Nonparametric inference on manifolds : with applications to shape spaces
 Author/Creator
 Bhattacharya, Abhishek.
 Language
 English.
 Imprint
 Cambridge ; New York : Cambridge University Press, 2012.
 Physical description
 xiii, 237 p. : ill ; 23 cm.
 Series
 Institute of Mathematical Statistics monographs 2.
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Contributors
 Contributor
 Bhattacharya, R. N. (Rabindra Nath), 1937
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 229234) and index.
 Contents

 1. Introduction 2. Examples 3. Location and spread on metric spaces 4. Extrinsic analysis on manifolds 5. Intrinsic analysis on manifolds 6. Landmarkbased shape spaces 7. Kendall's similarity shape spaces SIGMAkm 8. The planar shape space SIGMAk2 9. Reflection similarity shape spaces RSIGMAkm 10. Stiefel manifolds 11. Affine shape spaces ASIGMAkm 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 SIGMAk2 References Subject index.
 (source: Nielsen Book Data)
 Publisher's Summary
 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 Responsibility
 Abhishek Bhattacharya, Rabi Bhattacharya.
 Series
 Institute of mathematical statistics monographs ; 2
 ISBN
 9781107019584
 1107019583