---
_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: '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: '3127'
abstract:
- lang: eng
text: "When searching for characteristic subpatterns in potentially noisy graph
data, it appears self-evident that having multiple observations would be better
than having just one. However, it turns out that the inconsistencies introduced
when different graph instances have different edge sets pose a serious challenge.
In this work we address this challenge for the problem of finding maximum weighted
cliques.\r\n We introduce the concept of most persistent soft-clique. This
is subset of vertices, that 1) is almost fully or at least densely connected,
2) occurs in all or almost all graph instances, and 3) has the maximum weight.
We present a measure of clique-ness, that essentially counts the number of edge
missing to make a subset of vertices into a clique. With this measure, we show
that the problem of finding the most persistent soft-clique problem can be cast
either as: a) a max-min two person game optimization problem, or b) a min-min
soft margin optimization problem. Both formulations lead to the same solution
when using a partial Lagrangian method to solve the optimization problems. By
experiments on synthetic data and on real social network data, we show that the
proposed method is able to reliably find soft cliques in graph data, even if that
is distorted by random noise or unreliable observations."
article_processing_charge: No
author:
- first_name: Novi
full_name: Quadrianto, Novi
last_name: Quadrianto
- first_name: Christoph
full_name: Lampert, Christoph
id: 40C20FD2-F248-11E8-B48F-1D18A9856A87
last_name: Lampert
orcid: 0000-0001-8622-7887
- first_name: Chao
full_name: Chen, Chao
id: 3E92416E-F248-11E8-B48F-1D18A9856A87
last_name: Chen
citation:
ama: 'Quadrianto N, Lampert C, Chen C. The most persistent soft-clique in a set
of sampled graphs. In: Proceedings of the 29th International Conference on
Machine Learning. ML Research Press; 2012:211-218.'
apa: 'Quadrianto, N., Lampert, C., & Chen, C. (2012). The most persistent soft-clique
in a set of sampled graphs. In Proceedings of the 29th International Conference
on Machine Learning (pp. 211–218). Edinburgh, United Kingdom: ML Research
Press.'
chicago: Quadrianto, Novi, Christoph Lampert, and Chao Chen. “The Most Persistent
Soft-Clique in a Set of Sampled Graphs.” In Proceedings of the 29th International
Conference on Machine Learning, 211–18. ML Research Press, 2012.
ieee: N. Quadrianto, C. Lampert, and C. Chen, “The most persistent soft-clique in
a set of sampled graphs,” in Proceedings of the 29th International Conference
on Machine Learning, Edinburgh, United Kingdom, 2012, pp. 211–218.
ista: 'Quadrianto N, Lampert C, Chen C. 2012. The most persistent soft-clique in
a set of sampled graphs. Proceedings of the 29th International Conference on Machine
Learning. ICML: International Conference on Machine Learning, 211–218.'
mla: Quadrianto, Novi, et al. “The Most Persistent Soft-Clique in a Set of Sampled
Graphs.” Proceedings of the 29th International Conference on Machine Learning,
ML Research Press, 2012, pp. 211–18.
short: N. Quadrianto, C. Lampert, C. Chen, in:, Proceedings of the 29th International
Conference on Machine Learning, ML Research Press, 2012, pp. 211–218.
conference:
end_date: 2012-07-01
location: Edinburgh, United Kingdom
name: 'ICML: International Conference on Machine Learning'
start_date: 2012-06-26
date_created: 2018-12-11T12:01:33Z
date_published: 2012-06-01T00:00:00Z
date_updated: 2023-10-17T11:55:06Z
day: '01'
department:
- _id: ChLa
- _id: HeEd
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1206.4652
month: '06'
oa: 1
oa_version: Preprint
page: 211-218
publication: Proceedings of the 29th International Conference on Machine Learning
publication_status: published
publisher: ML Research Press
publist_id: '3572'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The most persistent soft-clique in a set of sampled graphs
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2012'
...
---
_id: '3129'
abstract:
- lang: eng
text: "Let K be a simplicial complex and g the rank of its p-th homology group Hp(K)
defined with ℤ2 coefficients. We show that we can compute a basis H of Hp(K) and
annotate each p-simplex of K with a binary vector of length g with the following
property: the annotations, summed over all p-simplices in any p-cycle z, provide
the coordinate vector of the homology class [z] in the basis H. The basis and
the annotations for all simplices can be computed in O(n ω ) time, where n is
the size of K and ω < 2.376 is a quantity so that two n×n matrices can be multiplied
in O(n ω ) time. The precomputed annotations permit answering queries about the
independence or the triviality of p-cycles efficiently.\r\n\r\nUsing annotations
of edges in 2-complexes, we derive better algorithms for computing optimal basis
and optimal homologous cycles in 1 - dimensional homology. Specifically, for computing
an optimal basis of H1(K) , we improve the previously known time complexity from
O(n 4) to O(n ω + n 2 g ω − 1). Here n denotes the size of the 2-skeleton of
K and g the rank of H1(K) . Computing an optimal cycle homologous to a given 1-cycle
is NP-hard even for surfaces and an algorithm taking 2 O(g) nlogn time is known
for surfaces. We extend this algorithm to work with arbitrary 2-complexes in O(n
ω ) + 2 O(g) n 2logn time using annotations.\r\n"
alternative_title:
- LNCS
arxiv: 1
author:
- first_name: Oleksiy
full_name: Busaryev, Oleksiy
last_name: Busaryev
- first_name: Sergio
full_name: Cabello, Sergio
last_name: Cabello
- first_name: Chao
full_name: Chen, Chao
id: 3E92416E-F248-11E8-B48F-1D18A9856A87
last_name: Chen
- first_name: Tamal
full_name: Dey, Tamal
last_name: Dey
- first_name: Yusu
full_name: Wang, Yusu
last_name: Wang
citation:
ama: 'Busaryev O, Cabello S, Chen C, Dey T, Wang Y. Annotating simplices with a
homology basis and its applications. In: Vol 7357. Springer; 2012:189-200. doi:10.1007/978-3-642-31155-0_17'
apa: 'Busaryev, O., Cabello, S., Chen, C., Dey, T., & Wang, Y. (2012). Annotating
simplices with a homology basis and its applications (Vol. 7357, pp. 189–200).
Presented at the SWAT: Symposium and Workshops on Algorithm Theory, Helsinki,
Finland: Springer. https://doi.org/10.1007/978-3-642-31155-0_17'
chicago: Busaryev, Oleksiy, Sergio Cabello, Chao Chen, Tamal Dey, and Yusu Wang.
“Annotating Simplices with a Homology Basis and Its Applications,” 7357:189–200.
Springer, 2012. https://doi.org/10.1007/978-3-642-31155-0_17.
ieee: 'O. Busaryev, S. Cabello, C. Chen, T. Dey, and Y. Wang, “Annotating simplices
with a homology basis and its applications,” presented at the SWAT: Symposium
and Workshops on Algorithm Theory, Helsinki, Finland, 2012, vol. 7357, pp. 189–200.'
ista: 'Busaryev O, Cabello S, Chen C, Dey T, Wang Y. 2012. Annotating simplices
with a homology basis and its applications. SWAT: Symposium and Workshops on Algorithm
Theory, LNCS, vol. 7357, 189–200.'
mla: Busaryev, Oleksiy, et al. Annotating Simplices with a Homology Basis and
Its Applications. Vol. 7357, Springer, 2012, pp. 189–200, doi:10.1007/978-3-642-31155-0_17.
short: O. Busaryev, S. Cabello, C. Chen, T. Dey, Y. Wang, in:, Springer, 2012, pp.
189–200.
conference:
end_date: 2012-07-06
location: Helsinki, Finland
name: 'SWAT: Symposium and Workshops on Algorithm Theory'
start_date: 2012-07-04
date_created: 2018-12-11T12:01:33Z
date_published: 2012-06-19T00:00:00Z
date_updated: 2021-01-12T07:41:15Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-642-31155-0_17
external_id:
arxiv:
- '1107.3793'
intvolume: ' 7357'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1107.3793
month: '06'
oa: 1
oa_version: Preprint
page: 189 - 200
publication_status: published
publisher: Springer
publist_id: '3569'
quality_controlled: '1'
scopus_import: 1
status: public
title: Annotating simplices with a homology basis and its applications
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7357
year: '2012'
...
---
_id: '3267'
abstract:
- lang: eng
text: 'We address the problem of localizing homology classes, namely, finding the
cycle representing a given class with the most concise geometric measure. We study
the problem with different measures: volume, diameter and radius. For volume,
that is, the 1-norm of a cycle, two main results are presented. First, we prove
that the problem is NP-hard to approximate within any constant factor. Second,
we prove that for homology of dimension two or higher, the problem is NP-hard
to approximate even when the Betti number is O(1). The latter result leads to
the inapproximability of the problem of computing the nonbounding cycle with the
smallest volume and computing cycles representing a homology basis with the minimal
total volume. As for the other two measures defined by pairwise geodesic distance,
diameter and radius, we show that the localization problem is NP-hard for diameter
but is polynomial for radius. Our work is restricted to homology over the ℤ2 field.'
author:
- first_name: Chao
full_name: Chen, Chao
id: 3E92416E-F248-11E8-B48F-1D18A9856A87
last_name: Chen
- first_name: Daniel
full_name: Freedman, Daniel
last_name: Freedman
citation:
ama: Chen C, Freedman D. Hardness results for homology localization. Discrete
& Computational Geometry. 2011;45(3):425-448. doi:10.1007/s00454-010-9322-8
apa: Chen, C., & Freedman, D. (2011). Hardness results for homology localization.
Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-010-9322-8
chicago: Chen, Chao, and Daniel Freedman. “Hardness Results for Homology Localization.”
Discrete & Computational Geometry. Springer, 2011. https://doi.org/10.1007/s00454-010-9322-8.
ieee: C. Chen and D. Freedman, “Hardness results for homology localization,” Discrete
& Computational Geometry, vol. 45, no. 3. Springer, pp. 425–448, 2011.
ista: Chen C, Freedman D. 2011. Hardness results for homology localization. Discrete
& Computational Geometry. 45(3), 425–448.
mla: Chen, Chao, and Daniel Freedman. “Hardness Results for Homology Localization.”
Discrete & Computational Geometry, vol. 45, no. 3, Springer, 2011,
pp. 425–48, doi:10.1007/s00454-010-9322-8.
short: C. Chen, D. Freedman, Discrete & Computational Geometry 45 (2011) 425–448.
date_created: 2018-12-11T12:02:21Z
date_published: 2011-01-14T00:00:00Z
date_updated: 2023-02-21T16:07:10Z
day: '14'
department:
- _id: HeEd
doi: 10.1007/s00454-010-9322-8
intvolume: ' 45'
issue: '3'
language:
- iso: eng
month: '01'
oa_version: None
page: 425 - 448
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '3379'
quality_controlled: '1'
related_material:
record:
- id: '10909'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: Hardness results for homology localization
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 45
year: '2011'
...
---
_id: '3268'
abstract:
- lang: eng
text: 'Algebraic topology is generally considered one of the purest subfield of
mathematics. However, over the last decade two interesting new lines of research
have emerged, one focusing on algorithms for algebraic topology, and the other
on applications of algebraic topology in engineering and science. Amongst the
new areas in which the techniques have been applied are computer vision and image
processing. In this paper, we survey the results of these endeavours. Because
algebraic topology is an area of mathematics with which most computer vision practitioners
have no experience, we review the machinery behind the theories of homology and
persistent homology; our review emphasizes intuitive explanations. In terms of
applications to computer vision, we focus on four illustrative problems: shape
signatures, natural image statistics, image denoising, and segmentation. Our hope
is that this review will stimulate interest on the part of computer vision researchers
to both use and extend the tools of this new field. '
alternative_title:
- Computer Science, Technology and Applications
author:
- first_name: Daniel
full_name: Freedman, Daniel
last_name: Freedman
- first_name: Chao
full_name: Chen, Chao
id: 3E92416E-F248-11E8-B48F-1D18A9856A87
last_name: Chen
citation:
ama: 'Freedman D, Chen C. Algebraic topology for computer vision. In: Computer
Vision. Nova Science Publishers; 2011:239-268.'
apa: Freedman, D., & Chen, C. (2011). Algebraic topology for computer vision.
In Computer Vision (pp. 239–268). Nova Science Publishers.
chicago: Freedman, Daniel, and Chao Chen. “Algebraic Topology for Computer Vision.”
In Computer Vision, 239–68. Nova Science Publishers, 2011.
ieee: D. Freedman and C. Chen, “Algebraic topology for computer vision,” in Computer
Vision, Nova Science Publishers, 2011, pp. 239–268.
ista: 'Freedman D, Chen C. 2011.Algebraic topology for computer vision. In: Computer
Vision. Computer Science, Technology and Applications, , 239–268.'
mla: Freedman, Daniel, and Chao Chen. “Algebraic Topology for Computer Vision.”
Computer Vision, Nova Science Publishers, 2011, pp. 239–68.
short: D. Freedman, C. Chen, in:, Computer Vision, Nova Science Publishers, 2011,
pp. 239–268.
date_created: 2018-12-11T12:02:22Z
date_published: 2011-11-30T00:00:00Z
date_updated: 2021-01-12T07:42:16Z
day: '30'
extern: '1'
language:
- iso: eng
main_file_link:
- url: http://www.hpl.hp.com/techreports/2009/HPL-2009-375.pdf
month: '11'
oa_version: None
page: 239 - 268
publication: Computer Vision
publication_status: published
publisher: Nova Science Publishers
publist_id: '3378'
quality_controlled: '1'
status: public
title: Algebraic topology for computer vision
type: book_chapter
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2011'
...
---
_id: '3269'
abstract:
- lang: eng
text: The unintentional scattering of light between neighboring surfaces in complex
projection environments increases the brightness and decreases the contrast, disrupting
the appearance of the desired imagery. To achieve satisfactory projection results,
the inverse problem of global illumination must be solved to cancel this secondary
scattering. In this paper, we propose a global illumination cancellation method
that minimizes the perceptual difference between the desired imagery and the actual
total illumination in the resulting physical environment. Using Gauss-Newton and
active set methods, we design a fast solver for the bound constrained nonlinear
least squares problem raised by the perceptual error metrics. Our solver is further
accelerated with a CUDA implementation and multi-resolution method to achieve
1–2 fps for problems with approximately 3000 variables. We demonstrate the global
illumination cancellation algorithm with our multi-projector system. Results show
that our method preserves the color fidelity of the desired imagery significantly
better than previous methods.
article_processing_charge: No
article_type: original
author:
- first_name: Yu
full_name: Sheng, Yu
last_name: Sheng
- first_name: Barbara
full_name: Cutler, Barbara
last_name: Cutler
- first_name: Chao
full_name: Chen, Chao
id: 3E92416E-F248-11E8-B48F-1D18A9856A87
last_name: Chen
- first_name: Joshua
full_name: Nasman, Joshua
last_name: Nasman
citation:
ama: Sheng Y, Cutler B, Chen C, Nasman J. Perceptual global illumination cancellation
in complex projection environments. Computer Graphics Forum. 2011;30(4):1261-1268.
doi:10.1111/j.1467-8659.2011.01985.x
apa: Sheng, Y., Cutler, B., Chen, C., & Nasman, J. (2011). Perceptual global
illumination cancellation in complex projection environments. Computer Graphics
Forum. Wiley-Blackwell. https://doi.org/10.1111/j.1467-8659.2011.01985.x
chicago: Sheng, Yu, Barbara Cutler, Chao Chen, and Joshua Nasman. “Perceptual Global
Illumination Cancellation in Complex Projection Environments.” Computer Graphics
Forum. Wiley-Blackwell, 2011. https://doi.org/10.1111/j.1467-8659.2011.01985.x.
ieee: Y. Sheng, B. Cutler, C. Chen, and J. Nasman, “Perceptual global illumination
cancellation in complex projection environments,” Computer Graphics Forum,
vol. 30, no. 4. Wiley-Blackwell, pp. 1261–1268, 2011.
ista: Sheng Y, Cutler B, Chen C, Nasman J. 2011. Perceptual global illumination
cancellation in complex projection environments. Computer Graphics Forum. 30(4),
1261–1268.
mla: Sheng, Yu, et al. “Perceptual Global Illumination Cancellation in Complex Projection
Environments.” Computer Graphics Forum, vol. 30, no. 4, Wiley-Blackwell,
2011, pp. 1261–68, doi:10.1111/j.1467-8659.2011.01985.x.
short: Y. Sheng, B. Cutler, C. Chen, J. Nasman, Computer Graphics Forum 30 (2011)
1261–1268.
date_created: 2018-12-11T12:02:22Z
date_published: 2011-07-19T00:00:00Z
date_updated: 2021-01-12T07:42:16Z
day: '19'
department:
- _id: HeEd
doi: 10.1111/j.1467-8659.2011.01985.x
intvolume: ' 30'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.cs.cmu.edu/%7Eshengyu/download/egsr2011_paper.pdf
month: '07'
oa: 1
oa_version: Published Version
page: 1261 - 1268
publication: Computer Graphics Forum
publication_status: published
publisher: Wiley-Blackwell
publist_id: '3377'
quality_controlled: '1'
scopus_import: 1
status: public
title: Perceptual global illumination cancellation in complex projection environments
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 30
year: '2011'
...
---
_id: '3270'
abstract:
- lang: eng
text: 'The persistence diagram of a filtered simplicial com- plex is usually computed
by reducing the boundary matrix of the complex. We introduce a simple op- timization
technique: by processing the simplices of the complex in decreasing dimension,
we can “kill” columns (i.e., set them to zero) without reducing them. This technique
completely avoids reduction on roughly half of the columns. We demonstrate that
this idea significantly improves the running time of the reduction algorithm in
practice. We also give an output-sensitive complexity analysis for the new al-
gorithm which yields to sub-cubic asymptotic bounds under certain assumptions.'
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. Persistent homology computation with a twist. In: TU Dortmund;
2011:197-200.'
apa: 'Chen, C., & Kerber, M. (2011). Persistent homology computation with a
twist (pp. 197–200). Presented at the EuroCG: European Workshop on Computational
Geometry, Morschach, Switzerland: TU Dortmund.'
chicago: Chen, Chao, and Michael Kerber. “Persistent Homology Computation with a
Twist,” 197–200. TU Dortmund, 2011.
ieee: 'C. Chen and M. Kerber, “Persistent homology computation with a twist,” presented
at the EuroCG: European Workshop on Computational Geometry, Morschach, Switzerland,
2011, pp. 197–200.'
ista: 'Chen C, Kerber M. 2011. Persistent homology computation with a twist. EuroCG:
European Workshop on Computational Geometry, 197–200.'
mla: Chen, Chao, and Michael Kerber. Persistent Homology Computation with a Twist.
TU Dortmund, 2011, pp. 197–200.
short: C. Chen, M. Kerber, in:, TU Dortmund, 2011, pp. 197–200.
conference:
end_date: 2011-03-30
location: Morschach, Switzerland
name: 'EuroCG: European Workshop on Computational Geometry'
start_date: 2011-03-28
date_created: 2018-12-11T12:02:22Z
date_published: 2011-01-01T00:00:00Z
date_updated: 2021-01-12T07:42:17Z
day: '01'
department:
- _id: HeEd
language:
- iso: eng
month: '01'
oa_version: None
page: 197 - 200
publication_status: published
publisher: TU Dortmund
publist_id: '3376'
quality_controlled: '1'
status: public
title: Persistent homology computation with a twist
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2011'
...
---
_id: '3271'
abstract:
- lang: eng
text: In this paper we present an efficient framework for computation of persis-
tent homology of cubical data in arbitrary dimensions. An existing algorithm using
simplicial complexes is adapted to the setting of cubical complexes. The proposed
approach enables efficient application of persistent homology in domains where
the data is naturally given in a cubical form. By avoiding triangulation of the
data, we significantly reduce the size of the complex. We also present a data-structure
de- signed to compactly store and quickly manipulate cubical complexes. By means
of numerical experiments, we show high speed and memory efficiency of our ap-
proach. We compare our framework to other available implementations, showing its
superiority. Finally, we report performance on selected 3D and 4D data-sets.
alternative_title:
- Theory, Algorithms, and Applications
author:
- first_name: Hubert
full_name: Wagner, Hubert
last_name: Wagner
- first_name: Chao
full_name: Chen, Chao
id: 3E92416E-F248-11E8-B48F-1D18A9856A87
last_name: Chen
- first_name: Erald
full_name: Vuçini, Erald
last_name: Vuçini
citation:
ama: 'Wagner H, Chen C, Vuçini E. Efficient computation of persistent homology for
cubical data. In: Peikert R, Hauser H, Carr H, Fuchs R, eds. Topological Methods
in Data Analysis and Visualization II. Springer; 2011:91-106. doi:10.1007/978-3-642-23175-9_7'
apa: Wagner, H., Chen, C., & Vuçini, E. (2011). Efficient computation of persistent
homology for cubical data. In R. Peikert, H. Hauser, H. Carr, & R. Fuchs (Eds.),
Topological Methods in Data Analysis and Visualization II (pp. 91–106).
Springer. https://doi.org/10.1007/978-3-642-23175-9_7
chicago: Wagner, Hubert, Chao Chen, and Erald Vuçini. “Efficient Computation of
Persistent Homology for Cubical Data.” In Topological Methods in Data Analysis
and Visualization II, edited by Ronald Peikert, Helwig Hauser, Hamish Carr,
and Raphael Fuchs, 91–106. Springer, 2011. https://doi.org/10.1007/978-3-642-23175-9_7.
ieee: H. Wagner, C. Chen, and E. Vuçini, “Efficient computation of persistent homology
for cubical data,” in Topological Methods in Data Analysis and Visualization
II, R. Peikert, H. Hauser, H. Carr, and R. Fuchs, Eds. Springer, 2011, pp.
91–106.
ista: 'Wagner H, Chen C, Vuçini E. 2011.Efficient computation of persistent homology
for cubical data. In: Topological Methods in Data Analysis and Visualization II.
Theory, Algorithms, and Applications, , 91–106.'
mla: Wagner, Hubert, et al. “Efficient Computation of Persistent Homology for Cubical
Data.” Topological Methods in Data Analysis and Visualization II, edited
by Ronald Peikert et al., Springer, 2011, pp. 91–106, doi:10.1007/978-3-642-23175-9_7.
short: H. Wagner, C. Chen, E. Vuçini, in:, R. Peikert, H. Hauser, H. Carr, R. Fuchs
(Eds.), Topological Methods in Data Analysis and Visualization II, Springer, 2011,
pp. 91–106.
date_created: 2018-12-11T12:02:23Z
date_published: 2011-11-14T00:00:00Z
date_updated: 2021-01-12T07:42:18Z
day: '14'
department:
- _id: HeEd
doi: 10.1007/978-3-642-23175-9_7
editor:
- first_name: Ronald
full_name: Peikert, Ronald
last_name: Peikert
- first_name: Helwig
full_name: Hauser, Helwig
last_name: Hauser
- first_name: Hamish
full_name: Carr, Hamish
last_name: Carr
- first_name: Raphael
full_name: Fuchs, Raphael
last_name: Fuchs
language:
- iso: eng
month: '11'
oa_version: None
page: 91 - 106
publication: Topological Methods in Data Analysis and Visualization II
publication_status: published
publisher: Springer
publist_id: '3375'
quality_controlled: '1'
scopus_import: 1
status: public
title: Efficient computation of persistent homology for cubical data
type: book_chapter
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2011'
...
---
_id: '3313'
abstract:
- lang: eng
text: Interpreting an image as a function on a compact sub- set of the Euclidean
plane, we get its scale-space by diffu- sion, spreading the image over the entire
plane. This gener- ates a 1-parameter family of functions alternatively defined
as convolutions with a progressively wider Gaussian ker- nel. We prove that the
corresponding 1-parameter family of persistence diagrams have norms that go rapidly
to zero as time goes to infinity. This result rationalizes experimental observations
about scale-space. We hope this will lead to targeted improvements of related
computer vision methods.
article_number: '6126271'
author:
- first_name: Chao
full_name: Chen, Chao
id: 3E92416E-F248-11E8-B48F-1D18A9856A87
last_name: Chen
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: 'Chen C, Edelsbrunner H. Diffusion runs low on persistence fast. In: Proceedings
of the IEEE International Conference on Computer Vision. IEEE; 2011. doi:10.1109/ICCV.2011.6126271'
apa: 'Chen, C., & Edelsbrunner, H. (2011). Diffusion runs low on persistence
fast. In Proceedings of the IEEE International Conference on Computer Vision.
Barcelona, Spain: IEEE. https://doi.org/10.1109/ICCV.2011.6126271'
chicago: Chen, Chao, and Herbert Edelsbrunner. “Diffusion Runs Low on Persistence
Fast.” In Proceedings of the IEEE International Conference on Computer Vision.
IEEE, 2011. https://doi.org/10.1109/ICCV.2011.6126271.
ieee: C. Chen and H. Edelsbrunner, “Diffusion runs low on persistence fast,” in
Proceedings of the IEEE International Conference on Computer Vision, Barcelona,
Spain, 2011.
ista: 'Chen C, Edelsbrunner H. 2011. Diffusion runs low on persistence fast. Proceedings
of the IEEE International Conference on Computer Vision. ICCV: International Conference
on Computer Vision, 6126271.'
mla: Chen, Chao, and Herbert Edelsbrunner. “Diffusion Runs Low on Persistence Fast.”
Proceedings of the IEEE International Conference on Computer Vision, 6126271,
IEEE, 2011, doi:10.1109/ICCV.2011.6126271.
short: C. Chen, H. Edelsbrunner, in:, Proceedings of the IEEE International Conference
on Computer Vision, IEEE, 2011.
conference:
end_date: 2011-11-13
location: Barcelona, Spain
name: 'ICCV: International Conference on Computer Vision'
start_date: 2011-11-06
date_created: 2018-12-11T12:02:37Z
date_published: 2011-11-06T00:00:00Z
date_updated: 2021-01-12T07:42:35Z
day: '06'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1109/ICCV.2011.6126271
file:
- access_level: open_access
checksum: 6984684081ba123808b344f9f2e64a8f
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:17:28Z
date_updated: 2020-07-14T12:46:07Z
file_id: '5282'
file_name: IST-2016-540-v1+1_2011-P-08-RunEmpty.pdf
file_size: 614050
relation: main_file
file_date_updated: 2020-07-14T12:46:07Z
has_accepted_license: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Submitted Version
publication: Proceedings of the IEEE International Conference on Computer Vision
publication_status: published
publisher: IEEE
publist_id: '3327'
pubrep_id: '540'
quality_controlled: '1'
scopus_import: 1
status: public
title: Diffusion runs low on persistence fast
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2011'
...
---
_id: '3336'
abstract:
- lang: eng
text: 'We introduce TopoCut: a new way to integrate knowledge about topological
properties (TPs) into random field image segmentation model. Instead of including
TPs as additional constraints during minimization of the energy function, we devise
an efficient algorithm for modifying the unary potentials such that the resulting
segmentation is guaranteed with the desired properties. Our method is more flexible
in the sense that it handles more topology constraints than previous methods,
which were only able to enforce pairwise or global connectivity. In particular,
our method is very fast, making it for the first time possible to enforce global
topological properties in practical image segmentation tasks.'
acknowledgement: The first author is supported by the Austrian Science Fund (FWF)
grant No. P20134-N13. The authors would like to thank Sebastian Nowozin for helpful
discussions.
article_processing_charge: No
author:
- first_name: Chao
full_name: Chen, Chao
id: 3E92416E-F248-11E8-B48F-1D18A9856A87
last_name: Chen
- first_name: Daniel
full_name: Freedman, Daniel
last_name: Freedman
- 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, Freedman D, Lampert C. Enforcing topological constraints in random
field image segmentation. In: CVPR: Computer Vision and Pattern Recognition.
IEEE; 2011:2089-2096. doi:10.1109/CVPR.2011.5995503'
apa: 'Chen, C., Freedman, D., & Lampert, C. (2011). Enforcing topological constraints
in random field image segmentation. In CVPR: Computer Vision and Pattern Recognition
(pp. 2089–2096). Colorado Springs, CO, United States: IEEE. https://doi.org/10.1109/CVPR.2011.5995503'
chicago: 'Chen, Chao, Daniel Freedman, and Christoph Lampert. “Enforcing Topological
Constraints in Random Field Image Segmentation.” In CVPR: Computer Vision and
Pattern Recognition, 2089–96. IEEE, 2011. https://doi.org/10.1109/CVPR.2011.5995503.'
ieee: 'C. Chen, D. Freedman, and C. Lampert, “Enforcing topological constraints
in random field image segmentation,” in CVPR: Computer Vision and Pattern Recognition,
Colorado Springs, CO, United States, 2011, pp. 2089–2096.'
ista: 'Chen C, Freedman D, Lampert C. 2011. Enforcing topological constraints in
random field image segmentation. CVPR: Computer Vision and Pattern Recognition.
CVPR: Conference on Computer Vision and Pattern Recognition, 2089–2096.'
mla: 'Chen, Chao, et al. “Enforcing Topological Constraints in Random Field Image
Segmentation.” CVPR: Computer Vision and Pattern Recognition, IEEE, 2011,
pp. 2089–96, doi:10.1109/CVPR.2011.5995503.'
short: 'C. Chen, D. Freedman, C. Lampert, in:, CVPR: Computer Vision and Pattern
Recognition, IEEE, 2011, pp. 2089–2096.'
conference:
end_date: 2011-06-25
location: Colorado Springs, CO, United States
name: 'CVPR: Conference on Computer Vision and Pattern Recognition'
start_date: 2011-06-20
date_created: 2018-12-11T12:02:45Z
date_published: 2011-07-22T00:00:00Z
date_updated: 2023-02-23T12:23:56Z
day: '22'
department:
- _id: HeEd
- _id: ChLa
doi: 10.1109/CVPR.2011.5995503
language:
- iso: eng
month: '07'
oa_version: None
page: 2089 - 2096
publication: 'CVPR: Computer Vision and Pattern Recognition'
publication_identifier:
eisbn:
- 978-1-4577-0395-9
isbn:
- 978-1-4577-0394-2
publication_status: published
publisher: IEEE
publist_id: '3294'
quality_controlled: '1'
related_material:
record:
- id: '5386'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Enforcing topological constraints in random field image segmentation
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2011'
...
---
_id: '5386'
abstract:
- lang: eng
text: 'We introduce TopoCut: a new way to integrate knowledge about topological
properties (TPs) into random field image segmentation model. Instead of including
TPs as additional constraints during minimization of the energy function, we devise
an efficient algorithm for modifying the unary potentials such that the resulting
segmentation is guaranteed with the desired properties. Our method is more flexible
in the sense that it handles more topology constraints than previous methods,
which were only able to enforce pairwise or global connectivity. In particular,
our method is very fast, making it for the first time possible to enforce global
topological properties in practical image segmentation tasks.'
alternative_title:
- IST Austria Technical Report
author:
- first_name: Chao
full_name: Chen, Chao
id: 3E92416E-F248-11E8-B48F-1D18A9856A87
last_name: Chen
- first_name: Daniel
full_name: Freedman, Daniel
last_name: Freedman
- 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, Freedman D, Lampert C. Enforcing Topological Constraints in Random
Field Image Segmentation. IST Austria; 2011. doi:10.15479/AT:IST-2011-0002
apa: Chen, C., Freedman, D., & Lampert, C. (2011). Enforcing topological
constraints in random field image segmentation. IST Austria. https://doi.org/10.15479/AT:IST-2011-0002
chicago: Chen, Chao, Daniel Freedman, and Christoph Lampert. Enforcing Topological
Constraints in Random Field Image Segmentation. IST Austria, 2011. https://doi.org/10.15479/AT:IST-2011-0002.
ieee: C. Chen, D. Freedman, and C. Lampert, Enforcing topological constraints
in random field image segmentation. IST Austria, 2011.
ista: Chen C, Freedman D, Lampert C. 2011. Enforcing topological constraints in
random field image segmentation, IST Austria, 69p.
mla: Chen, Chao, et al. Enforcing Topological Constraints in Random Field Image
Segmentation. IST Austria, 2011, doi:10.15479/AT:IST-2011-0002.
short: C. Chen, D. Freedman, C. Lampert, Enforcing Topological Constraints in Random
Field Image Segmentation, IST Austria, 2011.
date_created: 2018-12-12T11:39:02Z
date_published: 2011-03-28T00:00:00Z
date_updated: 2023-02-23T11:22:48Z
day: '28'
ddc:
- '000'
department:
- _id: ChLa
doi: 10.15479/AT:IST-2011-0002
file:
- access_level: open_access
checksum: ad64c2add5fe2ad10e9d5c669f3f9526
content_type: application/pdf
creator: system
date_created: 2018-12-12T11:53:34Z
date_updated: 2020-07-14T12:46:41Z
file_id: '5495'
file_name: IST-2011-0002_IST-2011-0002.pdf
file_size: 26390601
relation: main_file
file_date_updated: 2020-07-14T12:46:41Z
has_accepted_license: '1'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: '69'
publication_identifier:
issn:
- 2664-1690
publication_status: published
publisher: IST Austria
pubrep_id: '22'
related_material:
record:
- id: '3336'
relation: later_version
status: public
status: public
title: Enforcing topological constraints in random field image segmentation
type: technical_report
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2011'
...
---
_id: '3367'
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)ΓR(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, and R(n) is the complexity
of computing the rank of an n x n matrix with O(n) nonzero entries. Depending
on the choice of the rank algorithm, this yields a deterministic O(C(1-δ)Γn2.376)
algorithm, a O(C(1-δ)Γn2.28) Las-Vegas algorithm, or a O(C(1-δ)Γn2+ε) Monte-Carlo
algorithm for an arbitrary ε>0.
article_processing_charge: No
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. In:
ACM; 2011:207-216. doi:10.1145/1998196.1998228'
apa: 'Chen, C., & Kerber, M. (2011). An output sensitive algorithm for persistent
homology (pp. 207–216). Presented at the SoCG: Symposium on Computational Geometry,
Paris, France: ACM. https://doi.org/10.1145/1998196.1998228'
chicago: Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent
Homology,” 207–16. ACM, 2011. https://doi.org/10.1145/1998196.1998228.
ieee: 'C. Chen and M. Kerber, “An output sensitive algorithm for persistent homology,”
presented at the SoCG: Symposium on Computational Geometry, Paris, France, 2011,
pp. 207–216.'
ista: 'Chen C, Kerber M. 2011. An output sensitive algorithm for persistent homology.
SoCG: Symposium on Computational Geometry, 207–216.'
mla: Chen, Chao, and Michael Kerber. An Output Sensitive Algorithm for Persistent
Homology. ACM, 2011, pp. 207–16, doi:10.1145/1998196.1998228.
short: C. Chen, M. Kerber, in:, ACM, 2011, pp. 207–216.
conference:
end_date: 2011-06-15
location: Paris, France
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2011-06-13
date_created: 2018-12-11T12:02:56Z
date_published: 2011-06-13T00:00:00Z
date_updated: 2023-02-23T11:05:04Z
day: '13'
department:
- _id: HeEd
doi: 10.1145/1998196.1998228
language:
- iso: eng
month: '06'
oa_version: None
page: 207 - 216
publication_status: published
publisher: ACM
publist_id: '3245'
quality_controlled: '1'
related_material:
record:
- id: '2939'
relation: later_version
status: public
scopus_import: 1
status: public
title: An output sensitive algorithm for persistent homology
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2011'
...
---
_id: '10909'
abstract:
- lang: eng
text: We address the problem of localizing homology classes, namely, finding the
cycle representing a given class with the most concise geometric measure. We focus
on the volume measure, that is, the 1-norm of a cycle. Two main results are presented.
First, we prove the problem is NP-hard to approximate within any constant factor.
Second, we prove that for homology of dimension two or higher, the problem is
NP-hard to approximate even when the Betti number is O(1). A side effect is the
inapproximability of the problem of computing the nonbounding cycle with the smallest
volume, and computing cycles representing a homology basis with the minimal total
volume. We also discuss other geometric measures (diameter and radius) and show
their disadvantages in homology localization. Our work is restricted to homology
over the ℤ2 field.
acknowledgement: Partially supported by the Austrian Science Fund under grantFSP-S9103-N04
and P20134-N13.
article_processing_charge: No
author:
- first_name: Chao
full_name: Chen, Chao
id: 3E92416E-F248-11E8-B48F-1D18A9856A87
last_name: Chen
- first_name: Daniel
full_name: Freedman, Daniel
last_name: Freedman
citation:
ama: 'Chen C, Freedman D. Hardness results for homology localization. In: Proceedings
of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms. Society for
Industrial and Applied Mathematics; 2010:1594-1604. doi:10.1137/1.9781611973075.129'
apa: 'Chen, C., & Freedman, D. (2010). Hardness results for homology localization.
In Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms
(pp. 1594–1604). Austin, TX, United States: Society for Industrial and Applied
Mathematics. https://doi.org/10.1137/1.9781611973075.129'
chicago: Chen, Chao, and Daniel Freedman. “Hardness Results for Homology Localization.”
In Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms,
1594–1604. Society for Industrial and Applied Mathematics, 2010. https://doi.org/10.1137/1.9781611973075.129.
ieee: C. Chen and D. Freedman, “Hardness results for homology localization,” in
Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms,
Austin, TX, United States, 2010, pp. 1594–1604.
ista: 'Chen C, Freedman D. 2010. Hardness results for homology localization. Proceedings
of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium
on Discrete Algorithms, 1594–1604.'
mla: Chen, Chao, and Daniel Freedman. “Hardness Results for Homology Localization.”
Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms,
Society for Industrial and Applied Mathematics, 2010, pp. 1594–604, doi:10.1137/1.9781611973075.129.
short: C. Chen, D. Freedman, in:, Proceedings of the 2010 Annual ACM-SIAM Symposium
on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2010,
pp. 1594–1604.
conference:
end_date: 2010-01-19
location: Austin, TX, United States
name: 'SODA: Symposium on Discrete Algorithms'
start_date: 2010-01-17
date_created: 2022-03-21T08:24:07Z
date_published: 2010-02-01T00:00:00Z
date_updated: 2023-02-23T11:19:46Z
day: '01'
department:
- _id: HeEd
doi: 10.1137/1.9781611973075.129
language:
- iso: eng
month: '02'
oa_version: None
page: 1594-1604
publication: Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms
publication_identifier:
eisbn:
- '9781611973075'
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
related_material:
record:
- id: '3267'
relation: later_version
status: public
scopus_import: '1'
status: public
title: Hardness results for homology localization
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2010'
...
---
_id: '3782'
abstract:
- lang: eng
text: In cortex surface segmentation, the extracted surface is required to have
a particular topology, namely, a two-sphere. We present a new method for removing
topology noise of a curve or surface within the level set framework, and thus
produce a cortical surface with correct topology. We define a new energy term
which quantifies topology noise. We then show how to minimize this term by computing
its functional derivative with respect to the level set function. This method
differs from existing methods in that it is inherently continuous and not digital;
and in the way that our energy directly relates to the topology of the underlying
curve or surface, versus existing knot-based measures which are related in a more
indirect fashion. The proposed flow is validated empirically.
acknowledgement: "Partially supported by the Austri an Science Fund unde r grant P20134-N13.\r\nWe
thank Helena Molina-Abril for very helpful discussion. We thank anonymous reviewers
for helpful comments."
alternative_title:
- LNCS
author:
- first_name: Chao
full_name: Chen, Chao
id: 3E92416E-F248-11E8-B48F-1D18A9856A87
last_name: Chen
- first_name: Daniel
full_name: Freedman, Daniel
last_name: Freedman
citation:
ama: 'Chen C, Freedman D. Topology noise removal for curve and surface evolution.
In: Conference Proceedings MCV 2010. Vol 6533. Springer; 2010:31-42. doi:10.1007/978-3-642-18421-5_4'
apa: 'Chen, C., & Freedman, D. (2010). Topology noise removal for curve and
surface evolution. In Conference proceedings MCV 2010 (Vol. 6533, pp.
31–42). Beijing, China: Springer. https://doi.org/10.1007/978-3-642-18421-5_4'
chicago: Chen, Chao, and Daniel Freedman. “Topology Noise Removal for Curve and
Surface Evolution.” In Conference Proceedings MCV 2010, 6533:31–42. Springer,
2010. https://doi.org/10.1007/978-3-642-18421-5_4.
ieee: C. Chen and D. Freedman, “Topology noise removal for curve and surface evolution,”
in Conference proceedings MCV 2010, Beijing, China, 2010, vol. 6533, pp.
31–42.
ista: 'Chen C, Freedman D. 2010. Topology noise removal for curve and surface evolution. Conference
proceedings MCV 2010. MCV: Medical Computer Vision, LNCS, vol. 6533, 31–42.'
mla: Chen, Chao, and Daniel Freedman. “Topology Noise Removal for Curve and Surface
Evolution.” Conference Proceedings MCV 2010, vol. 6533, Springer, 2010,
pp. 31–42, doi:10.1007/978-3-642-18421-5_4.
short: C. Chen, D. Freedman, in:, Conference Proceedings MCV 2010, Springer, 2010,
pp. 31–42.
conference:
end_date: 2010-09-20
location: Beijing, China
name: 'MCV: Medical Computer Vision'
start_date: 2010-09-20
date_created: 2018-12-11T12:05:08Z
date_published: 2010-12-31T00:00:00Z
date_updated: 2021-01-12T07:52:10Z
day: '31'
department:
- _id: HeEd
doi: 10.1007/978-3-642-18421-5_4
intvolume: ' 6533'
language:
- iso: eng
month: '12'
oa_version: None
page: 31 - 42
publication: ' Conference proceedings MCV 2010'
publication_status: published
publisher: Springer
publist_id: '2445'
quality_controlled: '1'
scopus_import: 1
status: public
title: Topology noise removal for curve and surface evolution
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 6533
year: '2010'
...