Nonparametric Inference on Manifolds
With Applications to Shape Spaces
1st Edition
Published on 23. April 2012
978-1-139-33528-7 (ISBN)
Description
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 Frechet 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.
Reviews / Votes
'... this is an excellent text that will benefit many students in computer science, mathematics, and physics ... A significant plus of the book is the library of MATLAB codes and datasets available for download from the authors' site.' Alexander Tzanov, Computing ReviewsMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
15 Halftones, unspecified; 5 Line drawings, unspecified
File size
2,41 MB
ISBN-13
978-1-139-33528-7 (9781139335287)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Abhishek Bhattacharya | Rabi Bhattacharya
Nonparametric Inference on Manifolds
With Applications to Shape Spaces
Book
04/2015
Cambridge University Press
€54.60
Shipment within 15-20 days
Abhishek Bhattacharya | Rabi Bhattacharya
Nonparametric Inference on Manifolds
With Applications to Shape Spaces
Book
04/2012
Cambridge University Press
€73.40
Shipment within 15-20 days
Persons
Abhishek Bhattacharya is currently working as an assistant professor at the Indian Statistical Institute. After gaining BStat and MStat degrees from the Institute in 2002 and 2004 respectively, and a PhD from the University of Arizona in 2008, he was a postdoctoral researcher at Duke University until the end of 2010, before joining ISI in 2011. Before writing this book, he published several articles in areas as diverse as nonparametric frequentist and Bayesian statistics on non-Euclidean manifolds. All those articles can be accessed from his website. Rabi Bhattacharya is Professor in the Department of Mathematics at the University of Arizona, Tucson.
Content
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 ?km; 8. The planar shape space ?k2; 9. Reflection similarity shape spaces R?km; 10. Stiefel manifolds; 11. Affine shape spaces A?km; 12. Real projective spaces and projective shape spaces; 13. Nonparametric Bayes inference; 14. Regression, classification and testing; i. Differentiable manifolds; ii. Riemannian manifolds; iii. Dirichlet processes; iv. Parametric models on Sd and ?k2; References; Subject index.
