Treffer: Entropic Optimal Transport with Data-Driven Metrics on the Roto-Translation Group
Title:
Entropic Optimal Transport with Data-Driven Metrics on the Roto-Translation Group
Authors:
Contributors:
Bubba, Tatiana A., Gaburro, Romina, Gazzola, Silvia, Papafitsoros, Kostas, Pereyra, Marcelo, Schönlieb, Carola-Bibiane
Source:
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. Lecture Notes in Computer Science (LNCS), vol. 15668, Springer, Cham, 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
Publisher Information:
Springer
Publication Year:
2025
Subject Terms:
Document Type:
Fachzeitschrift
article in journal/newspaper
File Description:
application/pdf
Language:
English
Relation:
info:eu-repo/semantics/altIdentifier/isbn/978-3-031-92368-5
DOI:
10.1007/978-3-031-92369-2_27
Availability:
Rights:
info:eu-repo/semantics/openAccess
Accession Number:
edsbas.913B9BFE
Database:
BASE
Weitere Informationen
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).