03386nam a22004575i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001200153072001700165072002300182072001600205100007600221245010800297250001800405264006900423300006500492336002600557337002600583338003600609347002400645505046700669520122901136650003402365650004202399650002102441650002902462650005402491650006402545650002902609700007602638710003402714773002602748776003602774776003602810776003602846856004602882978-3-031-61712-6DE-He21320251030112647.0cr nn 008mamaa240724s2024    sz |    s    |||| 0|eng d  a97830316171267 a10.1007/978-3-031-61712-62doi 4aQA71-90 7aPBKS2bicssc 7aMAT0410002bisacsh 7aPBKS2thema1 aAdouani, Ines.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aRegression and Fitting on Manifold-valued Datah[electronic resource] /cby Ines Adouani, Chafik Samir.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aVII, 181 p. 47 illus., 45 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 aIntroduction -- 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.  aThis 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. 0aMathematicsxData processing. 0aImage processingxDigital techniques. 0aComputer vision. 0aEngineering mathematics.14aComputational Mathematics and Numerical Analysis.24aComputer Imaging, Vision, Pattern Recognition and Graphics.24aEngineering Mathematics.1 aSamir, Chafik.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303161711908iPrinted edition:z978303161713308iPrinted edition:z978303161714040uhttps://doi.org/10.1007/978-3-031-61712-6