Nonparametric Inference on Manifolds
With Applications to Shape Spaces
- English
- PDF
- Available on iOS & Android
Nonparametric Inference on Manifolds
With Applications to Shape Spaces
About this book
This book introduces in a systematic manner a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. The theory has important and varied applications in medical diagnostics, image analysis, and machine vision. An early chapter of examples establishes the effectiveness of the new methods and demonstrates how they outperform their parametric counterparts. Inference is developed for both intrinsic and extrinsic Fréchet means of probability distributions on manifolds, then applied to shape spaces defined as orbits of landmarks under a Lie group of transformations - in particular, similarity, reflection similarity, affine and projective transformations. In addition, nonparametric Bayesian theory is adapted and extended to manifolds for the purposes of density estimation, regression and classification. Ideal for statisticians who analyze manifold data and wish to develop their own methodology, this book is also of interest to probabilists, mathematicians, computer scientists, and morphometricians with mathematical training.
Frequently asked questions
- Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
- Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Information
Table of contents
- Cover
- Nonparametric Inference on Manifolds
- Title
- Copyright
- Contents
- Commonly used notation
- Preface
- 1: Introduction
- 2: Examples
- 3: Location and spread on metric spaces
- 4: Extrinsic analysis on manifolds
- 5: Intrinsic analysis on manifolds
- 6: Landmark-based shape spaces
- 7: Kendall's similarity shape spaces Σkm
- 8: The planar shape space Σk2
- 9: Reflection similarity shape spaces RΣkm
- 10: Stiefel manifolds Vk,m
- 11: Affine shape spaces AΣkm
- 12: Real projective spaces and projective shape spaces
- 13: Nonparametric Bayes inference on manifolds
- 14: Nonparametric Bayes regression, classification and hypothesis testing on manifolds
- Appendix
- References
- Index