---
_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.
article_processing_charge: No
arxiv: 1
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: 2025-09-29T13:38:09Z
day: '01'
department:
- _id: HeEd
doi: 10.4310/HHA.2013.v15.n1.a3
external_id:
arxiv:
- '1102.3389'
isi:
- '000322423600003'
intvolume: ' 15'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 15
year: '2013'
...
---
_id: '3310'
abstract:
- lang: eng
text: The theory of persistent homology opens up the possibility to reason about
topological features of a space or a function quantitatively and in combinatorial
terms. We refer to this new angle at a classical subject within algebraic topology
as a point calculus, which we present for the family of interlevel sets of a real-valued
function. Our account of the subject is expository, devoid of proofs, and written
for non-experts in algebraic topology.
acknowledgement: Research by the third author is partially supported by the National
Science Foundation (NSF) under grant DBI-0820624.
article_processing_charge: No
author:
- first_name: Paul
full_name: Bendich, Paul
id: 43F6EC54-F248-11E8-B48F-1D18A9856A87
last_name: Bendich
- first_name: Sergio
full_name: Cabello, Sergio
last_name: Cabello
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Bendich P, Cabello S, Edelsbrunner H. A point calculus for interlevel set homology.
Pattern Recognition Letters. 2012;33(11):1436-1444. doi:10.1016/j.patrec.2011.10.007
apa: Bendich, P., Cabello, S., & Edelsbrunner, H. (2012). A point calculus for
interlevel set homology. Pattern Recognition Letters. Elsevier. https://doi.org/10.1016/j.patrec.2011.10.007
chicago: Bendich, Paul, Sergio Cabello, and Herbert Edelsbrunner. “A Point Calculus
for Interlevel Set Homology.” Pattern Recognition Letters. Elsevier, 2012.
https://doi.org/10.1016/j.patrec.2011.10.007.
ieee: P. Bendich, S. Cabello, and H. Edelsbrunner, “A point calculus for interlevel
set homology,” Pattern Recognition Letters, vol. 33, no. 11. Elsevier,
pp. 1436–1444, 2012.
ista: Bendich P, Cabello S, Edelsbrunner H. 2012. A point calculus for interlevel
set homology. Pattern Recognition Letters. 33(11), 1436–1444.
mla: Bendich, Paul, et al. “A Point Calculus for Interlevel Set Homology.” Pattern
Recognition Letters, vol. 33, no. 11, Elsevier, 2012, pp. 1436–44, doi:10.1016/j.patrec.2011.10.007.
short: P. Bendich, S. Cabello, H. Edelsbrunner, Pattern Recognition Letters 33 (2012)
1436–1444.
date_created: 2018-12-11T12:02:36Z
date_published: 2012-08-01T00:00:00Z
date_updated: 2025-09-30T07:39:47Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.patrec.2011.10.007
external_id:
isi:
- '000307204300002'
file:
- access_level: open_access
checksum: d65f79775b51258a604ca5ec741297cc
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:15:00Z
date_updated: 2020-07-14T12:46:06Z
file_id: '5116'
file_name: IST-2016-542-v1+1_2012-J-01-Poinculus.pdf
file_size: 280280
relation: main_file
file_date_updated: 2020-07-14T12:46:06Z
has_accepted_license: '1'
intvolume: ' 33'
isi: 1
issue: '11'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Submitted Version
page: 1436 - 1444
publication: Pattern Recognition Letters
publication_status: published
publisher: Elsevier
publist_id: '3330'
pubrep_id: '542'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A point calculus for interlevel set homology
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 33
year: '2012'
...
---
_id: '3378'
abstract:
- lang: eng
text: The theory of intersection homology was developed to study the singularities
of a topologically stratified space. This paper in- corporates this theory into
the already developed framework of persistent homology. We demonstrate that persistent
intersec- tion homology gives useful information about the relationship between
an embedded stratified space and its singularities. We give, and prove the correctness
of, an algorithm for the computa- tion of the persistent intersection homology
groups of a filtered simplicial complex equipped with a stratification by subcom-
plexes. We also derive, from Poincare ́ Duality, some structural results about
persistent intersection homology.
acknowledgement: This research was partially supported by the Defense Advanced Research
Projects Agency (DARPA) under grant HR0011-05-1-0007.
article_processing_charge: No
author:
- first_name: Paul
full_name: Bendich, Paul
id: 43F6EC54-F248-11E8-B48F-1D18A9856A87
last_name: Bendich
- first_name: John
full_name: Harer, John
last_name: Harer
citation:
ama: Bendich P, Harer J. Persistent intersection homology. Foundations of Computational
Mathematics. 2011;11(3):305-336. doi:10.1007/s10208-010-9081-1
apa: Bendich, P., & Harer, J. (2011). Persistent intersection homology. Foundations
of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-010-9081-1
chicago: Bendich, Paul, and John Harer. “Persistent Intersection Homology.” Foundations
of Computational Mathematics. Springer, 2011. https://doi.org/10.1007/s10208-010-9081-1.
ieee: P. Bendich and J. Harer, “Persistent intersection homology,” Foundations
of Computational Mathematics, vol. 11, no. 3. Springer, pp. 305–336, 2011.
ista: Bendich P, Harer J. 2011. Persistent intersection homology. Foundations of
Computational Mathematics. 11(3), 305–336.
mla: Bendich, Paul, and John Harer. “Persistent Intersection Homology.” Foundations
of Computational Mathematics, vol. 11, no. 3, Springer, 2011, pp. 305–36,
doi:10.1007/s10208-010-9081-1.
short: P. Bendich, J. Harer, Foundations of Computational Mathematics 11 (2011)
305–336.
corr_author: '1'
date_created: 2018-12-11T12:02:59Z
date_published: 2011-06-01T00:00:00Z
date_updated: 2025-09-30T08:53:15Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s10208-010-9081-1
external_id:
isi:
- '000290038800002'
intvolume: ' 11'
isi: 1
issue: '3'
language:
- iso: eng
month: '06'
oa_version: None
page: 305 - 336
publication: Foundations of Computational Mathematics
publication_status: published
publisher: Springer
publist_id: '3229'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Persistent intersection homology
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 11
year: '2011'
...
---
_id: '3848'
abstract:
- lang: eng
text: We define the robustness of a level set homology class of a function f:XR
as the magnitude of a perturbation necessary to kill the class. Casting this notion
into a group theoretic framework, we compute the robustness for each class, using
a connection to extended persistent homology. The special case X=R3 has ramifications
in medical imaging and scientific visualization.
alternative_title:
- LNCS
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. The robustness of level sets.
In: Vol 6346. Springer; 2010:1-10. doi:10.1007/978-3-642-15775-2_1'
apa: 'Bendich, P., Edelsbrunner, H., Morozov, D., & Patel, A. (2010). The robustness
of level sets (Vol. 6346, pp. 1–10). Presented at the ESA: European Symposium
on Algorithms, Liverpool, UK: Springer. https://doi.org/10.1007/978-3-642-15775-2_1'
chicago: Bendich, Paul, Herbert Edelsbrunner, Dmitriy Morozov, and Amit Patel. “The
Robustness of Level Sets,” 6346:1–10. Springer, 2010. https://doi.org/10.1007/978-3-642-15775-2_1.
ieee: 'P. Bendich, H. Edelsbrunner, D. Morozov, and A. Patel, “The robustness of
level sets,” presented at the ESA: European Symposium on Algorithms, Liverpool,
UK, 2010, vol. 6346, pp. 1–10.'
ista: 'Bendich P, Edelsbrunner H, Morozov D, Patel A. 2010. The robustness of level
sets. ESA: European Symposium on Algorithms, LNCS, vol. 6346, 1–10.'
mla: Bendich, Paul, et al. The Robustness of Level Sets. Vol. 6346, Springer,
2010, pp. 1–10, doi:10.1007/978-3-642-15775-2_1.
short: P. Bendich, H. Edelsbrunner, D. Morozov, A. Patel, in:, Springer, 2010, pp.
1–10.
conference:
end_date: 2010-09-08
location: Liverpool, UK
name: 'ESA: European Symposium on Algorithms'
start_date: 2010-09-06
corr_author: '1'
date_created: 2018-12-11T12:05:30Z
date_published: 2010-09-01T00:00:00Z
date_updated: 2024-10-09T20:54:09Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-642-15775-2_1
intvolume: ' 6346'
language:
- iso: eng
month: '09'
oa_version: None
page: 1 - 10
publication_status: published
publisher: Springer
publist_id: '2336'
quality_controlled: '1'
scopus_import: 1
status: public
title: The robustness of level sets
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 6346
year: '2010'
...
---
_id: '3849'
abstract:
- lang: eng
text: Using ideas from persistent homology, the robustness of a level set of a real-valued
function is defined in terms of the magnitude of the perturbation necessary to
kill the classes. Prior work has shown that the homology and robustness information
can be read off the extended persistence diagram of the function. This paper extends
these results to a non-uniform error model in which perturbations vary in their
magnitude across the domain.
alternative_title:
- LNCS
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: Michael
full_name: Kerber, Michael
id: 36E4574A-F248-11E8-B48F-1D18A9856A87
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Amit
full_name: Patel, Amit
id: 34A254A0-F248-11E8-B48F-1D18A9856A87
last_name: Patel
citation:
ama: 'Bendich P, Edelsbrunner H, Kerber M, Patel A. Persistent homology under non-uniform
error. In: Vol 6281. Springer; 2010:12-23. doi:10.1007/978-3-642-15155-2_2'
apa: 'Bendich, P., Edelsbrunner, H., Kerber, M., & Patel, A. (2010). Persistent
homology under non-uniform error (Vol. 6281, pp. 12–23). Presented at the MFCS:
Mathematical Foundations of Computer Science, Brno, Czech Republic: Springer.
https://doi.org/10.1007/978-3-642-15155-2_2'
chicago: Bendich, Paul, Herbert Edelsbrunner, Michael Kerber, and Amit Patel. “Persistent
Homology under Non-Uniform Error,” 6281:12–23. Springer, 2010. https://doi.org/10.1007/978-3-642-15155-2_2.
ieee: 'P. Bendich, H. Edelsbrunner, M. Kerber, and A. Patel, “Persistent homology
under non-uniform error,” presented at the MFCS: Mathematical Foundations of Computer
Science, Brno, Czech Republic, 2010, vol. 6281, pp. 12–23.'
ista: 'Bendich P, Edelsbrunner H, Kerber M, Patel A. 2010. Persistent homology under
non-uniform error. MFCS: Mathematical Foundations of Computer Science, LNCS, vol.
6281, 12–23.'
mla: Bendich, Paul, et al. Persistent Homology under Non-Uniform Error. Vol.
6281, Springer, 2010, pp. 12–23, doi:10.1007/978-3-642-15155-2_2.
short: P. Bendich, H. Edelsbrunner, M. Kerber, A. Patel, in:, Springer, 2010, pp.
12–23.
conference:
end_date: 2010-08-27
location: Brno, Czech Republic
name: 'MFCS: Mathematical Foundations of Computer Science'
start_date: 2010-08-23
date_created: 2018-12-11T12:05:30Z
date_published: 2010-08-10T00:00:00Z
date_updated: 2021-01-12T07:52:38Z
day: '10'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/978-3-642-15155-2_2
file:
- access_level: open_access
checksum: af61e1c2bb42f3d556179d4692caeb1b
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:13:13Z
date_updated: 2020-07-14T12:46:17Z
file_id: '4994'
file_name: IST-2016-537-v1+1_2010-P-05-NonuniformError.pdf
file_size: 142357
relation: main_file
file_date_updated: 2020-07-14T12:46:17Z
has_accepted_license: '1'
intvolume: ' 6281'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Submitted Version
page: 12 - 23
publication_status: published
publisher: Springer
publist_id: '2333'
pubrep_id: '537'
quality_controlled: '1'
scopus_import: 1
status: public
title: Persistent homology under non-uniform error
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 6281
year: '2010'
...
---
_id: '3901'
abstract:
- lang: eng
text: We are interested in 3-dimensional images given as arrays of voxels with intensity
values. Extending these values to acontinuous function, we study the robustness
of homology classes in its level and interlevel sets, that is, the amount of perturbationneeded
to destroy these classes. The structure of the homology classes and their robustness,
over all level and interlevel sets, can bevisualized by a triangular diagram of
dots obtained by computing the extended persistence of the function. We give a
fast hierarchicalalgorithm using the dual complexes of oct-tree approximations
of the function. In addition, we show that for balanced oct-trees, thedual complexes
are geometrically realized in $R^3$ and can thus be used to construct level and
interlevel sets. We apply these tools tostudy 3-dimensional images of plant root
systems.
article_processing_charge: No
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: Michael
full_name: Kerber, Michael
id: 36E4574A-F248-11E8-B48F-1D18A9856A87
last_name: Kerber
orcid: 0000-0002-8030-9299
citation:
ama: Bendich P, Edelsbrunner H, Kerber M. Computing robustness and persistence for
images. IEEE Transactions of Visualization and Computer Graphics. 2010;16(6):1251-1260.
doi:10.1109/TVCG.2010.139
apa: Bendich, P., Edelsbrunner, H., & Kerber, M. (2010). Computing robustness
and persistence for images. IEEE Transactions of Visualization and Computer
Graphics. IEEE. https://doi.org/10.1109/TVCG.2010.139
chicago: Bendich, Paul, Herbert Edelsbrunner, and Michael Kerber. “Computing Robustness
and Persistence for Images.” IEEE Transactions of Visualization and Computer
Graphics. IEEE, 2010. https://doi.org/10.1109/TVCG.2010.139.
ieee: P. Bendich, H. Edelsbrunner, and M. Kerber, “Computing robustness and persistence
for images,” IEEE Transactions of Visualization and Computer Graphics,
vol. 16, no. 6. IEEE, pp. 1251–1260, 2010.
ista: Bendich P, Edelsbrunner H, Kerber M. 2010. Computing robustness and persistence
for images. IEEE Transactions of Visualization and Computer Graphics. 16(6), 1251–1260.
mla: Bendich, Paul, et al. “Computing Robustness and Persistence for Images.” IEEE
Transactions of Visualization and Computer Graphics, vol. 16, no. 6, IEEE,
2010, pp. 1251–60, doi:10.1109/TVCG.2010.139.
short: P. Bendich, H. Edelsbrunner, M. Kerber, IEEE Transactions of Visualization
and Computer Graphics 16 (2010) 1251–1260.
corr_author: '1'
date_created: 2018-12-11T12:05:47Z
date_published: 2010-10-28T00:00:00Z
date_updated: 2025-09-30T09:30:22Z
day: '28'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1109/TVCG.2010.139
external_id:
isi:
- '000283758600045'
file:
- access_level: open_access
checksum: f6d813c04f4b46023cec6b9a17f15472
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:17:10Z
date_updated: 2020-07-14T12:46:21Z
file_id: '5262'
file_name: IST-2016-536-v1+1_2010-J-02-PersistenceforImages.pdf
file_size: 721994
relation: main_file
file_date_updated: 2020-07-14T12:46:21Z
has_accepted_license: '1'
intvolume: ' 16'
isi: 1
issue: '6'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Submitted Version
page: 1251 - 1260
publication: IEEE Transactions of Visualization and Computer Graphics
publication_status: published
publisher: IEEE
publist_id: '2253'
pubrep_id: '536'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Computing robustness and persistence for images
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 16
year: '2010'
...
---
_id: '3975'
abstract:
- lang: eng
text: We study the reconstruction of a stratified space from a possibly noisy point
sample. Specifically, we use the vineyard of the distance function restricted
to a I-parameter family of neighborhoods of a point to assess the local homology
of the stratified space at that point. We prove the correctness of this assessment
under the assumption of a sufficiently dense sample. We also give an algorithm
that constructs the vineyard and makes the local assessment in time at most cubic
in the size of the Delaunay triangulation of the point sample.
author:
- first_name: Paul
full_name: Paul Bendich
id: 43F6EC54-F248-11E8-B48F-1D18A9856A87
last_name: Bendich
- first_name: David
full_name: Cohen-Steiner, David
last_name: Cohen Steiner
- first_name: Herbert
full_name: Herbert Edelsbrunner
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: John
full_name: Harer, John
last_name: Harer
- first_name: Dmitriy
full_name: Morozov, Dmitriy
last_name: Morozov
citation:
ama: 'Bendich P, Cohen Steiner D, Edelsbrunner H, Harer J, Morozov D. Inferring
local homology from sampled stratified spaces. In: IEEE; 2007:536-546. doi:10.1109/FOCS.2007.33'
apa: 'Bendich, P., Cohen Steiner, D., Edelsbrunner, H., Harer, J., & Morozov,
D. (2007). Inferring local homology from sampled stratified spaces (pp. 536–546).
Presented at the FOCS: Foundations of Computer Science, IEEE. https://doi.org/10.1109/FOCS.2007.33'
chicago: Bendich, Paul, David Cohen Steiner, Herbert Edelsbrunner, John Harer, and
Dmitriy Morozov. “Inferring Local Homology from Sampled Stratified Spaces,” 536–46.
IEEE, 2007. https://doi.org/10.1109/FOCS.2007.33.
ieee: 'P. Bendich, D. Cohen Steiner, H. Edelsbrunner, J. Harer, and D. Morozov,
“Inferring local homology from sampled stratified spaces,” presented at the FOCS:
Foundations of Computer Science, 2007, pp. 536–546.'
ista: 'Bendich P, Cohen Steiner D, Edelsbrunner H, Harer J, Morozov D. 2007. Inferring
local homology from sampled stratified spaces. FOCS: Foundations of Computer Science,
536–546.'
mla: Bendich, Paul, et al. Inferring Local Homology from Sampled Stratified Spaces.
IEEE, 2007, pp. 536–46, doi:10.1109/FOCS.2007.33.
short: P. Bendich, D. Cohen Steiner, H. Edelsbrunner, J. Harer, D. Morozov, in:,
IEEE, 2007, pp. 536–546.
conference:
name: 'FOCS: Foundations of Computer Science'
date_created: 2018-12-11T12:06:13Z
date_published: 2007-01-01T00:00:00Z
date_updated: 2021-01-12T07:53:35Z
day: '01'
doi: 10.1109/FOCS.2007.33
extern: 1
month: '01'
page: 536 - 546
publication_status: published
publisher: IEEE
publist_id: '2150'
quality_controlled: 0
status: public
title: Inferring local homology from sampled stratified spaces
type: conference
year: '2007'
...