---
OA_place: repository
OA_type: green
_id: '18242'
abstract:
- lang: eng
  text: Fiber tractography is an important tool of computational neuroscience that
    enables reconstructing the spatial connectivity and organization of white matter
    of the brain. Fiber tractography takes advantage of diffusion Magnetic Resonance
    Imaging (dMRI) which allows measuring the apparent diffusivity of cerebral water
    along different spatial directions. Unfortunately, collecting such data comes
    at the price of reduced spatial resolution and substantially elevated acquisition
    times, which limits the clinical applicability of dMRI. This problem has been
    thus far addressed using two principal strategies. Most of the efforts have been
    extended towards improving the quality of signal estimation for any, yet fixed
    sampling scheme (defined through the choice of diffusion-encoding gradients).
    On the other hand, optimization over the sampling scheme has also proven to be
    effective. Inspired by the previous results, the present work consolidates the
    above strategies into a unified estimation framework, in which the optimization
    is carried out with respect to both estimation model and sampling design concurrently.
    The proposed solution offers substantial improvements in the quality of signal
    estimation as well as the accuracy of ensuing analysis by means of fiber tractography.
    While proving the optimality of the learned estimation models would probably need
    more extensive evaluation, we nevertheless claim that the learned sampling schemes
    can be of immediate use, offering a way to improve the dMRI analysis without the
    necessity of deploying the neural network used for their estimation. We present
    a comprehensive comparative analysis based on the Human Connectome Project data.
    Code and learned sampling designs available at https://github.com/tomer196/Learned_dMRI.
alternative_title:
- Mathematics and Visualization
article_processing_charge: No
arxiv: 1
author:
- first_name: Tomer
  full_name: Weiss, Tomer
  last_name: Weiss
- first_name: Sanketh
  full_name: Vedula, Sanketh
  last_name: Vedula
- first_name: Ortal
  full_name: Senouf, Ortal
  last_name: Senouf
- first_name: Oleg
  full_name: Michailovich, Oleg
  last_name: Michailovich
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
citation:
  ama: 'Weiss T, Vedula S, Senouf O, Michailovich O, Bronstein AM. Towards learned
    optimal q-space sampling in diffusion MRI. In: Gyori N, Hutter J, Nath V, Palombo
    M, Pizzolato M, Zhang F, eds. <i>Computational Diffusion MRI</i>. Cham: Springer
    Nature; 2021:13-28. doi:<a href="https://doi.org/10.1007/978-3-030-73018-5_2">10.1007/978-3-030-73018-5_2</a>'
  apa: 'Weiss, T., Vedula, S., Senouf, O., Michailovich, O., &#38; Bronstein, A. M.
    (2021). Towards learned optimal q-space sampling in diffusion MRI. In N. Gyori,
    J. Hutter, V. Nath, M. Palombo, M. Pizzolato, &#38; F. Zhang (Eds.), <i>Computational
    Diffusion MRI</i> (pp. 13–28). Cham: Springer Nature. <a href="https://doi.org/10.1007/978-3-030-73018-5_2">https://doi.org/10.1007/978-3-030-73018-5_2</a>'
  chicago: 'Weiss, Tomer, Sanketh Vedula, Ortal Senouf, Oleg Michailovich, and Alex
    M. Bronstein. “Towards Learned Optimal Q-Space Sampling in Diffusion MRI.” In
    <i>Computational Diffusion MRI</i>, edited by Noemi Gyori, Jana Hutter, Vishwesh
    Nath, Marco Palombo, Marco Pizzolato, and Fan Zhang, 13–28. Cham: Springer Nature,
    2021. <a href="https://doi.org/10.1007/978-3-030-73018-5_2">https://doi.org/10.1007/978-3-030-73018-5_2</a>.'
  ieee: 'T. Weiss, S. Vedula, O. Senouf, O. Michailovich, and A. M. Bronstein, “Towards
    learned optimal q-space sampling in diffusion MRI,” in <i>Computational Diffusion
    MRI</i>, N. Gyori, J. Hutter, V. Nath, M. Palombo, M. Pizzolato, and F. Zhang,
    Eds. Cham: Springer Nature, 2021, pp. 13–28.'
  ista: 'Weiss T, Vedula S, Senouf O, Michailovich O, Bronstein AM. 2021.Towards learned
    optimal q-space sampling in diffusion MRI. In: Computational Diffusion MRI. Mathematics
    and Visualization, , 13–28.'
  mla: Weiss, Tomer, et al. “Towards Learned Optimal Q-Space Sampling in Diffusion
    MRI.” <i>Computational Diffusion MRI</i>, edited by Noemi Gyori et al., Springer
    Nature, 2021, pp. 13–28, doi:<a href="https://doi.org/10.1007/978-3-030-73018-5_2">10.1007/978-3-030-73018-5_2</a>.
  short: T. Weiss, S. Vedula, O. Senouf, O. Michailovich, A.M. Bronstein, in:, N.
    Gyori, J. Hutter, V. Nath, M. Palombo, M. Pizzolato, F. Zhang (Eds.), Computational
    Diffusion MRI, Springer Nature, Cham, 2021, pp. 13–28.
conference:
  end_date: 2020-10-08
  location: Lima, Peru/Virtual
  name: 'MICCAI: Conference on Medical Image Computing and Computer-Assisted Intervention'
  start_date: 2020-10-08
date_created: 2024-10-08T13:03:26Z
date_published: 2021-09-30T00:00:00Z
date_updated: 2024-10-16T09:51:45Z
day: '30'
doi: 10.1007/978-3-030-73018-5_2
editor:
- first_name: Noemi
  full_name: Gyori, Noemi
  last_name: Gyori
- first_name: Jana
  full_name: Hutter, Jana
  last_name: Hutter
- first_name: Vishwesh
  full_name: Nath, Vishwesh
  last_name: Nath
- first_name: Marco
  full_name: Palombo, Marco
  last_name: Palombo
- first_name: Marco
  full_name: Pizzolato, Marco
  last_name: Pizzolato
- first_name: Fan
  full_name: Zhang, Fan
  last_name: Zhang
extern: '1'
external_id:
  arxiv:
  - '2009.03008'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2009.03008
month: '09'
oa: 1
oa_version: Preprint
page: 13-28
place: Cham
publication: Computational Diffusion MRI
publication_identifier:
  eisbn:
  - '9783030730185'
  isbn:
  - '9783030730178'
  issn:
  - 1612-3786
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
  link:
  - relation: software
    url: https://github.com/tomer196/Learned_dMRI
scopus_import: '1'
status: public
title: Towards learned optimal q-space sampling in diffusion MRI
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
OA_type: closed access
_id: '18328'
abstract:
- lang: eng
  text: We present a novel sparse modeling approach to non-rigid shape matching using
    only the ability to detect repeatable regions. As the input to our algorithm,
    we are given only two sets of regions in two shapes; no descriptors are provided
    so the correspondence between the regions is not know, nor do we know how many
    regions correspond in the two shapes. We show that even with such scarce information,
    it is possible to establish very accurate correspondence between the shapes by
    using methods from the field of sparse modeling, being this, the first non-trivial
    use of sparse models in shape correspondence. We formulate the problem of permuted
    sparse coding, in which we solve simultaneously for an unknown permutation ordering
    the regions on two shapes and for an unknown correspondence in functional representation.
    We also propose a robust variant capable of handling incomplete matches. Numerically,
    the problem is solved efficiently by alternating the solution of a linear assignment
    and a sparse coding problem. The proposed methods are evaluated qualitatively
    and quantitatively on standard benchmarks containing both synthetic and scanned
    objects.
alternative_title:
- Mathematics and Visualization
article_processing_charge: No
author:
- first_name: Jonathan
  full_name: Pokrass, Jonathan
  last_name: Pokrass
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- first_name: Michael M.
  full_name: Bronstein, Michael M.
  last_name: Bronstein
- first_name: Pablo
  full_name: Sprechmann, Pablo
  last_name: Sprechmann
- first_name: Guillermo
  full_name: Sapiro, Guillermo
  last_name: Sapiro
citation:
  ama: 'Pokrass J, Bronstein AM, Bronstein MM, Sprechmann P, Sapiro G. Sparse Models
    for Intrinsic Shape Correspondence. In: Breuß M, Bruckstein A, Maragos P, Wuhrer
    S, eds. <i>Perspectives in Shape Analysis</i>. 1st ed. Cham: Springer International
    Publishing; 2016:211-230. doi:<a href="https://doi.org/10.1007/978-3-319-24726-7_10">10.1007/978-3-319-24726-7_10</a>'
  apa: 'Pokrass, J., Bronstein, A. M., Bronstein, M. M., Sprechmann, P., &#38; Sapiro,
    G. (2016). Sparse Models for Intrinsic Shape Correspondence. In M. Breuß, A. Bruckstein,
    P. Maragos, &#38; S. Wuhrer (Eds.), <i>Perspectives in Shape Analysis</i> (1st
    ed., pp. 211–230). Cham: Springer International Publishing. <a href="https://doi.org/10.1007/978-3-319-24726-7_10">https://doi.org/10.1007/978-3-319-24726-7_10</a>'
  chicago: 'Pokrass, Jonathan, Alex M. Bronstein, Michael M. Bronstein, Pablo Sprechmann,
    and Guillermo Sapiro. “Sparse Models for Intrinsic Shape Correspondence.” In <i>Perspectives
    in Shape Analysis</i>, edited by Michael Breuß, Alfred Bruckstein, Petros Maragos,
    and Stefanie Wuhrer, 1st ed., 211–30. Cham: Springer International Publishing,
    2016. <a href="https://doi.org/10.1007/978-3-319-24726-7_10">https://doi.org/10.1007/978-3-319-24726-7_10</a>.'
  ieee: 'J. Pokrass, A. M. Bronstein, M. M. Bronstein, P. Sprechmann, and G. Sapiro,
    “Sparse Models for Intrinsic Shape Correspondence,” in <i>Perspectives in Shape
    Analysis</i>, 1st ed., M. Breuß, A. Bruckstein, P. Maragos, and S. Wuhrer, Eds.
    Cham: Springer International Publishing, 2016, pp. 211–230.'
  ista: 'Pokrass J, Bronstein AM, Bronstein MM, Sprechmann P, Sapiro G. 2016.Sparse
    Models for Intrinsic Shape Correspondence. In: Perspectives in Shape Analysis.
    Mathematics and Visualization, , 211–230.'
  mla: Pokrass, Jonathan, et al. “Sparse Models for Intrinsic Shape Correspondence.”
    <i>Perspectives in Shape Analysis</i>, edited by Michael Breuß et al., 1st ed.,
    Springer International Publishing, 2016, pp. 211–30, doi:<a href="https://doi.org/10.1007/978-3-319-24726-7_10">10.1007/978-3-319-24726-7_10</a>.
  short: J. Pokrass, A.M. Bronstein, M.M. Bronstein, P. Sprechmann, G. Sapiro, in:,
    M. Breuß, A. Bruckstein, P. Maragos, S. Wuhrer (Eds.), Perspectives in Shape Analysis,
    1st ed., Springer International Publishing, Cham, 2016, pp. 211–230.
date_created: 2024-10-15T11:20:53Z
date_published: 2016-10-01T00:00:00Z
date_updated: 2024-10-22T08:17:06Z
day: '01'
doi: 10.1007/978-3-319-24726-7_10
edition: '1'
editor:
- first_name: Michael
  full_name: Breuß, Michael
  last_name: Breuß
- first_name: Alfred
  full_name: Bruckstein, Alfred
  last_name: Bruckstein
- first_name: Petros
  full_name: Maragos, Petros
  last_name: Maragos
- first_name: Stefanie
  full_name: Wuhrer, Stefanie
  last_name: Wuhrer
extern: '1'
language:
- iso: eng
month: '10'
oa_version: None
page: 211-230
place: Cham
publication: Perspectives in Shape Analysis
publication_identifier:
  eisbn:
  - '9783319247267'
  eissn:
  - 2197-666X
  isbn:
  - '9783319247243'
  issn:
  - 1612-3786
publication_status: published
publisher: Springer International Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sparse Models for Intrinsic Shape Correspondence
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2016'
...
---
_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.
    <i>Topological Methods in Data Analysis and Visualization III.</i> Mathematics
    and Visualization. Cham: Springer Nature; 2014:135-150. doi:<a href="https://doi.org/10.1007/978-3-319-04099-8_9">10.1007/978-3-319-04099-8_9</a>'
  apa: 'Günther, D., Reininghaus, J., Seidel, H.-P., &#38; Weinkauf, T. (2014). Notes
    on the simplification of the Morse-Smale complex. In P.-T. Bremer, I. Hotz, V.
    Pascucci, &#38; R. Peikert (Eds.), <i>Topological Methods in Data Analysis and
    Visualization III.</i> (pp. 135–150). Cham: Springer Nature. <a href="https://doi.org/10.1007/978-3-319-04099-8_9">https://doi.org/10.1007/978-3-319-04099-8_9</a>'
  chicago: 'Günther, David, Jan Reininghaus, Hans-Peter Seidel, and Tino Weinkauf.
    “Notes on the Simplification of the Morse-Smale Complex.” In <i>Topological Methods
    in Data Analysis and Visualization III.</i>, edited by Peer-Timo Bremer, Ingrid
    Hotz, Valerio Pascucci, and Ronald Peikert, 135–50. Mathematics and Visualization.
    Cham: Springer Nature, 2014. <a href="https://doi.org/10.1007/978-3-319-04099-8_9">https://doi.org/10.1007/978-3-319-04099-8_9</a>.'
  ieee: 'D. Günther, J. Reininghaus, H.-P. Seidel, and T. Weinkauf, “Notes on the
    simplification of the Morse-Smale complex,” in <i>Topological Methods in Data
    Analysis and Visualization III.</i>, 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.”
    <i>Topological Methods in Data Analysis and Visualization III.</i>, edited by
    Peer-Timo Bremer et al., Springer Nature, 2014, pp. 135–50, doi:<a href="https://doi.org/10.1007/978-3-319-04099-8_9">10.1007/978-3-319-04099-8_9</a>.
  short: D. Günther, J. Reininghaus, H.-P. Seidel, T. Weinkauf, in:, P.-T. Bremer,
    I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis
    and Visualization III., Springer Nature, Cham, 2014, pp. 135–150.
date_created: 2022-03-04T08:33:57Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2025-04-15T08:37:54Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-319-04099-8_9
ec_funded: 1
editor:
- first_name: Peer-Timo
  full_name: Bremer, Peer-Timo
  last_name: Bremer
- first_name: Ingrid
  full_name: Hotz, Ingrid
  last_name: Hotz
- first_name: Valerio
  full_name: Pascucci, Valerio
  last_name: Pascucci
- first_name: Ronald
  full_name: Peikert, Ronald
  last_name: Peikert
language:
- iso: eng
month: '03'
oa_version: None
page: 135-150
place: Cham
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '318493'
  name: Topological Complex Systems
publication: Topological Methods in Data Analysis and Visualization III.
publication_identifier:
  eisbn:
  - '9783319040998'
  eissn:
  - 2197-666X
  isbn:
  - '9783319040981'
  issn:
  - 1612-3786
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: Mathematics and Visualization
status: public
title: Notes on the simplification of the Morse-Smale complex
type: book_chapter
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2014'
...
---
_id: '10886'
abstract:
- lang: eng
  text: We propose a method for visualizing two-dimensional symmetric positive definite
    tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the
    heat kernel and was originally introduced as an isometry invariant shape signature.
    Each positive definite tensor field defines a Riemannian manifold by considering
    the tensor field as a Riemannian metric. On this Riemmanian manifold we can apply
    the definition of the HKS. The resulting scalar quantity is used for the visualization
    of tensor fields. The HKS is closely related to the Gaussian curvature of the
    Riemannian manifold and the time parameter of the heat kernel allows a multiscale
    analysis in a natural way. In this way, the HKS represents field related scale
    space properties, enabling a level of detail analysis of tensor fields. This makes
    the HKS an interesting new scalar quantity for tensor fields, which differs significantly
    from usual tensor invariants like the trace or the determinant. A method for visualization
    and a numerical realization of the HKS for tensor fields is proposed in this chapter.
    To validate the approach we apply it to some illustrating simple examples as isolated
    critical points and to a medical diffusion tensor data set.
acknowledgement: This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP.
alternative_title:
- Mathematics and Visualization
article_processing_charge: No
author:
- first_name: Valentin
  full_name: Zobel, Valentin
  last_name: Zobel
- first_name: Jan
  full_name: Reininghaus, Jan
  id: 4505473A-F248-11E8-B48F-1D18A9856A87
  last_name: Reininghaus
- first_name: Ingrid
  full_name: Hotz, Ingrid
  last_name: Hotz
citation:
  ama: 'Zobel V, Reininghaus J, Hotz I. Visualization of two-dimensional symmetric
    positive definite tensor fields using the heat kernel signature. In: <i>Topological
    Methods in Data Analysis and Visualization III </i>. Springer; 2014:249-262. doi:<a
    href="https://doi.org/10.1007/978-3-319-04099-8_16">10.1007/978-3-319-04099-8_16</a>'
  apa: Zobel, V., Reininghaus, J., &#38; Hotz, I. (2014). Visualization of two-dimensional
    symmetric positive definite tensor fields using the heat kernel signature. In
    <i>Topological Methods in Data Analysis and Visualization III </i> (pp. 249–262).
    Springer. <a href="https://doi.org/10.1007/978-3-319-04099-8_16">https://doi.org/10.1007/978-3-319-04099-8_16</a>
  chicago: Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualization of Two-Dimensional
    Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” In
    <i>Topological Methods in Data Analysis and Visualization III </i>, 249–62. Springer,
    2014. <a href="https://doi.org/10.1007/978-3-319-04099-8_16">https://doi.org/10.1007/978-3-319-04099-8_16</a>.
  ieee: V. Zobel, J. Reininghaus, and I. Hotz, “Visualization of two-dimensional symmetric
    positive definite tensor fields using the heat kernel signature,” in <i>Topological
    Methods in Data Analysis and Visualization III </i>, 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.” <i>Topological Methods
    in Data Analysis and Visualization III </i>, Springer, 2014, pp. 249–62, doi:<a
    href="https://doi.org/10.1007/978-3-319-04099-8_16">10.1007/978-3-319-04099-8_16</a>.
  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: '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. <i>Topological
    Methods in Data Analysis and Visualization III </i>. Vol 1. Mathematics and Visualization.
    Cham: Springer; 2014:55-69. doi:<a href="https://doi.org/10.1007/978-3-319-04099-8_4">10.1007/978-3-319-04099-8_4</a>'
  apa: 'Kasten, J., Reininghaus, J., Reich, W., &#38; Scheuermann, G. (2014). Toward
    the extraction of saddle periodic orbits. In P.-T. Bremer, I. Hotz, V. Pascucci,
    &#38; R. Peikert (Eds.), <i>Topological Methods in Data Analysis and Visualization
    III </i> (Vol. 1, pp. 55–69). Cham: Springer. <a href="https://doi.org/10.1007/978-3-319-04099-8_4">https://doi.org/10.1007/978-3-319-04099-8_4</a>'
  chicago: 'Kasten, Jens, Jan Reininghaus, Wieland Reich, and Gerik Scheuermann. “Toward
    the Extraction of Saddle Periodic Orbits.” In <i>Topological Methods in Data Analysis
    and Visualization III </i>, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci,
    and Ronald Peikert, 1:55–69. Mathematics and Visualization. Cham: Springer, 2014.
    <a href="https://doi.org/10.1007/978-3-319-04099-8_4">https://doi.org/10.1007/978-3-319-04099-8_4</a>.'
  ieee: 'J. Kasten, J. Reininghaus, W. Reich, and G. Scheuermann, “Toward the extraction
    of saddle periodic orbits,” in <i>Topological Methods in Data Analysis and Visualization
    III </i>, 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.” <i>Topological
    Methods in Data Analysis and Visualization III </i>, edited by Peer-Timo Bremer
    et al., vol. 1, Springer, 2014, pp. 55–69, doi:<a href="https://doi.org/10.1007/978-3-319-04099-8_4">10.1007/978-3-319-04099-8_4</a>.
  short: J. Kasten, J. Reininghaus, W. Reich, G. Scheuermann, in:, P.-T. Bremer, I.
    Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and
    Visualization III , Springer, Cham, 2014, pp. 55–69.
date_created: 2022-03-21T07:11:23Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2025-04-15T08:37:54Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-319-04099-8_4
ec_funded: 1
editor:
- first_name: Peer-Timo
  full_name: Bremer, Peer-Timo
  last_name: Bremer
- first_name: Ingrid
  full_name: Hotz, Ingrid
  last_name: Hotz
- first_name: Valerio
  full_name: Pascucci, Valerio
  last_name: Pascucci
- first_name: Ronald
  full_name: Peikert, Ronald
  last_name: Peikert
intvolume: '         1'
language:
- iso: eng
month: '03'
oa_version: None
page: 55-69
place: Cham
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '318493'
  name: Topological Complex Systems
publication: 'Topological Methods in Data Analysis and Visualization III '
publication_identifier:
  eisbn:
  - '9783319040998'
  eissn:
  - 2197-666X
  isbn:
  - '9783319040981'
  issn:
  - 1612-3786
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
series_title: Mathematics and Visualization
status: public
title: Toward the extraction of saddle periodic orbits
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 1
year: '2014'
...
---
_id: '18351'
abstract:
- lang: eng
  text: Motion-based segmentation is an important tool for the analysis of articulated
    shapes. As such, it plays an important role in mechanical engineering, computer
    graphics, and computer vision. In this chapter, we study motion-based segmentation
    of 3D articulated shapes. We formulate motion-based surface segmentation as a
    piecewise-smooth regularization problem for the transformations between several
    poses. Using Lie-group representation for the transformation at each surface point,
    we obtain a simple regularized fitting problem. An Ambrosio-Tortorelli scheme
    of a generalized Mumford-Shah model gives us the segmentation functional without
    assuming prior knowledge on the number of parts or even the articulated nature
    of the object. Experiments on several standard datasets compare the results of
    the proposed method to state-of-the-art algorithms.
alternative_title:
- Mathematics and Visualization
article_processing_charge: No
author:
- first_name: Guy
  full_name: Rosman, Guy
  last_name: Rosman
- first_name: Michael M.
  full_name: Bronstein, Michael M.
  last_name: Bronstein
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- first_name: Alon
  full_name: Wolf, Alon
  last_name: Wolf
- first_name: Ron
  full_name: Kimmel, Ron
  last_name: Kimmel
citation:
  ama: 'Rosman G, Bronstein MM, Bronstein AM, Wolf A, Kimmel R. Group-Valued Regularization
    for Motion Segmentation of Articulated Shapes. In: Breuß M, Bruckstein A, Maragos
    P, eds. <i>Innovations for Shape Analysis</i>. MATHVISUAL. Berlin, Heidelberg:
    Springer Nature; 2013:263-281. doi:<a href="https://doi.org/10.1007/978-3-642-34141-0_12">10.1007/978-3-642-34141-0_12</a>'
  apa: 'Rosman, G., Bronstein, M. M., Bronstein, A. M., Wolf, A., &#38; Kimmel, R.
    (2013). Group-Valued Regularization for Motion Segmentation of Articulated Shapes.
    In M. Breuß, A. Bruckstein, &#38; P. Maragos (Eds.), <i>Innovations for Shape
    Analysis</i> (pp. 263–281). Berlin, Heidelberg: Springer Nature. <a href="https://doi.org/10.1007/978-3-642-34141-0_12">https://doi.org/10.1007/978-3-642-34141-0_12</a>'
  chicago: 'Rosman, Guy, Michael M. Bronstein, Alex M. Bronstein, Alon Wolf, and Ron
    Kimmel. “Group-Valued Regularization for Motion Segmentation of Articulated Shapes.”
    In <i>Innovations for Shape Analysis</i>, edited by Michael Breuß, Alfred Bruckstein,
    and Petros Maragos, 263–81. MATHVISUAL. Berlin, Heidelberg: Springer Nature, 2013.
    <a href="https://doi.org/10.1007/978-3-642-34141-0_12">https://doi.org/10.1007/978-3-642-34141-0_12</a>.'
  ieee: 'G. Rosman, M. M. Bronstein, A. M. Bronstein, A. Wolf, and R. Kimmel, “Group-Valued
    Regularization for Motion Segmentation of Articulated Shapes,” in <i>Innovations
    for Shape Analysis</i>, M. Breuß, A. Bruckstein, and P. Maragos, Eds. Berlin,
    Heidelberg: Springer Nature, 2013, pp. 263–281.'
  ista: 'Rosman G, Bronstein MM, Bronstein AM, Wolf A, Kimmel R. 2013.Group-Valued
    Regularization for Motion Segmentation of Articulated Shapes. In: Innovations
    for Shape Analysis. Mathematics and Visualization, , 263–281.'
  mla: Rosman, Guy, et al. “Group-Valued Regularization for Motion Segmentation of
    Articulated Shapes.” <i>Innovations for Shape Analysis</i>, edited by Michael
    Breuß et al., Springer Nature, 2013, pp. 263–81, doi:<a href="https://doi.org/10.1007/978-3-642-34141-0_12">10.1007/978-3-642-34141-0_12</a>.
  short: G. Rosman, M.M. Bronstein, A.M. Bronstein, A. Wolf, R. Kimmel, in:, M. Breuß,
    A. Bruckstein, P. Maragos (Eds.), Innovations for Shape Analysis, Springer Nature,
    Berlin, Heidelberg, 2013, pp. 263–281.
date_created: 2024-10-15T11:20:54Z
date_published: 2013-04-04T00:00:00Z
date_updated: 2025-01-16T15:57:36Z
day: '04'
doi: 10.1007/978-3-642-34141-0_12
editor:
- first_name: Michael
  full_name: Breuß, Michael
  last_name: Breuß
- first_name: Alfred
  full_name: Bruckstein, Alfred
  last_name: Bruckstein
- first_name: Petros
  full_name: Maragos, Petros
  last_name: Maragos
extern: '1'
language:
- iso: eng
month: '04'
oa_version: None
page: 263-281
place: Berlin, Heidelberg
publication: Innovations for Shape Analysis
publication_identifier:
  eisbn:
  - '9783642341410'
  isbn:
  - '9783642341403'
  issn:
  - 1612-3786
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: MATHVISUAL
status: public
title: Group-Valued Regularization for Motion Segmentation of Articulated Shapes
type: book_chapter
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2013'
...
---
_id: '18352'
abstract:
- lang: eng
  text: Feature-based analysis is becoming a very popular approach for geometric shape
    analysis. Following the success of this approach in image analysis, there is a
    growing interest in finding analogous methods in the 3D world. Maximally stable
    component detection is a low computation cost and high repeatability method for
    feature detection in images.In this study, a diffusion-geometry based framework
    for stable component detection is presented, which can be used for geometric feature
    detection in deformable shapes.The vast majority of studies of deformable 3D shapes
    models them as the two-dimensional boundary of the volume of the shape. Recent
    works have shown that a volumetric shape model is advantageous in numerous ways
    as it better captures the natural behavior of non-rigid deformations. We show
    that our framework easily adapts to this volumetric approach, and even demonstrates
    superior performance.A quantitative evaluation of our methods on the SHREC’10
    and SHREC’11 feature detection benchmarks as well as qualitative tests on the
    SCAPE dataset show its potential as a source of high-quality features. Examples
    demonstrating the drawbacks of surface stable components and the advantage of
    their volumetric counterparts are also presented.
alternative_title:
- Mathematics and Visualization
article_processing_charge: No
author:
- first_name: Roee
  full_name: Litman, Roee
  last_name: Litman
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- first_name: Michael M.
  full_name: Bronstein, Michael M.
  last_name: Bronstein
citation:
  ama: 'Litman R, Bronstein AM, Bronstein MM. Stable Semi-local Features for Non-rigid
    Shapes. In: Breuß M, Bruckstein A, Maragos P, eds. <i>Innovations for Shape Analysis</i>.
    MATHVISUAL. Berlin, Heidelberg: Springer Nature; 2013:161-189. doi:<a href="https://doi.org/10.1007/978-3-642-34141-0_8">10.1007/978-3-642-34141-0_8</a>'
  apa: 'Litman, R., Bronstein, A. M., &#38; Bronstein, M. M. (2013). Stable Semi-local
    Features for Non-rigid Shapes. In M. Breuß, A. Bruckstein, &#38; P. Maragos (Eds.),
    <i>Innovations for Shape Analysis</i> (pp. 161–189). Berlin, Heidelberg: Springer
    Nature. <a href="https://doi.org/10.1007/978-3-642-34141-0_8">https://doi.org/10.1007/978-3-642-34141-0_8</a>'
  chicago: 'Litman, Roee, Alex M. Bronstein, and Michael M. Bronstein. “Stable Semi-Local
    Features for Non-Rigid Shapes.” In <i>Innovations for Shape Analysis</i>, edited
    by Michael Breuß, Alfred Bruckstein, and Petros Maragos, 161–89. MATHVISUAL. Berlin,
    Heidelberg: Springer Nature, 2013. <a href="https://doi.org/10.1007/978-3-642-34141-0_8">https://doi.org/10.1007/978-3-642-34141-0_8</a>.'
  ieee: 'R. Litman, A. M. Bronstein, and M. M. Bronstein, “Stable Semi-local Features
    for Non-rigid Shapes,” in <i>Innovations for Shape Analysis</i>, M. Breuß, A.
    Bruckstein, and P. Maragos, Eds. Berlin, Heidelberg: Springer Nature, 2013, pp.
    161–189.'
  ista: 'Litman R, Bronstein AM, Bronstein MM. 2013.Stable Semi-local Features for
    Non-rigid Shapes. In: Innovations for Shape Analysis. Mathematics and Visualization,
    , 161–189.'
  mla: Litman, Roee, et al. “Stable Semi-Local Features for Non-Rigid Shapes.” <i>Innovations
    for Shape Analysis</i>, edited by Michael Breuß et al., Springer Nature, 2013,
    pp. 161–89, doi:<a href="https://doi.org/10.1007/978-3-642-34141-0_8">10.1007/978-3-642-34141-0_8</a>.
  short: R. Litman, A.M. Bronstein, M.M. Bronstein, in:, M. Breuß, A. Bruckstein,
    P. Maragos (Eds.), Innovations for Shape Analysis, Springer Nature, Berlin, Heidelberg,
    2013, pp. 161–189.
date_created: 2024-10-15T11:20:54Z
date_published: 2013-04-04T00:00:00Z
date_updated: 2025-01-16T15:50:22Z
day: '04'
doi: 10.1007/978-3-642-34141-0_8
editor:
- first_name: Michael
  full_name: Breuß, Michael
  last_name: Breuß
- first_name: Alfred
  full_name: Bruckstein, Alfred
  last_name: Bruckstein
- first_name: Petros
  full_name: Maragos, Petros
  last_name: Maragos
extern: '1'
language:
- iso: eng
month: '04'
oa_version: None
page: 161 - 189
place: Berlin, Heidelberg
publication: Innovations for Shape Analysis
publication_identifier:
  eisbn:
  - '9783642341410'
  isbn:
  - '9783642341403'
  issn:
  - 1612-3786
publication_status: published
publisher: Springer Nature
series_title: MATHVISUAL
status: public
title: Stable Semi-local Features for Non-rigid Shapes
type: book_chapter
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2013'
...