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978-3-031-61712-6
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9783031617126
978-3-031-61712-6
10.1007/978-3-031-61712-6
doi
QA71-90
PBKS
bicssc
MAT041000
bisacsh
PBKS
thema
Adouani, Ines.
author.
aut
http://id.loc.gov/vocabulary/relators/aut
81194
Regression and Fitting on Manifold-valued Data
[electronic resource] /
by Ines Adouani, Chafik Samir.
1st ed. 2024.
Cham :
Springer Nature Switzerland :
Imprint: Springer,
2024.
VII, 181 p. 47 illus., 45 illus. in color.
online resource.
text
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rdacontent
computer
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rdamedia
online resource
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rda
Introduction -- Spline Interpolation and Fitting in Rπ -- Spline Interpolation on the Sphere Sπ -- Spline Interpolation on the Special Orthogonal Group πΊπΆ(π) -- 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.
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.
Mathematics
Data processing.
65715
Image processing
Digital techniques.
64228
Computer vision.
Engineering mathematics.
64145
Computational Mathematics and Numerical Analysis.
66073
Computer Imaging, Vision, Pattern Recognition and Graphics.
65550
Engineering Mathematics.
64145
Samir, Chafik.
author.
aut
http://id.loc.gov/vocabulary/relators/aut
81195
SpringerLink (Online service)
Springer Nature eBook
Printed edition:
9783031617119
Printed edition:
9783031617133
Printed edition:
9783031617140
https://doi.org/10.1007/978-3-031-61712-6
ZDB-2-SMA
ZDB-2-SXMS
61873
61873