Entropic Optimal Transport with Data-Driven Metrics on the Roto-Translation Group

Gautam Pai; Gijs Bellaard; Rick Sengers; Luc Florack; Remco Duits

doi:10.1007/978-3-031-92369-2_27

Entropic Optimal Transport with Data-Driven Metrics on the Roto-Translation Group

Gautam Pai^*
, Gijs Bellaard
, Rick Sengers
, Luc Florack
, Remco Duits

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

We enumerate a framework for optimal transportation on Lie Groups using costs that depend on geodesic distances derived from spatially varying data-driven metrics. We build on the entropic regularized formulation which can be efficiently solved using Sinkhorn iterations. We estimate local distances on the Lie group using logarithmic distance approximations and formulate their extension to a more general setting of data-driven metric tensors. Our formulation leads to a data-driven approximation of the Gibbs kernel which is essential to the Sinkhorn framework. We demonstrate our method with two experiments: Tractography with Diffusion-Weighted MRI and crossing-preserving interpolations of measures in SE(2).

Original language	English
Title of host publication	Scale Space and Variational Methods in Computer Vision
Subtitle of host publication	10th International Conference, SSVM 2025, Dartington, UK, May 18–22, 2025, Proceedings, Part II
Editors	Tatiana A. Bubba, Romina Gaburro, Silvia Gazzola, Kostas Papafitsoros, Marcelo Pereyra, Carola-Bibiane Schönlieb
Publisher	Springer
Pages	350-363
Number of pages	14
ISBN (Electronic)	978-3-031-92369-2
ISBN (Print)	978-3-031-92368-5
DOIs	https://doi.org/10.1007/978-3-031-92369-2_27
Publication status	Published - 17 May 2025
Event	10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025 - Dartington, United Kingdom Duration: 18 May 2025 → 22 May 2025 Conference number: 10

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	15668
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025
Abbreviated title	SSVM 2025
Country/Territory	United Kingdom
City	Dartington
Period	18/05/25 → 22/05/25

Keywords

2025 OA procedure
Metric geometry
Optimal transport
Wasserstein Barycenters
Lie groups

Access to Document

10.1007/978-3-031-92369-2_27

ArticleFinal published version, 2.25 MBLicence: Taverne

Cite this

Pai, G., Bellaard, G., Sengers, R., Florack, L., & Duits, R. (2025). Entropic Optimal Transport with Data-Driven Metrics on the Roto-Translation Group. In T. A. Bubba, R. Gaburro, S. Gazzola, K. Papafitsoros, M. Pereyra, & C.-B. Schönlieb (Eds.), Scale Space and Variational Methods in Computer Vision: 10th International Conference, SSVM 2025, Dartington, UK, May 18–22, 2025, Proceedings, Part II (pp. 350-363). (Lecture Notes in Computer Science; Vol. 15668). Springer. https://doi.org/10.1007/978-3-031-92369-2_27

Pai, Gautam ; Bellaard, Gijs ; Sengers, Rick et al. / Entropic Optimal Transport with Data-Driven Metrics on the Roto-Translation Group. Scale Space and Variational Methods in Computer Vision: 10th International Conference, SSVM 2025, Dartington, UK, May 18–22, 2025, Proceedings, Part II. editor / Tatiana A. Bubba ; Romina Gaburro ; Silvia Gazzola ; Kostas Papafitsoros ; Marcelo Pereyra ; Carola-Bibiane Schönlieb. Springer, 2025. pp. 350-363 (Lecture Notes in Computer Science).

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title = "Entropic Optimal Transport with Data-Driven Metrics on the Roto-Translation Group",

abstract = "We enumerate a framework for optimal transportation on Lie Groups using costs that depend on geodesic distances derived from spatially varying data-driven metrics. We build on the entropic regularized formulation which can be efficiently solved using Sinkhorn iterations. We estimate local distances on the Lie group using logarithmic distance approximations and formulate their extension to a more general setting of data-driven metric tensors. Our formulation leads to a data-driven approximation of the Gibbs kernel which is essential to the Sinkhorn framework. We demonstrate our method with two experiments: Tractography with Diffusion-Weighted MRI and crossing-preserving interpolations of measures in SE(2).",

keywords = "2025 OA procedure, Metric geometry, Optimal transport, Wasserstein Barycenters, Lie groups",

author = "Gautam Pai and Gijs Bellaard and Rick Sengers and Luc Florack and Remco Duits",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.; 10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025, SSVM 2025 ; Conference date: 18-05-2025 Through 22-05-2025",

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doi = "10.1007/978-3-031-92369-2\_27",

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Pai, G, Bellaard, G, Sengers, R, Florack, L & Duits, R 2025, Entropic Optimal Transport with Data-Driven Metrics on the Roto-Translation Group. in TA Bubba, R Gaburro, S Gazzola, K Papafitsoros, M Pereyra & C-B Schönlieb (eds), Scale Space and Variational Methods in Computer Vision: 10th International Conference, SSVM 2025, Dartington, UK, May 18–22, 2025, Proceedings, Part II. Lecture Notes in Computer Science, vol. 15668, Springer, pp. 350-363, 10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025, Dartington, United Kingdom, 18/05/25. https://doi.org/10.1007/978-3-031-92369-2_27

Entropic Optimal Transport with Data-Driven Metrics on the Roto-Translation Group. / Pai, Gautam; Bellaard, Gijs; Sengers, Rick et al.
Scale Space and Variational Methods in Computer Vision: 10th International Conference, SSVM 2025, Dartington, UK, May 18–22, 2025, Proceedings, Part II. ed. / Tatiana A. Bubba; Romina Gaburro; Silvia Gazzola; Kostas Papafitsoros; Marcelo Pereyra; Carola-Bibiane Schönlieb. Springer, 2025. p. 350-363 (Lecture Notes in Computer Science; Vol. 15668).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Entropic Optimal Transport with Data-Driven Metrics on the Roto-Translation Group

AU - Pai, Gautam

AU - Bellaard, Gijs

AU - Sengers, Rick

AU - Florack, Luc

AU - Duits, Remco

N1 - Conference code: 10

PY - 2025/5/17

Y1 - 2025/5/17

N2 - We enumerate a framework for optimal transportation on Lie Groups using costs that depend on geodesic distances derived from spatially varying data-driven metrics. We build on the entropic regularized formulation which can be efficiently solved using Sinkhorn iterations. We estimate local distances on the Lie group using logarithmic distance approximations and formulate their extension to a more general setting of data-driven metric tensors. Our formulation leads to a data-driven approximation of the Gibbs kernel which is essential to the Sinkhorn framework. We demonstrate our method with two experiments: Tractography with Diffusion-Weighted MRI and crossing-preserving interpolations of measures in SE(2).

AB - We enumerate a framework for optimal transportation on Lie Groups using costs that depend on geodesic distances derived from spatially varying data-driven metrics. We build on the entropic regularized formulation which can be efficiently solved using Sinkhorn iterations. We estimate local distances on the Lie group using logarithmic distance approximations and formulate their extension to a more general setting of data-driven metric tensors. Our formulation leads to a data-driven approximation of the Gibbs kernel which is essential to the Sinkhorn framework. We demonstrate our method with two experiments: Tractography with Diffusion-Weighted MRI and crossing-preserving interpolations of measures in SE(2).

KW - 2025 OA procedure

KW - Metric geometry

KW - Optimal transport

KW - Wasserstein Barycenters

KW - Lie groups

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M3 - Conference contribution

SN - 978-3-031-92368-5

T3 - Lecture Notes in Computer Science

SP - 350

EP - 363

BT - Scale Space and Variational Methods in Computer Vision

A2 - Bubba, Tatiana A.

A2 - Gaburro, Romina

A2 - Gazzola, Silvia

A2 - Papafitsoros, Kostas

A2 - Pereyra, Marcelo

A2 - Schönlieb, Carola-Bibiane

PB - Springer

T2 - 10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025

Y2 - 18 May 2025 through 22 May 2025

ER -

Pai G, Bellaard G, Sengers R, Florack L, Duits R. Entropic Optimal Transport with Data-Driven Metrics on the Roto-Translation Group. In Bubba TA, Gaburro R, Gazzola S, Papafitsoros K, Pereyra M, Schönlieb CB, editors, Scale Space and Variational Methods in Computer Vision: 10th International Conference, SSVM 2025, Dartington, UK, May 18–22, 2025, Proceedings, Part II. Springer. 2025. p. 350-363. (Lecture Notes in Computer Science). doi: 10.1007/978-3-031-92369-2_27

Entropic Optimal Transport with Data-Driven Metrics on the Roto-Translation Group

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