---
_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
license: https://creativecommons.org/licenses/by/4.0/
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'
...