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Advances in Computer Vision and Pattern Recognition

Algorithmic Advances in Riemannian Geometry and Applications

For Machine Learning, Computer Vision, Statistics, and Optimization

Editors: Minh, Hà Quang, Murino, Vittorio (Eds.)

  • Showcases Riemannian geometry as a foundational mathematical framework for solving many problems in machine learning, statistics, optimization, computer vision, and related fields
  • Describes comprehensively the state-of-the-art theory and algorithms in the Riemannian framework along with their concrete practical applications
  • Written by leading experts in statistics, machine learning, optimization, pattern recognition, and computer vision
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eBook $89.00
price for USA (gross)
  • ISBN 978-3-319-45026-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA
  • ISBN 978-3-319-45025-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book presents a selection of the most recent algorithmic advances in Riemannian geometry in the context of machine learning, statistics, optimization, computer vision, and related fields. The unifying theme of the different chapters in the book is the exploitation of the geometry of data using the mathematical machinery of Riemannian geometry. As demonstrated by all the chapters in the book, when the data is intrinsically non-Euclidean, the utilization of this geometrical information can lead to better algorithms that can capture more accurately the structures inherent in the data, leading ultimately to better empirical performance. This book is not intended to be an encyclopedic compilation of the applications of Riemannian geometry. Instead, it focuses on several important research directions that are currently actively pursued by researchers in the field. These include statistical modeling and analysis on manifolds,optimization on manifolds, Riemannian manifolds and kernel methods, and dictionary learning and sparse coding on manifolds. Examples of applications include novel algorithms for Monte Carlo sampling and Gaussian Mixture Model fitting,  3D brain image analysis,image classification, action recognition, and motion tracking.

About the authors

Dr. Hà Quang Minh is a researcher in the Pattern Analysis and Computer Vision (PAVIS) group, at the Italian Institute of Technology (IIT), in Genoa, Italy.

Dr. Vittorio Murino is a full professor at the University of Verona Department of Computer Science, and the Director of the PAVIS group at the IIT.

Reviews

“The book under review consists of eight chapters, each introducing techniques for solving problems on manifolds and illustrating these with examples. … reading this book would add to my collection of tools for working with data on manifolds and expose me to new problems treatable by these tools. … In each case an effort has been made to provide enough of the underlying theory supporting the techniques, with explicit references where the interested reader can go for further details.” (Tim Zajic, IAPR Newsletter, Vol. 39 (3), July, 2017)


Table of contents (8 chapters)

  • Bayesian Statistical Shape Analysis on the Manifold of Diffeomorphisms

    Zhang, Miaomiao (et al.)

    Pages 1-23

  • Sampling Constrained Probability Distributions Using Spherical Augmentation

    Lan, Shiwei (et al.)

    Pages 25-71

  • Geometric Optimization in Machine Learning

    Sra, Suvrit (et al.)

    Pages 73-91

  • Positive Definite Matrices: Data Representation and Applications to Computer Vision

    Cherian, Anoop (et al.)

    Pages 93-114

  • From Covariance Matrices to Covariance Operators: Data Representation from Finite to Infinite-Dimensional Settings

    Minh, Hà Quang (et al.)

    Pages 115-143

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-3-319-45026-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA
  • ISBN 978-3-319-45025-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Algorithmic Advances in Riemannian Geometry and Applications
Book Subtitle
For Machine Learning, Computer Vision, Statistics, and Optimization
Editors
  • Hà Quang Minh
  • Vittorio Murino
Series Title
Advances in Computer Vision and Pattern Recognition
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-45026-1
DOI
10.1007/978-3-319-45026-1
Hardcover ISBN
978-3-319-45025-4
Series ISSN
2191-6586
Edition Number
1
Number of Pages
XIV, 208
Number of Illustrations and Tables
4 b/w illustrations, 51 illustrations in colour
Topics