Nonparametric inference on manifolds: With applications to shape spaces

Abhishek Bhattacharya, Rabi Bhattacharya

Research output: Book/ReportBook

30 Scopus citations

Abstract

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.

Original languageEnglish (US)
PublisherCambridge University Press
Number of pages237
ISBN (Electronic)9781139094764
ISBN (Print)9781107019584
DOIs
StatePublished - Jan 1 2012

ASJC Scopus subject areas

  • Mathematics(all)

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