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Nonparametric Inference on Manifolds

With Applications to Shape Spaces

Abhishek Bhattacharya author Rabi Bhattacharya author

Format:Hardback

Publisher:Cambridge University Press

Published:5th Apr '12

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Nonparametric Inference on Manifolds cover

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

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.

'… 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

ISBN: 9781107019584

Dimensions: 234mm x 156mm x 20mm

Weight: 520g

252 pages