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.

A systematic introduction to a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes.

About the Author
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.

Reviews
'... 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 Reviews



Book Information
ISBN 9781107019584
Author Abhishek Bhattacharya
Format Hardback
Page Count 252
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 520g
Dimensions(mm) 234mm * 156mm * 20mm