---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21954'
abstract:
- lang: eng
  text: We investigate a framework for train-free MRI segmentation based on Topological
    Data Analysis. The pipeline proceeds in three steps, first identifying the whole
    object to segment via automatic thresholding, then detecting a distinctive subset
    whose topology is known in advance, and finally deducing the various components
    of the segmentation. A key ingredient is the extraction of approximate representative
    cycles from persistence diagrams, which provides an interpretable link between
    persistent features and anatomical components. To clarify the method’s scope,
    we make the underlying topological and intensity assumptions explicit, quantify
    when they hold on real data, and analyze typical failure modes. We evaluate the
    approach on glioblastoma and on fetal cortical plate segmentation, with comparisons
    to unsupervised and deep-learning references. By operating without large annotated
    datasets, the method is well suited to scarce-data settings and provides an interpretable
    baseline and practical initialization for expert refinement or learning-based
    pipelines.
acknowledgement: Open access funding provided by Institute of Science and Technology
  (IST Austria).
article_number: '20'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Anton
  full_name: François, Anton
  last_name: François
- first_name: Raphaël
  full_name: Tinarrage, Raphaël
  id: 40ebcc9d-905f-11ef-bf0a-dc475da8a04e
  last_name: Tinarrage
  orcid: 0000-0002-1404-1095
citation:
  ama: François A, Tinarrage R. Train-free segmentation in MRI with cubical persistent
    homology. <i>Journal of Mathematical Imaging and Vision</i>. 2026;68(3). doi:<a
    href="https://doi.org/10.1007/s10851-026-01300-1">10.1007/s10851-026-01300-1</a>
  apa: François, A., &#38; Tinarrage, R. (2026). Train-free segmentation in MRI with
    cubical persistent homology. <i>Journal of Mathematical Imaging and Vision</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s10851-026-01300-1">https://doi.org/10.1007/s10851-026-01300-1</a>
  chicago: François, Anton, and Raphaël Tinarrage. “Train-Free Segmentation in MRI
    with Cubical Persistent Homology.” <i>Journal of Mathematical Imaging and Vision</i>.
    Springer Nature, 2026. <a href="https://doi.org/10.1007/s10851-026-01300-1">https://doi.org/10.1007/s10851-026-01300-1</a>.
  ieee: A. François and R. Tinarrage, “Train-free segmentation in MRI with cubical
    persistent homology,” <i>Journal of Mathematical Imaging and Vision</i>, vol.
    68, no. 3. Springer Nature, 2026.
  ista: François A, Tinarrage R. 2026. Train-free segmentation in MRI with cubical
    persistent homology. Journal of Mathematical Imaging and Vision. 68(3), 20.
  mla: François, Anton, and Raphaël Tinarrage. “Train-Free Segmentation in MRI with
    Cubical Persistent Homology.” <i>Journal of Mathematical Imaging and Vision</i>,
    vol. 68, no. 3, 20, Springer Nature, 2026, doi:<a href="https://doi.org/10.1007/s10851-026-01300-1">10.1007/s10851-026-01300-1</a>.
  short: A. François, R. Tinarrage, Journal of Mathematical Imaging and Vision 68
    (2026).
corr_author: '1'
date_created: 2026-06-08T08:34:43Z
date_published: 2026-05-25T00:00:00Z
date_updated: 2026-06-10T08:00:52Z
day: '25'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1007/s10851-026-01300-1
external_id:
  arxiv:
  - '2401.01160'
file:
- access_level: open_access
  checksum: 34080653e0f9c6160856a6bbca9b5248
  content_type: application/pdf
  creator: dernst
  date_created: 2026-06-10T07:58:58Z
  date_updated: 2026-06-10T07:58:58Z
  file_id: '21990'
  file_name: 2026_JourMathImaging_Francois.pdf
  file_size: 6070434
  relation: main_file
  success: 1
file_date_updated: 2026-06-10T07:58:58Z
has_accepted_license: '1'
intvolume: '        68'
issue: '3'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
publication: Journal of Mathematical Imaging and Vision
publication_identifier:
  eissn:
  - 1573-7683
  issn:
  - 0924-9907
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Train-free segmentation in MRI with cubical persistent homology
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 68
year: '2026'
...
---
_id: '18353'
abstract:
- lang: eng
  text: Traditional models of bendable surfaces are based on the exact or approximate
    invariance to deformations that do not tear or stretch the shape, leaving intact
    an intrinsic geometry associated with it. These geometries are typically defined
    using either the shortest path length (geodesic distance), or properties of heat
    diffusion (diffusion distance) on the surface. Both measures are implicitly derived
    from the metric induced by the ambient Euclidean space. In this paper, we depart
    from this restrictive assumption by observing that a different choice of the metric
    results in a richer set of geometric invariants. We apply equi-affine geometry
    for analyzing arbitrary shapes with positive Gaussian curvature. The potential
    of the proposed framework is explored in a range of applications such as shape
    matching and retrieval, symmetry detection, and computation of Voroni tessellation.
    We show that in some shape analysis tasks, equi-affine-invariant intrinsic geometries
    often outperform their Euclidean-based counterparts. We further explore the potential
    of this metric in facial anthropometry of newborns. We show that intrinsic properties
    of this homogeneous group are better captured using the equi-affine metric.
article_processing_charge: No
article_type: original
author:
- first_name: Dan
  full_name: Raviv, Dan
  last_name: Raviv
- 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: Dan
  full_name: Waisman, Dan
  last_name: Waisman
- first_name: Nir
  full_name: Sochen, Nir
  last_name: Sochen
- first_name: Ron
  full_name: Kimmel, Ron
  last_name: Kimmel
citation:
  ama: Raviv D, Bronstein AM, Bronstein MM, Waisman D, Sochen N, Kimmel R. Equi-affine
    invariant geometry for shape analysis. <i>Journal of Mathematical Imaging and
    Vision</i>. 2014;50:144-163. doi:<a href="https://doi.org/10.1007/s10851-013-0467-y">10.1007/s10851-013-0467-y</a>
  apa: Raviv, D., Bronstein, A. M., Bronstein, M. M., Waisman, D., Sochen, N., &#38;
    Kimmel, R. (2014). Equi-affine invariant geometry for shape analysis. <i>Journal
    of Mathematical Imaging and Vision</i>. Springer Nature. <a href="https://doi.org/10.1007/s10851-013-0467-y">https://doi.org/10.1007/s10851-013-0467-y</a>
  chicago: Raviv, Dan, Alex M. Bronstein, Michael M. Bronstein, Dan Waisman, Nir Sochen,
    and Ron Kimmel. “Equi-Affine Invariant Geometry for Shape Analysis.” <i>Journal
    of Mathematical Imaging and Vision</i>. Springer Nature, 2014. <a href="https://doi.org/10.1007/s10851-013-0467-y">https://doi.org/10.1007/s10851-013-0467-y</a>.
  ieee: D. Raviv, A. M. Bronstein, M. M. Bronstein, D. Waisman, N. Sochen, and R.
    Kimmel, “Equi-affine invariant geometry for shape analysis,” <i>Journal of Mathematical
    Imaging and Vision</i>, vol. 50. Springer Nature, pp. 144–163, 2014.
  ista: Raviv D, Bronstein AM, Bronstein MM, Waisman D, Sochen N, Kimmel R. 2014.
    Equi-affine invariant geometry for shape analysis. Journal of Mathematical Imaging
    and Vision. 50, 144–163.
  mla: Raviv, Dan, et al. “Equi-Affine Invariant Geometry for Shape Analysis.” <i>Journal
    of Mathematical Imaging and Vision</i>, vol. 50, Springer Nature, 2014, pp. 144–63,
    doi:<a href="https://doi.org/10.1007/s10851-013-0467-y">10.1007/s10851-013-0467-y</a>.
  short: D. Raviv, A.M. Bronstein, M.M. Bronstein, D. Waisman, N. Sochen, R. Kimmel,
    Journal of Mathematical Imaging and Vision 50 (2014) 144–163.
date_created: 2024-10-15T11:20:54Z
date_published: 2014-09-01T00:00:00Z
date_updated: 2024-11-12T08:51:43Z
day: '01'
doi: 10.1007/s10851-013-0467-y
extern: '1'
intvolume: '        50'
language:
- iso: eng
month: '09'
oa_version: None
page: 144-163
publication: Journal of Mathematical Imaging and Vision
publication_identifier:
  eissn:
  - 1573-7683
  issn:
  - 0924-9907
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Equi-affine invariant geometry for shape analysis
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 50
year: '2014'
...