Regression and Fitting on Manifold-valued Data / by Ines Adouani, Chafik Samir.

Format:

Book

Author/Creator:

Adouani, Ines.

Contributor:

Samir, Chafik.

Series:

Mathematics and Statistics Series

Language:

English

Subjects (All):

Mathematics--Data processing.

Mathematics.

Image processing--Digital techniques.

Image processing.

Computer vision.

Engineering mathematics.

Computational Mathematics and Numerical Analysis.

Computer Imaging, Vision, Pattern Recognition and Graphics.

Engineering Mathematics.

Local Subjects:

Computational Mathematics and Numerical Analysis.

Computer Imaging, Vision, Pattern Recognition and Graphics.

Engineering Mathematics.

Physical Description:

1 online resource (0 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2024.

Summary:

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.

Contents:

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.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9783031617126

OCLC:

1450100471