---
_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'
...