Nonparametric Inference on Manifolds: With Applications to Shape Spaces (BOK)

Abhishek Bhattacharya, Rabi Bhattacharya

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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.

Produktfakta

Språk Engelsk Engelsk Innbinding Innbundet
Utgitt 2012 Forfatter Abhishek Bhattacharya, Rabi Bhattacharya
Forlag
CAMBRIDGE UNIVERSITY PRESS
ISBN 9781107019584
Antall sider 252 Dimensjoner 15,2cm x 22,8cm x 2cm
Vekt 520 gram Leverandør Bertram Trading Ltd
Emner og form Probability & statistics