Adouani, Ines. creator author. aut http://id.loc.gov/vocabulary/relators/aut Samir, Chafik. author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text sz 2024 1st ed. 2024. monographic eng

electronic

electronic resource

access VII, 181 p. 47 illus., 45 illus. in color. online resource. This book introduces in a constructive manner a general framework for regression and fitting methods for many applications and tasks involving data on manifolds. The methodology has important and varied applications in machine learning, medicine, robotics, biology, computer vision, human biometrics, nanomanufacturing, signal processing, and image analysis, etc. The first chapter gives motivation examples, a wide range of applications, raised challenges, raised challenges, and some concerns. The second chapter gives a comprehensive exploration and step-by-step illustrations for Euclidean cases. Another dedicated chapter covers the geometric tools needed for each manifold and provides expressions and key notions for any application for manifold-valued data. All loss functions and optimization methods are given as algorithms and can be easily implemented. In particular, many popular manifolds are considered with derived and specific formulations. The same philosophy is used in all chapters and all novelties are illustrated with intuitive examples. Additionally, each chapter includes simulations and experiments on real-world problems for understanding and potential extensions for a wide range of applications. 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. by Ines Adouani, Chafik Samir. Mathematics Data processing Image processing Digital techniques Computer vision Engineering mathematics Computational Mathematics and Numerical Analysis Computer Imaging, Vision, Pattern Recognition and Graphics Engineering Mathematics QA71-90 9783031617126 https://doi.org/10.1007/978-3-031-61712-6 https://doi.org/10.1007/978-3-031-61712-6 240724 20251030112647.0 978-3-031-61712-6