| Issue |
ESAIM: M2AN
Volume 59, Number 1, January-February 2025
|
|
|---|---|---|
| Page(s) | 73 - 99 | |
| DOI | https://doi.org/10.1051/m2an/2024056 | |
| Published online | 08 January 2025 | |
Computing regularized splines in the Riemannian manifold of probability measures
1
International School, Vietnam National University, Hanoi, Vietnam
2
Institut Supérieur des Sciences Appliquées et de Technologie de Sousse, Sousse, Tunisia
3
University of Clermont Auvergne, LIMOS, Clermont-Ferrand, France
* Corresponding author: chafik.samir@uca.fr
Received:
20
April
2023
Accepted:
4
July
2024
In this paper, we give new numerical methods to solve C2 splines for interpolating a finite set of probability measures. Due to the difficulties of generalizing interpolations and solving them with explicit expressions on manifolds, we first introduce a theoretical analysis with different structures on the Riemannian manifold of probability measures P+(I). Then, by combining standard numerical methods and a new mathematical modeling we generalize interpolating splines as a minimizer of an energy functional on P+(I). Finally, we show the efficiency of the proposed methods and their computational relevance with several applications including real medical data.
Mathematics Subject Classification: 49Q20 / 53C05 / 49K20 / 49M05 / 47N40 / 65K10
Key words: Regularized minimization / smooth splines / interpolations / probability measures / Riemannian manifold
© The authors. Published by EDP Sciences, SMAI 2025
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