Regression and Fitting on Manifold-valued Data

Ines ADOUANI received her PhD in complex analysis and Finsler geometry from the University of Pierre and Marie Curie, France, in 2015. Since then, she has been serving as an Assistant Professor at the Institute of Applied Sciences and Technology of Sousse, Tunisia. Additionally, from 2020 to 2021, she held a position as an Assistant Professor at King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. Her main research interests encompass complex geometry (including Finsler and Kähler geometry), optimization on Riemannian manifolds, regression, and fitting on Riemannian manifolds, as well as their applications to computer vision and medical imaging problems.Chafik SAMIR received his PhD on learning and analysis of shapes and patterns in 2007 at the University of Lille, France. After spending two years as a postdoc working on manifolds and related applications at UCL, he joined UCA in 2009. His main research interests are machine learning for manifold-valued data, such as functional and medical observations, optimization of loss functions, statistical shape analysis, spatio-temporal patterns and fusion, regression and fitting on Riemannian manifolds, and their applications to real-world problems.

• Introduction.- Spline Interpolation and Fitting in R𝒏.- Spline Interpolation on the Sphere S𝒏.- Spline Interpolation on the Special Orthogonal Group 𝑺𝑶(𝒏).- Spline Interpolation on Stiefel and Grassmann manifolds.- Spline Interpolation on the Manifold of Probability Measures.- Spline Interpolation on the Manifold of Probability Density Functions.- Spline Interpolation on Shape Space.- Spline Interpolation on Other Riemannian Manifolds.