lukáš
last_name: Vokřínek
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. Extending continuous maps:
Polynomiality and undecidability. In: 45th Annual ACM Symposium on Theory of
Computing. ACM; 2013:595-604. doi:10.1145/2488608.2488683'
apa: 'Čadek, M., Krcál, M., Matoušek, J., Vokřínek, L., & Wagner, U. (2013).
Extending continuous maps: Polynomiality and undecidability. In 45th Annual
ACM Symposium on theory of computing (pp. 595–604). Palo Alto, CA, United
States: ACM. https://doi.org/10.1145/2488608.2488683'
chicago: 'Čadek, Martin, Marek Krcál, Jiří Matoušek, Lukáš Vokřínek, and Uli Wagner.
“Extending Continuous Maps: Polynomiality and Undecidability.” In 45th Annual
ACM Symposium on Theory of Computing, 595–604. ACM, 2013. https://doi.org/10.1145/2488608.2488683.'
ieee: 'M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, and U. Wagner, “Extending continuous
maps: Polynomiality and undecidability,” in 45th Annual ACM Symposium on theory
of computing, Palo Alto, CA, United States, 2013, pp. 595–604.'
ista: 'Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. 2013. Extending continuous
maps: Polynomiality and undecidability. 45th Annual ACM Symposium on theory of
computing. STOC: Symposium on the Theory of Computing, 595–604.'
mla: 'Čadek, Martin, et al. “Extending Continuous Maps: Polynomiality and Undecidability.”
45th Annual ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604,
doi:10.1145/2488608.2488683.'
short: M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, U. Wagner, in:, 45th Annual
ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604.
conference:
end_date: 2013-06-04
location: Palo Alto, CA, United States
name: 'STOC: Symposium on the Theory of Computing'
start_date: 2013-06-01
date_created: 2018-12-11T11:59:42Z
date_published: 2013-06-01T00:00:00Z
date_updated: 2021-01-12T06:59:51Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1145/2488608.2488683
file:
- access_level: open_access
checksum: 06c2ce5c1135fbc1f71ca15eeb242dcf
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:14:29Z
date_updated: 2020-07-14T12:45:48Z
file_id: '5081'
file_name: IST-2016-533-v1+1_Extending_continuous_maps_polynomiality_and_undecidability.pdf
file_size: 447945
relation: main_file
file_date_updated: 2020-07-14T12:45:48Z
has_accepted_license: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
page: 595 - 604
publication: 45th Annual ACM Symposium on theory of computing
publication_status: published
publisher: ACM
publist_id: '4078'
pubrep_id: '533'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'Extending continuous maps: Polynomiality and undecidability'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2013'
...
---
_id: '2812'
abstract:
- lang: eng
text: 'We consider the problem of deciding whether the persistent homology group
of a simplicial pair (K, L) can be realized as the homology H* (X) of some complex
X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded
in ℝ3. As a consequence, we show that it is NP-hard to simplify level and sublevel
sets of scalar functions on S3 within a given tolerance constraint. This problem
has relevance to the visualization of medical images by isosurfaces. We also show
an implication to the theory of well groups of scalar functions: not every well
group can be realized by some level set, and deciding whether a well group can
be realized is NP-hard.'
acknowledgement: Some of the authors were partially supported by the GIGA ANR grant
(contract ANR-09-BLAN-0331-01) and the European project CG-Learning (contract 255827).
author:
- first_name: Dominique
full_name: Attali, Dominique
last_name: Attali
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Olivier
full_name: Devillers, Olivier
last_name: Devillers
- first_name: Marc
full_name: Glisse, Marc
last_name: Glisse
- first_name: André
full_name: Lieutier, André
last_name: Lieutier
citation:
ama: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction
and simplification in R3. In: Proceedings of the 29th Annual Symposium on Computational
Geometry. ACM; 2013:117-125. doi:10.1145/2462356.2462373'
apa: 'Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2013).
Homological reconstruction and simplification in R3. In Proceedings of the
29th annual symposium on Computational Geometry (pp. 117–125). Rio de Janeiro,
Brazil: ACM. https://doi.org/10.1145/2462356.2462373'
chicago: Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André
Lieutier. “Homological Reconstruction and Simplification in R3.” In Proceedings
of the 29th Annual Symposium on Computational Geometry, 117–25. ACM, 2013.
https://doi.org/10.1145/2462356.2462373.
ieee: D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological
reconstruction and simplification in R3,” in Proceedings of the 29th annual
symposium on Computational Geometry, Rio de Janeiro, Brazil, 2013, pp. 117–125.
ista: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2013. Homological reconstruction
and simplification in R3. Proceedings of the 29th annual symposium on Computational
Geometry. SoCG: Symposium on Computational Geometry, 117–125.'
mla: Attali, Dominique, et al. “Homological Reconstruction and Simplification in
R3.” Proceedings of the 29th Annual Symposium on Computational Geometry,
ACM, 2013, pp. 117–25, doi:10.1145/2462356.2462373.
short: D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, in:, Proceedings
of the 29th Annual Symposium on Computational Geometry, ACM, 2013, pp. 117–125.
conference:
end_date: 2013-06-20
location: Rio de Janeiro, Brazil
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2013-06-17
date_created: 2018-12-11T11:59:44Z
date_published: 2013-06-01T00:00:00Z
date_updated: 2023-02-23T10:15:15Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2462356.2462373
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://hal.archives-ouvertes.fr/hal-00833791/
month: '06'
oa: 1
oa_version: Submitted Version
page: 117 - 125
publication: Proceedings of the 29th annual symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4072'
quality_controlled: '1'
related_material:
record:
- id: '1805'
relation: later_version
status: public
scopus_import: 1
status: public
title: Homological reconstruction and simplification in R3
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2013'
...
---
_id: '2822'
abstract:
- lang: eng
text: Identification of genes that control root system architecture in crop plants
requires innovations that enable high-throughput and accurate measurements of
root system architecture through time. We demonstrate the ability of a semiautomated
3D in vivo imaging and digital phenotyping pipeline to interrogate the quantitative
genetic basis of root system growth in a rice biparental mapping population, Bala
x Azucena. We phenotyped >1,400 3D root models and >57,000 2D images for
a suite of 25 traits that quantified the distribution, shape, extent of exploration,
and the intrinsic size of root networks at days 12, 14, and 16 of growth in a
gellan gum medium. From these data we identified 89 quantitative trait loci, some
of which correspond to those found previously in soil-grown plants, and provide
evidence for genetic tradeoffs in root growth allocations, such as between the
extent and thoroughness of exploration. We also developed a multivariate method
for generating and mapping central root architecture phenotypes and used it to
identify five major quantitative trait loci (r2 = 24-37%), two of which were not
identified by our univariate analysis. Our imaging and analytical platform provides
a means to identify genes with high potential for improving root traits and agronomic
qualities of crops.
author:
- first_name: Christopher
full_name: Topp, Christopher
last_name: Topp
- first_name: Anjali
full_name: Iyer Pascuzzi, Anjali
last_name: Iyer Pascuzzi
- first_name: Jill
full_name: Anderson, Jill
last_name: Anderson
- first_name: Cheng
full_name: Lee, Cheng
last_name: Lee
- first_name: Paul
full_name: Zurek, Paul
last_name: Zurek
- first_name: Olga
full_name: Symonova, Olga
id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87
last_name: Symonova
- first_name: Ying
full_name: Zheng, Ying
last_name: Zheng
- first_name: Alexander
full_name: Bucksch, Alexander
last_name: Bucksch
- first_name: Yuriy
full_name: Mileyko, Yuriy
last_name: Mileyko
- first_name: Taras
full_name: Galkovskyi, Taras
last_name: Galkovskyi
- first_name: Brad
full_name: Moore, Brad
last_name: Moore
- first_name: John
full_name: Harer, John
last_name: Harer
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Thomas
full_name: Mitchell Olds, Thomas
last_name: Mitchell Olds
- first_name: Joshua
full_name: Weitz, Joshua
last_name: Weitz
- first_name: Philip
full_name: Benfey, Philip
last_name: Benfey
citation:
ama: Topp C, Iyer Pascuzzi A, Anderson J, et al. 3D phenotyping and quantitative
trait locus mapping identify core regions of the rice genome controlling root
architecture. PNAS. 2013;110(18):E1695-E1704. doi:10.1073/pnas.1304354110
apa: Topp, C., Iyer Pascuzzi, A., Anderson, J., Lee, C., Zurek, P., Symonova, O.,
… Benfey, P. (2013). 3D phenotyping and quantitative trait locus mapping identify
core regions of the rice genome controlling root architecture. PNAS. National
Academy of Sciences. https://doi.org/10.1073/pnas.1304354110
chicago: Topp, Christopher, Anjali Iyer Pascuzzi, Jill Anderson, Cheng Lee, Paul
Zurek, Olga Symonova, Ying Zheng, et al. “3D Phenotyping and Quantitative Trait
Locus Mapping Identify Core Regions of the Rice Genome Controlling Root Architecture.”
PNAS. National Academy of Sciences, 2013. https://doi.org/10.1073/pnas.1304354110.
ieee: C. Topp et al., “3D phenotyping and quantitative trait locus mapping
identify core regions of the rice genome controlling root architecture,” PNAS,
vol. 110, no. 18. National Academy of Sciences, pp. E1695–E1704, 2013.
ista: Topp C, Iyer Pascuzzi A, Anderson J, Lee C, Zurek P, Symonova O, Zheng Y,
Bucksch A, Mileyko Y, Galkovskyi T, Moore B, Harer J, Edelsbrunner H, Mitchell
Olds T, Weitz J, Benfey P. 2013. 3D phenotyping and quantitative trait locus mapping
identify core regions of the rice genome controlling root architecture. PNAS.
110(18), E1695–E1704.
mla: Topp, Christopher, et al. “3D Phenotyping and Quantitative Trait Locus Mapping
Identify Core Regions of the Rice Genome Controlling Root Architecture.” PNAS,
vol. 110, no. 18, National Academy of Sciences, 2013, pp. E1695–704, doi:10.1073/pnas.1304354110.
short: C. Topp, A. Iyer Pascuzzi, J. Anderson, C. Lee, P. Zurek, O. Symonova, Y.
Zheng, A. Bucksch, Y. Mileyko, T. Galkovskyi, B. Moore, J. Harer, H. Edelsbrunner,
T. Mitchell Olds, J. Weitz, P. Benfey, PNAS 110 (2013) E1695–E1704.
date_created: 2018-12-11T11:59:47Z
date_published: 2013-04-30T00:00:00Z
date_updated: 2021-01-12T06:59:58Z
day: '30'
department:
- _id: MaJö
- _id: HeEd
doi: 10.1073/pnas.1304354110
external_id:
pmid:
- '25673779'
intvolume: ' 110'
issue: '18'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4378147/
month: '04'
oa: 1
oa_version: Submitted Version
page: E1695 - E1704
pmid: 1
publication: PNAS
publication_status: published
publisher: National Academy of Sciences
publist_id: '3979'
quality_controlled: '1'
scopus_import: 1
status: public
title: 3D phenotyping and quantitative trait locus mapping identify core regions of
the rice genome controlling root architecture
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 110
year: '2013'
...
---
_id: '2843'
abstract:
- lang: eng
text: 'Mathematical objects can be measured unambiguously, but not so objects from
our physical world. Even the total length of tubelike shapes has its difficulties.
We introduce a combination of geometric, probabilistic, and topological methods
to design a stable length estimate for tube-like shapes; that is: one that is
insensitive to small shape changes.'
alternative_title:
- LNCS
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. Stable length estimates of tube-like shapes.
In: 17th IAPR International Conference on Discrete Geometry for Computer Imagery.
Vol 7749. Springer; 2013:XV-XIX. doi:10.1007/978-3-642-37067-0'
apa: 'Edelsbrunner, H., & Pausinger, F. (2013). Stable length estimates of tube-like
shapes. In 17th IAPR International Conference on Discrete Geometry for Computer
Imagery (Vol. 7749, pp. XV–XIX). Seville, Spain: Springer. https://doi.org/10.1007/978-3-642-37067-0'
chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates
of Tube-like Shapes.” In 17th IAPR International Conference on Discrete Geometry
for Computer Imagery, 7749:XV–XIX. Springer, 2013. https://doi.org/10.1007/978-3-642-37067-0.
ieee: H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,”
in 17th IAPR International Conference on Discrete Geometry for Computer Imagery,
Seville, Spain, 2013, vol. 7749, pp. XV–XIX.
ista: 'Edelsbrunner H, Pausinger F. 2013. Stable length estimates of tube-like shapes.
17th IAPR International Conference on Discrete Geometry for Computer Imagery.
DGCI: Discrete Geometry for Computer Imagery, LNCS, vol. 7749, XV–XIX.'
mla: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like
Shapes.” 17th IAPR International Conference on Discrete Geometry for Computer
Imagery, vol. 7749, Springer, 2013, pp. XV–XIX, doi:10.1007/978-3-642-37067-0.
short: H. Edelsbrunner, F. Pausinger, in:, 17th IAPR International Conference on
Discrete Geometry for Computer Imagery, Springer, 2013, pp. XV–XIX.
conference:
end_date: 2013-03-22
location: Seville, Spain
name: 'DGCI: Discrete Geometry for Computer Imagery'
start_date: 2013-03-20
date_created: 2018-12-11T11:59:53Z
date_published: 2013-02-21T00:00:00Z
date_updated: 2023-02-23T10:35:00Z
day: '21'
department:
- _id: HeEd
doi: 10.1007/978-3-642-37067-0
intvolume: ' 7749'
language:
- iso: eng
month: '02'
oa_version: None
page: XV - XIX
publication: 17th IAPR International Conference on Discrete Geometry for Computer
Imagery
publication_status: published
publisher: Springer
publist_id: '3952'
quality_controlled: '1'
related_material:
record:
- id: '2255'
relation: later_version
status: public
scopus_import: 1
status: public
title: Stable length estimates of tube-like shapes
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7749
year: '2013'
...
---
_id: '2859'
abstract:
- lang: eng
text: Given a continuous function f:X-R on a topological space, we consider the
preimages of intervals and their homology groups and show how to read the ranks
of these groups from the extended persistence diagram of f. In addition, we quantify
the robustness of the homology classes under perturbations of f using well groups,
and we show how to read the ranks of these groups from the same extended persistence
diagram. The special case X=R3 has ramifications in the fields of medical imaging
and scientific visualization.
author:
- first_name: Paul
full_name: Bendich, Paul
id: 43F6EC54-F248-11E8-B48F-1D18A9856A87
last_name: Bendich
- 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: Morozov, Dmitriy
last_name: Morozov
- first_name: Amit
full_name: Patel, Amit
id: 34A254A0-F248-11E8-B48F-1D18A9856A87
last_name: Patel
citation:
ama: Bendich P, Edelsbrunner H, Morozov D, Patel A. Homology and robustness of level
and interlevel sets. Homology, Homotopy and Applications. 2013;15(1):51-72.
doi:10.4310/HHA.2013.v15.n1.a3
apa: Bendich, P., Edelsbrunner, H., Morozov, D., & Patel, A. (2013). Homology
and robustness of level and interlevel sets. Homology, Homotopy and Applications.
International Press. https://doi.org/10.4310/HHA.2013.v15.n1.a3
chicago: Bendich, Paul, Herbert Edelsbrunner, Dmitriy Morozov, and Amit Patel. “Homology
and Robustness of Level and Interlevel Sets.” Homology, Homotopy and Applications.
International Press, 2013. https://doi.org/10.4310/HHA.2013.v15.n1.a3.
ieee: P. Bendich, H. Edelsbrunner, D. Morozov, and A. Patel, “Homology and robustness
of level and interlevel sets,” Homology, Homotopy and Applications, vol.
15, no. 1. International Press, pp. 51–72, 2013.
ista: Bendich P, Edelsbrunner H, Morozov D, Patel A. 2013. Homology and robustness
of level and interlevel sets. Homology, Homotopy and Applications. 15(1), 51–72.
mla: Bendich, Paul, et al. “Homology and Robustness of Level and Interlevel Sets.”
Homology, Homotopy and Applications, vol. 15, no. 1, International Press,
2013, pp. 51–72, doi:10.4310/HHA.2013.v15.n1.a3.
short: P. Bendich, H. Edelsbrunner, D. Morozov, A. Patel, Homology, Homotopy and
Applications 15 (2013) 51–72.
date_created: 2018-12-11T11:59:58Z
date_published: 2013-05-01T00:00:00Z
date_updated: 2021-01-12T07:00:18Z
day: '01'
department:
- _id: HeEd
doi: 10.4310/HHA.2013.v15.n1.a3
external_id:
arxiv:
- '1102.3389'
intvolume: ' 15'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1102.3389v1
month: '05'
oa: 1
oa_version: Preprint
page: 51 - 72
publication: Homology, Homotopy and Applications
publication_status: published
publisher: International Press
publist_id: '3930'
quality_controlled: '1'
scopus_import: 1
status: public
title: Homology and robustness of level and interlevel sets
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2013'
...
---
_id: '2887'
abstract:
- lang: eng
text: 'Root system growth and development is highly plastic and is influenced by
the surrounding environment. Roots frequently grow in heterogeneous environments
that include interactions from neighboring plants and physical impediments in
the rhizosphere. To investigate how planting density and physical objects affect
root system growth, we grew rice in a transparent gel system in close proximity
with another plant or a physical object. Root systems were imaged and reconstructed
in three dimensions. Root-root interaction strength was calculated using quantitative
metrics that characterize the extent towhich the reconstructed root systems overlap
each other. Surprisingly, we found the overlap of root systems of the same genotype
was significantly higher than that of root systems of different genotypes. Root
systems of the same genotype tended to grow toward each other but those of different
genotypes appeared to avoid each other. Shoot separation experiments excluded
the possibility of aerial interactions, suggesting root communication. Staggered
plantings indicated that interactions likely occur at root tips in close proximity.
Recognition of obstacles also occurred through root tips, but through physical
contact in a size-dependent manner. These results indicate that root systems use
two different forms of communication to recognize objects and alter root architecture:
root-root recognition, possibly mediated through root exudates, and root-object
recognition mediated by physical contact at the root tips. This finding suggests
that root tips act as local sensors that integrate rhizosphere information into
global root architectural changes.'
article_processing_charge: No
article_type: original
author:
- first_name: Suqin
full_name: Fang, Suqin
last_name: Fang
- first_name: Randy
full_name: Clark, Randy
last_name: Clark
- first_name: Ying
full_name: Zheng, Ying
last_name: Zheng
- first_name: Anjali
full_name: Iyer Pascuzzi, Anjali
last_name: Iyer Pascuzzi
- first_name: Joshua
full_name: Weitz, Joshua
last_name: Weitz
- first_name: Leon
full_name: Kochian, Leon
last_name: Kochian
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Hong
full_name: Liao, Hong
last_name: Liao
- first_name: Philip
full_name: Benfey, Philip
last_name: Benfey
citation:
ama: Fang S, Clark R, Zheng Y, et al. Genotypic recognition and spatial responses
by rice roots. PNAS. 2013;110(7):2670-2675. doi:10.1073/pnas.1222821110
apa: Fang, S., Clark, R., Zheng, Y., Iyer Pascuzzi, A., Weitz, J., Kochian, L.,
… Benfey, P. (2013). Genotypic recognition and spatial responses by rice roots.
PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1222821110
chicago: Fang, Suqin, Randy Clark, Ying Zheng, Anjali Iyer Pascuzzi, Joshua Weitz,
Leon Kochian, Herbert Edelsbrunner, Hong Liao, and Philip Benfey. “Genotypic Recognition
and Spatial Responses by Rice Roots.” PNAS. National Academy of Sciences,
2013. https://doi.org/10.1073/pnas.1222821110.
ieee: S. Fang et al., “Genotypic recognition and spatial responses by rice
roots,” PNAS, vol. 110, no. 7. National Academy of Sciences, pp. 2670–2675,
2013.
ista: Fang S, Clark R, Zheng Y, Iyer Pascuzzi A, Weitz J, Kochian L, Edelsbrunner
H, Liao H, Benfey P. 2013. Genotypic recognition and spatial responses by rice
roots. PNAS. 110(7), 2670–2675.
mla: Fang, Suqin, et al. “Genotypic Recognition and Spatial Responses by Rice Roots.”
PNAS, vol. 110, no. 7, National Academy of Sciences, 2013, pp. 2670–75,
doi:10.1073/pnas.1222821110.
short: S. Fang, R. Clark, Y. Zheng, A. Iyer Pascuzzi, J. Weitz, L. Kochian, H. Edelsbrunner,
H. Liao, P. Benfey, PNAS 110 (2013) 2670–2675.
date_created: 2018-12-11T12:00:09Z
date_published: 2013-02-12T00:00:00Z
date_updated: 2021-01-12T07:00:29Z
day: '12'
department:
- _id: HeEd
doi: 10.1073/pnas.1222821110
external_id:
pmid:
- '23362379'
intvolume: ' 110'
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3574932/
month: '02'
oa: 1
oa_version: Published Version
page: 2670 - 2675
pmid: 1
publication: PNAS
publication_status: published
publisher: National Academy of Sciences
publist_id: '3872'
quality_controlled: '1'
scopus_import: 1
status: public
title: Genotypic recognition and spatial responses by rice roots
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 110
year: '2013'
...
---
_id: '2901'
abstract:
- lang: eng
text: ' We introduce the M-modes problem for graphical models: predicting the M
label configurations of highest probability that are at the same time local maxima
of the probability landscape. M-modes have multiple possible applications: because
they are intrinsically diverse, they provide a principled alternative to non-maximum
suppression techniques for structured prediction, they can act as codebook vectors
for quantizing the configuration space, or they can form component centers for
mixture model approximation. We present two algorithms for solving the M-modes
problem. The first algorithm solves the problem in polynomial time when the underlying
graphical model is a simple chain. The second algorithm solves the problem for
junction chains. In synthetic and real dataset, we demonstrate how M-modes can
improve the performance of prediction. We also use the generated modes as a tool
to understand the topography of the probability distribution of configurations,
for example with relation to the training set size and amount of noise in the
data. '
alternative_title:
- ' JMLR: W&CP'
author:
- first_name: Chao
full_name: Chen, Chao
id: 3E92416E-F248-11E8-B48F-1D18A9856A87
last_name: Chen
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
- first_name: Zhu
full_name: Yan, Zhu
last_name: Yan
- first_name: Dimitris
full_name: Metaxas, Dimitris
last_name: Metaxas
- first_name: Christoph
full_name: Lampert, Christoph
id: 40C20FD2-F248-11E8-B48F-1D18A9856A87
last_name: Lampert
orcid: 0000-0001-8622-7887
citation:
ama: 'Chen C, Kolmogorov V, Yan Z, Metaxas D, Lampert C. Computing the M most probable
modes of a graphical model. In: Vol 31. JMLR; 2013:161-169.'
apa: 'Chen, C., Kolmogorov, V., Yan, Z., Metaxas, D., & Lampert, C. (2013).
Computing the M most probable modes of a graphical model (Vol. 31, pp. 161–169).
Presented at the AISTATS: Conference on Uncertainty in Artificial Intelligence,
Scottsdale, AZ, United States: JMLR.'
chicago: Chen, Chao, Vladimir Kolmogorov, Zhu Yan, Dimitris Metaxas, and Christoph
Lampert. “Computing the M Most Probable Modes of a Graphical Model,” 31:161–69.
JMLR, 2013.
ieee: 'C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, and C. Lampert, “Computing the
M most probable modes of a graphical model,” presented at the AISTATS: Conference
on Uncertainty in Artificial Intelligence, Scottsdale, AZ, United States, 2013,
vol. 31, pp. 161–169.'
ista: 'Chen C, Kolmogorov V, Yan Z, Metaxas D, Lampert C. 2013. Computing the M
most probable modes of a graphical model. AISTATS: Conference on Uncertainty
in Artificial Intelligence, JMLR: W&CP, vol. 31, 161–169.'
mla: Chen, Chao, et al. Computing the M Most Probable Modes of a Graphical Model.
Vol. 31, JMLR, 2013, pp. 161–69.
short: C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, C. Lampert, in:, JMLR, 2013,
pp. 161–169.
conference:
end_date: 2013-05-01
location: Scottsdale, AZ, United States
name: ' AISTATS: Conference on Uncertainty in Artificial Intelligence'
start_date: 2013-04-29
date_created: 2018-12-11T12:00:14Z
date_published: 2013-01-01T00:00:00Z
date_updated: 2021-01-12T07:00:35Z
day: '01'
department:
- _id: HeEd
- _id: VlKo
- _id: ChLa
intvolume: ' 31'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://jmlr.org/proceedings/papers/v31/chen13a.html
month: '01'
oa: 1
oa_version: None
page: 161 - 169
publication_status: published
publisher: JMLR
publist_id: '3846'
quality_controlled: '1'
scopus_import: 1
status: public
title: Computing the M most probable modes of a graphical model
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 31
year: '2013'
...
---
_id: '2906'
abstract:
- lang: eng
text: "Motivated by an application in cell biology, we describe an extension of
the kinetic data structures framework from Delaunay triangulations to fixed-radius
alpha complexes. Our algorithm is implemented\r\nusing CGAL, following the exact
geometric computation paradigm. We report on several\r\ntechniques to accelerate
the computation that turn our implementation applicable to the underlying biological\r\nproblem."
alternative_title:
- ALENEX
author:
- first_name: Michael
full_name: Kerber, Michael
id: 36E4574A-F248-11E8-B48F-1D18A9856A87
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: 'Kerber M, Edelsbrunner H. 3D kinetic alpha complexes and their implementation.
In: 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments.
Society of Industrial and Applied Mathematics; 2013:70-77. doi:10.1137/1.9781611972931.6'
apa: 'Kerber, M., & Edelsbrunner, H. (2013). 3D kinetic alpha complexes and
their implementation. In 2013 Proceedings of the 15th Workshop on Algorithm
Engineering and Experiments (pp. 70–77). New Orleans, LA, United States: Society
of Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611972931.6'
chicago: Kerber, Michael, and Herbert Edelsbrunner. “3D Kinetic Alpha Complexes
and Their Implementation.” In 2013 Proceedings of the 15th Workshop on Algorithm
Engineering and Experiments, 70–77. Society of Industrial and Applied Mathematics,
2013. https://doi.org/10.1137/1.9781611972931.6.
ieee: M. Kerber and H. Edelsbrunner, “3D kinetic alpha complexes and their implementation,”
in 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments,
New Orleans, LA, United States, 2013, pp. 70–77.
ista: 'Kerber M, Edelsbrunner H. 2013. 3D kinetic alpha complexes and their implementation.
2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments.
ALENEX: Algorithm Engineering and Experiments, ALENEX, , 70–77.'
mla: Kerber, Michael, and Herbert Edelsbrunner. “3D Kinetic Alpha Complexes and
Their Implementation.” 2013 Proceedings of the 15th Workshop on Algorithm Engineering
and Experiments, Society of Industrial and Applied Mathematics, 2013, pp.
70–77, doi:10.1137/1.9781611972931.6.
short: M. Kerber, H. Edelsbrunner, in:, 2013 Proceedings of the 15th Workshop on
Algorithm Engineering and Experiments, Society of Industrial and Applied Mathematics,
2013, pp. 70–77.
conference:
end_date: 2013-01-07
location: New Orleans, LA, United States
name: 'ALENEX: Algorithm Engineering and Experiments'
start_date: 2013-01-07
date_created: 2018-12-11T12:00:16Z
date_published: 2013-01-01T00:00:00Z
date_updated: 2021-01-12T07:00:36Z
day: '01'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1137/1.9781611972931.6
file:
- access_level: open_access
checksum: a15a3ba22df9445731507f3e06c9fcee
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:08:57Z
date_updated: 2020-07-14T12:45:52Z
file_id: '4720'
file_name: IST-2016-547-v1+1_2013-P-08-MedusaII.pdf
file_size: 403013
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: 70 - 77
publication: 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments
publication_status: published
publisher: Society of Industrial and Applied Mathematics
publist_id: '3841'
pubrep_id: '547'
quality_controlled: '1'
scopus_import: 1
status: public
title: 3D kinetic alpha complexes and their implementation
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2013'
...
---
_id: '2815'
abstract:
- lang: eng
text: The fact that a sum of isotropic Gaussian kernels can have more modes than
kernels is surprising. Extra (ghost) modes do not exist in ℝ1 and are generally
not well studied in higher dimensions. We study a configuration of n+1 Gaussian
kernels for which there are exactly n+2 modes. We show that all modes lie on a
finite set of lines, which we call axes, and study the restriction of the Gaussian
mixture to these axes in order to discover that there are an exponential number
of critical points in this configuration. Although the existence of ghost modes
remained unknown due to the difficulty of finding examples in ℝ2, we show that
the resilience of ghost modes grows like the square root of the dimension. In
addition, we exhibit finite configurations of isotropic Gaussian kernels with
superlinearly many modes.
acknowledgement: This research is partially supported by the National Science Foundation
(NSF) under Grant DBI-0820624, by the European Science Foundation under the Research
Networking Programme, and the Russian Government Project 11.G34.31.0053.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Brittany Terese
full_name: Fasy, Brittany Terese
id: F65D502E-E68D-11E9-9252-C644099818F6
last_name: Fasy
- first_name: Günter
full_name: Rote, Günter
last_name: Rote
citation:
ama: 'Edelsbrunner H, Fasy BT, Rote G. Add isotropic Gaussian kernels at own risk:
More and more resilient modes in higher dimensions. Discrete & Computational
Geometry. 2013;49(4):797-822. doi:10.1007/s00454-013-9517-x'
apa: 'Edelsbrunner, H., Fasy, B. T., & Rote, G. (2013). Add isotropic Gaussian
kernels at own risk: More and more resilient modes in higher dimensions. Discrete
& Computational Geometry. Springer. https://doi.org/10.1007/s00454-013-9517-x'
chicago: 'Edelsbrunner, Herbert, Brittany Terese Fasy, and Günter Rote. “Add Isotropic
Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.”
Discrete & Computational Geometry. Springer, 2013. https://doi.org/10.1007/s00454-013-9517-x.'
ieee: 'H. Edelsbrunner, B. T. Fasy, and G. Rote, “Add isotropic Gaussian kernels
at own risk: More and more resilient modes in higher dimensions,” Discrete
& Computational Geometry, vol. 49, no. 4. Springer, pp. 797–822, 2013.'
ista: 'Edelsbrunner H, Fasy BT, Rote G. 2013. Add isotropic Gaussian kernels at
own risk: More and more resilient modes in higher dimensions. Discrete & Computational
Geometry. 49(4), 797–822.'
mla: 'Edelsbrunner, Herbert, et al. “Add Isotropic Gaussian Kernels at Own Risk:
More and More Resilient Modes in Higher Dimensions.” Discrete & Computational
Geometry, vol. 49, no. 4, Springer, 2013, pp. 797–822, doi:10.1007/s00454-013-9517-x.'
short: H. Edelsbrunner, B.T. Fasy, G. Rote, Discrete & Computational Geometry
49 (2013) 797–822.
date_created: 2018-12-11T11:59:44Z
date_published: 2013-06-01T00:00:00Z
date_updated: 2023-02-23T11:13:49Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00454-013-9517-x
intvolume: ' 49'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00454-013-9517-x
month: '06'
oa: 1
oa_version: Published Version
page: 797 - 822
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer
publist_id: '3991'
quality_controlled: '1'
related_material:
record:
- id: '3134'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: 'Add isotropic Gaussian kernels at own risk: More and more resilient modes
in higher dimensions'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 49
year: '2013'
...
---
_id: '2939'
abstract:
- lang: eng
text: In this paper, we present the first output-sensitive algorithm to compute
the persistence diagram of a filtered simplicial complex. For any Γ > 0, it
returns only those homology classes with persistence at least Γ. Instead of the
classical reduction via column operations, our algorithm performs rank computations
on submatrices of the boundary matrix. For an arbitrary constant δ ∈ (0, 1), the
running time is O (C (1 - δ) Γ R d (n) log n), where C (1 - δ) Γ is the number
of homology classes with persistence at least (1 - δ) Γ, n is the total number
of simplices in the complex, d its dimension, and R d (n) is the complexity of
computing the rank of an n × n matrix with O (d n) nonzero entries. Depending
on the choice of the rank algorithm, this yields a deterministic O (C (1 - δ)
Γ n 2.376) algorithm, an O (C (1 - δ) Γ n 2.28) Las-Vegas algorithm, or an O (C
(1 - δ) Γ n 2 + ε{lunate}) Monte-Carlo algorithm for an arbitrary ε{lunate} >
0. The space complexity of the Monte-Carlo version is bounded by O (d n) = O (n
log n).
acknowledgement: The authors thank Herbert Edelsbrunner for many helpful discussions
and suggestions. Moreover, they are grateful for the careful reviews that helped
to improve the quality of the paper.
author:
- first_name: Chao
full_name: Chen, Chao
id: 3E92416E-F248-11E8-B48F-1D18A9856A87
last_name: Chen
- first_name: Michael
full_name: Kerber, Michael
id: 36E4574A-F248-11E8-B48F-1D18A9856A87
last_name: Kerber
orcid: 0000-0002-8030-9299
citation:
ama: 'Chen C, Kerber M. An output sensitive algorithm for persistent homology. Computational
Geometry: Theory and Applications. 2013;46(4):435-447. doi:10.1016/j.comgeo.2012.02.010'
apa: 'Chen, C., & Kerber, M. (2013). An output sensitive algorithm for persistent
homology. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2012.02.010'
chicago: 'Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent
Homology.” Computational Geometry: Theory and Applications. Elsevier, 2013.
https://doi.org/10.1016/j.comgeo.2012.02.010.'
ieee: 'C. Chen and M. Kerber, “An output sensitive algorithm for persistent homology,”
Computational Geometry: Theory and Applications, vol. 46, no. 4. Elsevier,
pp. 435–447, 2013.'
ista: 'Chen C, Kerber M. 2013. An output sensitive algorithm for persistent homology.
Computational Geometry: Theory and Applications. 46(4), 435–447.'
mla: 'Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent
Homology.” Computational Geometry: Theory and Applications, vol. 46, no.
4, Elsevier, 2013, pp. 435–47, doi:10.1016/j.comgeo.2012.02.010.'
short: 'C. Chen, M. Kerber, Computational Geometry: Theory and Applications 46 (2013)
435–447.'
date_created: 2018-12-11T12:00:27Z
date_published: 2013-05-01T00:00:00Z
date_updated: 2023-02-23T11:24:10Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2012.02.010
intvolume: ' 46'
issue: '4'
language:
- iso: eng
month: '05'
oa_version: None
page: 435 - 447
publication: 'Computational Geometry: Theory and Applications'
publication_status: published
publisher: Elsevier
publist_id: '3796'
quality_controlled: '1'
related_material:
record:
- id: '3367'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: An output sensitive algorithm for persistent homology
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 46
year: '2013'
...
---
_id: '10897'
abstract:
- lang: eng
text: Taking images is an efficient way to collect data about the physical world.
It can be done fast and in exquisite detail. By definition, image processing is
the field that concerns itself with the computation aimed at harnessing the information
contained in images [10]. This talk is concerned with topological information.
Our main thesis is that persistent homology [5] is a useful method to quantify
and summarize topological information, building a bridge that connects algebraic
topology with applications. We provide supporting evidence for this thesis by
touching upon four technical developments in the overlap between persistent homology
and image processing.
acknowledgement: This research is partially supported by the European Science Foundation
(ESF) under the Research Network Programme, the European Union under the Toposys
Project FP7-ICT-318493-STREP, the Russian Government under the Mega 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
citation:
ama: 'Edelsbrunner H. Persistent homology in image processing. In: Graph-Based
Representations in Pattern Recognition. Vol 7877. LNCS. Berlin, Heidelberg:
Springer Nature; 2013:182-183. doi:10.1007/978-3-642-38221-5_19'
apa: 'Edelsbrunner, H. (2013). Persistent homology in image processing. In Graph-Based
Representations in Pattern Recognition (Vol. 7877, pp. 182–183). Berlin, Heidelberg:
Springer Nature. https://doi.org/10.1007/978-3-642-38221-5_19'
chicago: 'Edelsbrunner, Herbert. “Persistent Homology in Image Processing.” In Graph-Based
Representations in Pattern Recognition, 7877:182–83. LNCS. Berlin, Heidelberg:
Springer Nature, 2013. https://doi.org/10.1007/978-3-642-38221-5_19.'
ieee: H. Edelsbrunner, “Persistent homology in image processing,” in Graph-Based
Representations in Pattern Recognition, Vienna, Austria, 2013, vol. 7877,
pp. 182–183.
ista: 'Edelsbrunner H. 2013. Persistent homology in image processing. Graph-Based
Representations in Pattern Recognition. GbRPR: Graph-based Representations in
Pattern RecognitionLNCS vol. 7877, 182–183.'
mla: Edelsbrunner, Herbert. “Persistent Homology in Image Processing.” Graph-Based
Representations in Pattern Recognition, vol. 7877, Springer Nature, 2013,
pp. 182–83, doi:10.1007/978-3-642-38221-5_19.
short: H. Edelsbrunner, in:, Graph-Based Representations in Pattern Recognition,
Springer Nature, Berlin, Heidelberg, 2013, pp. 182–183.
conference:
end_date: 2013-05-17
location: Vienna, Austria
name: 'GbRPR: Graph-based Representations in Pattern Recognition'
start_date: 2013-05-15
date_created: 2022-03-21T07:30:33Z
date_published: 2013-06-01T00:00:00Z
date_updated: 2023-09-05T15:10:20Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-642-38221-5_19
ec_funded: 1
intvolume: ' 7877'
language:
- iso: eng
month: '06'
oa_version: None
page: 182-183
place: Berlin, Heidelberg
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Graph-Based Representations in Pattern Recognition
publication_identifier:
eisbn:
- '9783642382215'
eissn:
- 1611-3349
isbn:
- '9783642382208'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: LNCS
status: public
title: Persistent homology in image processing
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 7877
year: '2013'
...
---
_id: '2849'
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Nataliya
full_name: Strelkova, Nataliya
last_name: Strelkova
citation:
ama: Edelsbrunner H, Strelkova N. On the configuration space of Steiner minimal
trees. Russian Mathematical Surveys. 2012;67(6):1167-1168. doi:10.1070/RM2012v067n06ABEH004820
apa: Edelsbrunner, H., & Strelkova, N. (2012). On the configuration space of
Steiner minimal trees. Russian Mathematical Surveys. IOP Publishing Ltd.
https://doi.org/10.1070/RM2012v067n06ABEH004820
chicago: Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space
of Steiner Minimal Trees.” Russian Mathematical Surveys. IOP Publishing
Ltd., 2012. https://doi.org/10.1070/RM2012v067n06ABEH004820.
ieee: H. Edelsbrunner and N. Strelkova, “On the configuration space of Steiner minimal
trees,” Russian Mathematical Surveys, vol. 67, no. 6. IOP Publishing Ltd.,
pp. 1167–1168, 2012.
ista: Edelsbrunner H, Strelkova N. 2012. On the configuration space of Steiner minimal
trees. Russian Mathematical Surveys. 67(6), 1167–1168.
mla: Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space
of Steiner Minimal Trees.” Russian Mathematical Surveys, vol. 67, no. 6,
IOP Publishing Ltd., 2012, pp. 1167–68, doi:10.1070/RM2012v067n06ABEH004820.
short: H. Edelsbrunner, N. Strelkova, Russian Mathematical Surveys 67 (2012) 1167–1168.
date_created: 2018-12-11T11:59:55Z
date_published: 2012-01-01T00:00:00Z
date_updated: 2021-01-12T07:00:13Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1070/RM2012v067n06ABEH004820
file:
- access_level: open_access
checksum: 44ee8d173487e8ed41a51136816bbeb4
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:14:26Z
date_updated: 2020-07-14T12:45:51Z
file_id: '5078'
file_name: IST-2016-546-v1+1_2014-J-05-SteinerMinTrees.pdf
file_size: 392021
relation: main_file
file_date_updated: 2020-07-14T12:45:51Z
has_accepted_license: '1'
intvolume: ' 67'
issue: '6'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Submitted Version
page: 1167 - 1168
publication: Russian Mathematical Surveys
publication_status: published
publisher: IOP Publishing Ltd.
publist_id: '3943'
pubrep_id: '546'
quality_controlled: '1'
scopus_import: 1
status: public
title: On the configuration space of Steiner minimal trees
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 67
year: '2012'
...
---
_id: '2903'
abstract:
- lang: eng
text: In order to enjoy a digital version of the Jordan Curve Theorem, it is common
to use the closed topology for the foreground and the open topology for the background
of a 2-dimensional binary image. In this paper, we introduce a single topology
that enjoys this theorem for all thresholds decomposing a real-valued image into
foreground and background. This topology is easy to construct and it generalizes
to n-dimensional images.
author:
- 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: Symonova, Olga
id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87
last_name: Symonova
citation:
ama: 'Edelsbrunner H, Symonova O. The adaptive topology of a digital image. In:
IEEE; 2012:41-48. doi:10.1109/ISVD.2012.11'
apa: 'Edelsbrunner, H., & Symonova, O. (2012). The adaptive topology of a digital
image (pp. 41–48). Presented at the ISVD: International Symposium on Voronoi Diagrams
in Science and Engineering, New Brunswick, NJ, USA : IEEE. https://doi.org/10.1109/ISVD.2012.11'
chicago: Edelsbrunner, Herbert, and Olga Symonova. “The Adaptive Topology of a Digital
Image,” 41–48. IEEE, 2012. https://doi.org/10.1109/ISVD.2012.11.
ieee: 'H. Edelsbrunner and O. Symonova, “The adaptive topology of a digital image,”
presented at the ISVD: International Symposium on Voronoi Diagrams in Science
and Engineering, New Brunswick, NJ, USA , 2012, pp. 41–48.'
ista: 'Edelsbrunner H, Symonova O. 2012. The adaptive topology of a digital image.
ISVD: International Symposium on Voronoi Diagrams in Science and Engineering,
41–48.'
mla: Edelsbrunner, Herbert, and Olga Symonova. The Adaptive Topology of a Digital
Image. IEEE, 2012, pp. 41–48, doi:10.1109/ISVD.2012.11.
short: H. Edelsbrunner, O. Symonova, in:, IEEE, 2012, pp. 41–48.
conference:
end_date: 2012-06-29
location: 'New Brunswick, NJ, USA '
name: 'ISVD: International Symposium on Voronoi Diagrams in Science and Engineering'
start_date: 2012-06-27
date_created: 2018-12-11T12:00:15Z
date_published: 2012-08-06T00:00:00Z
date_updated: 2021-01-12T07:00:35Z
day: '06'
ddc:
- '000'
department:
- _id: HeEd
- _id: MaJö
doi: 10.1109/ISVD.2012.11
file:
- access_level: open_access
checksum: 444869a4e8abf07834f88b6e5cb5e9c3
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:09:41Z
date_updated: 2020-07-14T12:45:52Z
file_id: '4765'
file_name: IST-2016-545-v1+1_2012-P-10-AdaptiveTopology.pdf
file_size: 760548
relation: main_file
file_date_updated: 2020-07-14T12:45:52Z
has_accepted_license: '1'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Submitted Version
page: 41 - 48
publication_status: published
publisher: IEEE
publist_id: '3844'
pubrep_id: '545'
quality_controlled: '1'
scopus_import: 1
status: public
title: The adaptive topology of a digital image
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2012'
...
---
_id: '2941'
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: Oleg
full_name: Musin, Oleg
last_name: Musin
citation:
ama: Dolbilin N, Edelsbrunner H, Musin O. On the optimality of functionals over
triangulations of Delaunay sets. Russian Mathematical Surveys. 2012;67(4):781-783.
doi:10.1070/RM2012v067n04ABEH004807
apa: Dolbilin, N., Edelsbrunner, H., & Musin, O. (2012). On the optimality of
functionals over triangulations of Delaunay sets. Russian Mathematical Surveys.
IOP Publishing. https://doi.org/10.1070/RM2012v067n04ABEH004807
chicago: Dolbilin, Nikolai, Herbert Edelsbrunner, and Oleg Musin. “On the Optimality
of Functionals over Triangulations of Delaunay Sets.” Russian Mathematical
Surveys. IOP Publishing, 2012. https://doi.org/10.1070/RM2012v067n04ABEH004807.
ieee: N. Dolbilin, H. Edelsbrunner, and O. Musin, “On the optimality of functionals
over triangulations of Delaunay sets,” Russian Mathematical Surveys, vol.
67, no. 4. IOP Publishing, pp. 781–783, 2012.
ista: Dolbilin N, Edelsbrunner H, Musin O. 2012. On the optimality of functionals
over triangulations of Delaunay sets. Russian Mathematical Surveys. 67(4), 781–783.
mla: Dolbilin, Nikolai, et al. “On the Optimality of Functionals over Triangulations
of Delaunay Sets.” Russian Mathematical Surveys, vol. 67, no. 4, IOP Publishing,
2012, pp. 781–83, doi:10.1070/RM2012v067n04ABEH004807.
short: N. Dolbilin, H. Edelsbrunner, O. Musin, Russian Mathematical Surveys 67 (2012)
781–783.
date_created: 2018-12-11T12:00:28Z
date_published: 2012-11-01T00:00:00Z
date_updated: 2021-01-12T07:39:55Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1070/RM2012v067n04ABEH004807
file:
- access_level: open_access
checksum: 389a5ae53d6347de36c3468034f2821d
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:49Z
date_updated: 2020-07-14T12:45:55Z
file_id: '5239'
file_name: IST-2013-132-v1+1_2012-J-04-Functional-E.pdf
file_size: 253816
relation: main_file
file_date_updated: 2020-07-14T12:45:55Z
has_accepted_license: '1'
intvolume: ' 67'
issue: '4'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Submitted Version
page: 781 - 783
publication: Russian Mathematical Surveys
publication_status: published
publisher: IOP Publishing
publist_id: '3792'
pubrep_id: '132'
quality_controlled: '1'
scopus_import: 1
status: public
title: On the optimality of functionals over triangulations of Delaunay sets
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 67
year: '2012'
...
---
_id: '2971'
abstract:
- lang: eng
text: 'We study the task of interactive semantic labeling of a segmentation hierarchy.
To this end we propose a framework interleaving two components: an automatic labeling
step, based on a Conditional Random Field whose dependencies are defined by the
inclusion tree of the segmentation hierarchy, and an interaction step that integrates
incremental input from a human user. Evaluated on two distinct datasets, the proposed
interactive approach efficiently integrates human interventions and illustrates
the advantages of structured prediction in an interactive framework. '
author:
- first_name: Georg
full_name: Zankl, Georg
last_name: Zankl
- first_name: Yll
full_name: Haxhimusa, Yll
last_name: Haxhimusa
- first_name: Adrian
full_name: Ion, Adrian
id: 29F89302-F248-11E8-B48F-1D18A9856A87
last_name: Ion
citation:
ama: 'Zankl G, Haxhimusa Y, Ion A. Interactive labeling of image segmentation hierarchies.
In: Vol 7476. Springer; 2012:11-20. doi:10.1007/978-3-642-32717-9_2'
apa: 'Zankl, G., Haxhimusa, Y., & Ion, A. (2012). Interactive labeling of image
segmentation hierarchies (Vol. 7476, pp. 11–20). Presented at the Pattern Recognition,
Graz, Austria: Springer. https://doi.org/10.1007/978-3-642-32717-9_2'
chicago: Zankl, Georg, Yll Haxhimusa, and Adrian Ion. “Interactive Labeling of Image
Segmentation Hierarchies,” 7476:11–20. Springer, 2012. https://doi.org/10.1007/978-3-642-32717-9_2.
ieee: G. Zankl, Y. Haxhimusa, and A. Ion, “Interactive labeling of image segmentation
hierarchies,” presented at the Pattern Recognition, Graz, Austria, 2012, vol.
7476, pp. 11–20.
ista: Zankl G, Haxhimusa Y, Ion A. 2012. Interactive labeling of image segmentation
hierarchies. Pattern Recognition vol. 7476, 11–20.
mla: Zankl, Georg, et al. Interactive Labeling of Image Segmentation Hierarchies.
Vol. 7476, Springer, 2012, pp. 11–20, doi:10.1007/978-3-642-32717-9_2.
short: G. Zankl, Y. Haxhimusa, A. Ion, in:, Springer, 2012, pp. 11–20.
conference:
end_date: 2012-08-31
location: Graz, Austria
name: Pattern Recognition
start_date: 2012-08-28
date_created: 2018-12-11T12:00:37Z
date_published: 2012-01-01T00:00:00Z
date_updated: 2021-01-12T07:40:10Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-642-32717-9_2
intvolume: ' 7476'
language:
- iso: eng
month: '01'
oa_version: None
page: 11 - 20
publication_status: published
publisher: Springer
publist_id: '3737'
quality_controlled: '1'
scopus_import: 1
status: public
title: Interactive labeling of image segmentation hierarchies
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 7476
year: '2012'
...
---
_id: '3120'
abstract:
- lang: eng
text: We introduce a strategy based on Kustin-Miller unprojection that allows us
to construct many hundreds of Gorenstein codimension 4 ideals with 9 × 16 resolutions
(that is, nine equations and sixteen first syzygies). Our two basic games are
called Tom and Jerry; the main application is the biregular construction of most
of the anticanonically polarised Mori Fano 3-folds of Altinok's thesis. There
are 115 cases whose numerical data (in effect, the Hilbert series) allow a Type
I projection. In every case, at least one Tom and one Jerry construction works,
providing at least two deformation families of quasismooth Fano 3-folds having
the same numerics but different topology. © 2012 Copyright Foundation Compositio
Mathematica.
acknowledgement: This research is supported by the Korean Government WCU Grant R33-2008-000-10101-0.
author:
- first_name: Gavin
full_name: Brown, Gavin
last_name: Brown
- first_name: Michael
full_name: Kerber, Michael
id: 36E4574A-F248-11E8-B48F-1D18A9856A87
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Miles
full_name: Reid, Miles
last_name: Reid
citation:
ama: Brown G, Kerber M, Reid M. Fano 3 folds in codimension 4 Tom and Jerry Part
I. Compositio Mathematica. 2012;148(4):1171-1194. doi:10.1112/S0010437X11007226
apa: Brown, G., Kerber, M., & Reid, M. (2012). Fano 3 folds in codimension 4
Tom and Jerry Part I. Compositio Mathematica. Cambridge University Press.
https://doi.org/10.1112/S0010437X11007226
chicago: Brown, Gavin, Michael Kerber, and Miles Reid. “Fano 3 Folds in Codimension
4 Tom and Jerry Part I.” Compositio Mathematica. Cambridge University Press,
2012. https://doi.org/10.1112/S0010437X11007226.
ieee: G. Brown, M. Kerber, and M. Reid, “Fano 3 folds in codimension 4 Tom and Jerry
Part I,” Compositio Mathematica, vol. 148, no. 4. Cambridge University
Press, pp. 1171–1194, 2012.
ista: Brown G, Kerber M, Reid M. 2012. Fano 3 folds in codimension 4 Tom and Jerry
Part I. Compositio Mathematica. 148(4), 1171–1194.
mla: Brown, Gavin, et al. “Fano 3 Folds in Codimension 4 Tom and Jerry Part I.”
Compositio Mathematica, vol. 148, no. 4, Cambridge University Press, 2012,
pp. 1171–94, doi:10.1112/S0010437X11007226.
short: G. Brown, M. Kerber, M. Reid, Compositio Mathematica 148 (2012) 1171–1194.
date_created: 2018-12-11T12:01:30Z
date_published: 2012-07-01T00:00:00Z
date_updated: 2021-01-12T07:41:12Z
day: '01'
department:
- _id: HeEd
doi: 10.1112/S0010437X11007226
intvolume: ' 148'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1009.4313
month: '07'
oa: 1
oa_version: Preprint
page: 1171 - 1194
publication: Compositio Mathematica
publication_status: published
publisher: Cambridge University Press
publist_id: '3579'
quality_controlled: '1'
scopus_import: 1
status: public
title: Fano 3 folds in codimension 4 Tom and Jerry Part I
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 148
year: '2012'
...
---
_id: '3133'
abstract:
- lang: eng
text: 'This note contributes to the point calculus of persistent homology by extending
Alexander duality from spaces to real-valued functions. Given a perfect Morse
function f: S n+1 →[0, 1 and a decomposition S n+1 = U ∪ V into two (n + 1)-manifolds
with common boundary M, we prove elementary relationships between the persistence
diagrams of f restricted to U, to V, and to M. '
acknowledgement: "his research is partially supported by the National Science Foundation
(NSF) under grant DBI-0820624, the European Science Foundation under the Research
Networking Programme, and the Russian Government Project 11.G34.31.0053.\r\nThe
authors thank an anonymous referee for suggesting the simplified proof of the Contravariant
PE Theorem given in this paper. They also thank Frederick Cohen, Yuriy Mileyko and
Amit Patel for helpful discussions."
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Michael
full_name: Kerber, Michael
id: 36E4574A-F248-11E8-B48F-1D18A9856A87
last_name: Kerber
orcid: 0000-0002-8030-9299
citation:
ama: 'Edelsbrunner H, Kerber M. Alexander duality for functions: The persistent
behavior of land and water and shore. In: Proceedings of the Twenty-Eighth
Annual Symposium on Computational Geometry . ACM; 2012:249-258. doi:10.1145/2261250.2261287'
apa: 'Edelsbrunner, H., & Kerber, M. (2012). Alexander duality for functions:
The persistent behavior of land and water and shore. In Proceedings of the
twenty-eighth annual symposium on Computational geometry (pp. 249–258). Chapel
Hill, NC, USA: ACM. https://doi.org/10.1145/2261250.2261287'
chicago: 'Edelsbrunner, Herbert, and Michael Kerber. “Alexander Duality for Functions:
The Persistent Behavior of Land and Water and Shore.” In Proceedings of the
Twenty-Eighth Annual Symposium on Computational Geometry , 249–58. ACM, 2012.
https://doi.org/10.1145/2261250.2261287.'
ieee: 'H. Edelsbrunner and M. Kerber, “Alexander duality for functions: The persistent
behavior of land and water and shore,” in Proceedings of the twenty-eighth
annual symposium on Computational geometry , Chapel Hill, NC, USA, 2012, pp.
249–258.'
ista: 'Edelsbrunner H, Kerber M. 2012. Alexander duality for functions: The persistent
behavior of land and water and shore. Proceedings of the twenty-eighth annual
symposium on Computational geometry . SCG: Symposium on Computational Geometry,
249–258.'
mla: 'Edelsbrunner, Herbert, and Michael Kerber. “Alexander Duality for Functions:
The Persistent Behavior of Land and Water and Shore.” Proceedings of the Twenty-Eighth
Annual Symposium on Computational Geometry , ACM, 2012, pp. 249–58, doi:10.1145/2261250.2261287.'
short: H. Edelsbrunner, M. Kerber, in:, Proceedings of the Twenty-Eighth Annual
Symposium on Computational Geometry , ACM, 2012, pp. 249–258.
conference:
end_date: 2012-06-20
location: Chapel Hill, NC, USA
name: 'SCG: Symposium on Computational Geometry'
start_date: 2012-06-17
date_created: 2018-12-11T12:01:35Z
date_published: 2012-06-20T00:00:00Z
date_updated: 2021-01-12T07:41:17Z
day: '20'
department:
- _id: HeEd
doi: 10.1145/2261250.2261287
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1109.5052
month: '06'
oa: 1
oa_version: Preprint
page: 249 - 258
publication: 'Proceedings of the twenty-eighth annual symposium on Computational geometry '
publication_status: published
publisher: ACM
publist_id: '3564'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'Alexander duality for functions: The persistent behavior of land and water
and shore'
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2012'
...
---
_id: '3134'
abstract:
- lang: eng
text: 'It has been an open question whether the sum of finitely many isotropic Gaussian
kernels in n ≥ 2 dimensions can have more modes than kernels, until in 2003 Carreira-Perpiñán
and Williams exhibited n +1 isotropic Gaussian kernels in ℝ n with n + 2 modes.
We give a detailed analysis of this example, showing that it has exponentially
many critical points and that the resilience of the extra mode grows like √n.
In addition, we exhibit finite configurations of isotropic Gaussian kernels with
superlinearly many modes. '
acknowledgement: This research is partially supported by the National Science Foun-
dation (NSF) under grant DBI-0820624, by the European Science Foundation under the
Research Networking Programme, and the Russian Government Project 11.G34.31.0053.
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Brittany
full_name: Fasy, Brittany
last_name: Fasy
- first_name: Günter
full_name: Rote, Günter
last_name: Rote
citation:
ama: 'Edelsbrunner H, Fasy B, Rote G. Add isotropic Gaussian kernels at own risk:
More and more resilient modes in higher dimensions. In: Proceedings of the
Twenty-Eighth Annual Symposium on Computational Geometry . ACM; 2012:91-100.
doi:10.1145/2261250.2261265'
apa: 'Edelsbrunner, H., Fasy, B., & Rote, G. (2012). Add isotropic Gaussian
kernels at own risk: More and more resilient modes in higher dimensions. In Proceedings
of the twenty-eighth annual symposium on Computational geometry (pp. 91–100).
Chapel Hill, NC, USA: ACM. https://doi.org/10.1145/2261250.2261265'
chicago: 'Edelsbrunner, Herbert, Brittany Fasy, and Günter Rote. “Add Isotropic
Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.”
In Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry
, 91–100. ACM, 2012. https://doi.org/10.1145/2261250.2261265.'
ieee: 'H. Edelsbrunner, B. Fasy, and G. Rote, “Add isotropic Gaussian kernels at
own risk: More and more resilient modes in higher dimensions,” in Proceedings
of the twenty-eighth annual symposium on Computational geometry , Chapel Hill,
NC, USA, 2012, pp. 91–100.'
ista: 'Edelsbrunner H, Fasy B, Rote G. 2012. Add isotropic Gaussian kernels at own
risk: More and more resilient modes in higher dimensions. Proceedings of the twenty-eighth
annual symposium on Computational geometry . SCG: Symposium on Computational Geometry,
91–100.'
mla: 'Edelsbrunner, Herbert, et al. “Add Isotropic Gaussian Kernels at Own Risk:
More and More Resilient Modes in Higher Dimensions.” Proceedings of the Twenty-Eighth
Annual Symposium on Computational Geometry , ACM, 2012, pp. 91–100, doi:10.1145/2261250.2261265.'
short: H. Edelsbrunner, B. Fasy, G. Rote, in:, Proceedings of the Twenty-Eighth
Annual Symposium on Computational Geometry , ACM, 2012, pp. 91–100.
conference:
end_date: 2012-06-20
location: Chapel Hill, NC, USA
name: 'SCG: Symposium on Computational Geometry'
start_date: 2012-06-17
date_created: 2018-12-11T12:01:35Z
date_published: 2012-06-20T00:00:00Z
date_updated: 2023-02-23T10:59:27Z
day: '20'
department:
- _id: HeEd
doi: 10.1145/2261250.2261265
language:
- iso: eng
month: '06'
oa_version: None
page: 91 - 100
publication: 'Proceedings of the twenty-eighth annual symposium on Computational geometry '
publication_status: published
publisher: ACM
publist_id: '3563'
quality_controlled: '1'
related_material:
record:
- id: '2815'
relation: later_version
status: public
scopus_import: 1
status: public
title: 'Add isotropic Gaussian kernels at own risk: More and more resilient modes
in higher dimensions'
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2012'
...
---
_id: '3256'
abstract:
- lang: eng
text: We use a distortion to define the dual complex of a cubical subdivision of
ℝ n as an n-dimensional subcomplex of the nerve of the set of n-cubes. Motivated
by the topological analysis of high-dimensional digital image data, we consider
such subdivisions defined by generalizations of quad- and oct-trees to n dimensions.
Assuming the subdivision is balanced, we show that mapping each vertex to the
center of the corresponding n-cube gives a geometric realization of the dual complex
in ℝ n.
acknowledgement: This research is partially supported by the Defense Advanced Research
Projects Agency (DARPA) under grants HR0011-05-1-0057 and HR0011-09-0065 as well
as the National Science Foundation (NSF) under grant DBI-0820624.
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Michael
full_name: Kerber, Michael
id: 36E4574A-F248-11E8-B48F-1D18A9856A87
last_name: Kerber
orcid: 0000-0002-8030-9299
citation:
ama: Edelsbrunner H, Kerber M. Dual complexes of cubical subdivisions of ℝn. Discrete
& Computational Geometry. 2012;47(2):393-414. doi:10.1007/s00454-011-9382-4
apa: Edelsbrunner, H., & Kerber, M. (2012). Dual complexes of cubical subdivisions
of ℝn. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-011-9382-4
chicago: Edelsbrunner, Herbert, and Michael Kerber. “Dual Complexes of Cubical Subdivisions
of ℝn.” Discrete & Computational Geometry. Springer, 2012. https://doi.org/10.1007/s00454-011-9382-4.
ieee: H. Edelsbrunner and M. Kerber, “Dual complexes of cubical subdivisions of
ℝn,” Discrete & Computational Geometry, vol. 47, no. 2. Springer, pp.
393–414, 2012.
ista: Edelsbrunner H, Kerber M. 2012. Dual complexes of cubical subdivisions of
ℝn. Discrete & Computational Geometry. 47(2), 393–414.
mla: Edelsbrunner, Herbert, and Michael Kerber. “Dual Complexes of Cubical Subdivisions
of ℝn.” Discrete & Computational Geometry, vol. 47, no. 2, Springer,
2012, pp. 393–414, doi:10.1007/s00454-011-9382-4.
short: H. Edelsbrunner, M. Kerber, Discrete & Computational Geometry 47 (2012)
393–414.
date_created: 2018-12-11T12:02:17Z
date_published: 2012-03-01T00:00:00Z
date_updated: 2021-01-12T07:42:10Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s00454-011-9382-4
file:
- access_level: open_access
checksum: 76486f3b2c9e7fd81342f3832ca387e7
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:08:15Z
date_updated: 2020-07-14T12:46:05Z
file_id: '4675'
file_name: IST-2016-543-v1+1_2012-J-08-HierarchyCubeComplex.pdf
file_size: 203636
relation: main_file
file_date_updated: 2020-07-14T12:46:05Z
has_accepted_license: '1'
intvolume: ' 47'
issue: '2'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Submitted Version
page: 393 - 414
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '3398'
pubrep_id: '543'
quality_controlled: '1'
scopus_import: 1
status: public
title: Dual complexes of cubical subdivisions of ℝn
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 47
year: '2012'
...
---
_id: '3265'
abstract:
- lang: eng
text: We propose a mid-level statistical model for image segmentation that composes
multiple figure-ground hypotheses (FG) obtained by applying constraints at different
locations and scales, into larger interpretations (tilings) of the entire image.
Inference is cast as optimization over sets of maximal cliques sampled from a
graph connecting all non-overlapping figure-ground segment hypotheses. Potential
functions over cliques combine unary, Gestalt-based figure qualities, and pairwise
compatibilities among spatially neighboring segments, constrained by T-junctions
and the boundary interface statistics of real scenes. Learning the model parameters
is based on maximum likelihood, alternating between sampling image tilings and
optimizing their potential function parameters. State of the art results are reported
on the Berkeley and Stanford segmentation datasets, as well as VOC2009, where
a 28% improvement was achieved.
article_number: '6126486'
author:
- first_name: Adrian
full_name: Ion, Adrian
id: 29F89302-F248-11E8-B48F-1D18A9856A87
last_name: Ion
- first_name: Joao
full_name: Carreira, Joao
last_name: Carreira
- first_name: Cristian
full_name: Sminchisescu, Cristian
last_name: Sminchisescu
citation:
ama: 'Ion A, Carreira J, Sminchisescu C. Image segmentation by figure-ground composition
into maximal cliques. In: IEEE; 2012. doi:10.1109/ICCV.2011.6126486'
apa: 'Ion, A., Carreira, J., & Sminchisescu, C. (2012). Image segmentation by
figure-ground composition into maximal cliques. Presented at the ICCV: International
Conference on Computer Vision, Barcelona, Spain: IEEE. https://doi.org/10.1109/ICCV.2011.6126486'
chicago: Ion, Adrian, Joao Carreira, and Cristian Sminchisescu. “Image Segmentation
by Figure-Ground Composition into Maximal Cliques.” IEEE, 2012. https://doi.org/10.1109/ICCV.2011.6126486.
ieee: 'A. Ion, J. Carreira, and C. Sminchisescu, “Image segmentation by figure-ground
composition into maximal cliques,” presented at the ICCV: International Conference
on Computer Vision, Barcelona, Spain, 2012.'
ista: 'Ion A, Carreira J, Sminchisescu C. 2012. Image segmentation by figure-ground
composition into maximal cliques. ICCV: International Conference on Computer Vision,
6126486.'
mla: Ion, Adrian, et al. Image Segmentation by Figure-Ground Composition into
Maximal Cliques. 6126486, IEEE, 2012, doi:10.1109/ICCV.2011.6126486.
short: A. Ion, J. Carreira, C. Sminchisescu, in:, IEEE, 2012.
conference:
end_date: 2011-11-13
location: Barcelona, Spain
name: 'ICCV: International Conference on Computer Vision'
start_date: 2011-11-06
date_created: 2018-12-11T12:02:21Z
date_published: 2012-01-12T00:00:00Z
date_updated: 2021-01-12T07:42:15Z
day: '12'
department:
- _id: HeEd
doi: 10.1109/ICCV.2011.6126486
language:
- iso: eng
month: '01'
oa_version: None
publication_status: published
publisher: IEEE
publist_id: '3382'
quality_controlled: '1'
status: public
title: Image segmentation by figure-ground composition into maximal cliques
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2012'
...
---
_id: '3115'
abstract:
- lang: eng
text: 'We consider the offset-deconstruction problem: Given a polygonal shape Q
with n vertices, can it be expressed, up to a tolerance ε in Hausdorff distance,
as the Minkowski sum of another polygonal shape P with a disk of fixed radius?
If it does, we also seek a preferably simple-looking solution P; then, P''s offset
constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We
give an O(nlogn)-time exact decision algorithm that handles any polygonal shape,
assuming the real-RAM model of computation. A variant of the algorithm, which
we have implemented using the cgal library, is based on rational arithmetic and
answers the same deconstruction problem up to an uncertainty parameter δ its running
time additionally depends on δ. If the input shape is found to be approximable,
this algorithm also computes an approximate solution for the problem. It also
allows us to solve parameter-optimization problems induced by the offset-deconstruction
problem. For convex shapes, the complexity of the exact decision algorithm drops
to O(n), which is also the time required to compute a solution P with at most
one more vertex than a vertex-minimal one.'
acknowledgement: "We thank Eyal Flato (Plataine Ltd.) for raising the offset-deconstruction
problem in connection with wood cutting. We also thank Tim Bretl (UIUC) for suggesting
the digital-pen offset-deconstruction problem. This work has been supported in part
by the Israel Science Foundation (grant no. 1102/11), by the German–Israeli Foundation
(grant no. 969/07), by the Hermann Minkowski–Minerva Center for Geometry at Tel
Aviv University, and by the EU Project under Contract No. 255827 (CGL—Computational
Geometry Learning).\r\n"
author:
- first_name: Eric
full_name: Berberich, Eric
last_name: Berberich
- first_name: Dan
full_name: Halperin, Dan
last_name: Halperin
- first_name: Michael
full_name: Kerber, Michael
id: 36E4574A-F248-11E8-B48F-1D18A9856A87
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Roza
full_name: Pogalnikova, Roza
last_name: Pogalnikova
citation:
ama: Berberich E, Halperin D, Kerber M, Pogalnikova R. Deconstructing approximate
offsets. Discrete & Computational Geometry. 2012;48(4):964-989. doi:10.1007/s00454-012-9441-5
apa: Berberich, E., Halperin, D., Kerber, M., & Pogalnikova, R. (2012). Deconstructing
approximate offsets. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-012-9441-5
chicago: Berberich, Eric, Dan Halperin, Michael Kerber, and Roza Pogalnikova. “Deconstructing
Approximate Offsets.” Discrete & Computational Geometry. Springer,
2012. https://doi.org/10.1007/s00454-012-9441-5.
ieee: E. Berberich, D. Halperin, M. Kerber, and R. Pogalnikova, “Deconstructing
approximate offsets,” Discrete & Computational Geometry, vol. 48, no.
4. Springer, pp. 964–989, 2012.
ista: Berberich E, Halperin D, Kerber M, Pogalnikova R. 2012. Deconstructing approximate
offsets. Discrete & Computational Geometry. 48(4), 964–989.
mla: Berberich, Eric, et al. “Deconstructing Approximate Offsets.” Discrete &
Computational Geometry, vol. 48, no. 4, Springer, 2012, pp. 964–89, doi:10.1007/s00454-012-9441-5.
short: E. Berberich, D. Halperin, M. Kerber, R. Pogalnikova, Discrete & Computational
Geometry 48 (2012) 964–989.
date_created: 2018-12-11T12:01:28Z
date_published: 2012-12-01T00:00:00Z
date_updated: 2023-02-23T11:22:30Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00454-012-9441-5
external_id:
arxiv:
- '1109.2158'
intvolume: ' 48'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1109.2158
month: '12'
oa: 1
oa_version: Preprint
page: 964 - 989
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '3584'
quality_controlled: '1'
related_material:
record:
- id: '3329'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: Deconstructing approximate offsets
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 48
year: '2012'
...