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Statistics And Analysis Of Shapes

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The Statistical Theory Of Shape

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Author : Christopher G. Small
language : en
Publisher: Springer
Release Date : 1996-08-09

The Statistical Theory Of Shape written by Christopher G. Small and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-09 with Mathematics categories.

In general terms, the shape of an object, data set, or image can be de fined as the total of all information that is invariant under translations, rotations, and isotropic rescalings. Thus two objects can be said to have the same shape if they are similar in the sense of Euclidean geometry. For example, all equilateral triangles have the same shape, and so do all cubes. In applications, bodies rarely have exactly the same shape within measure ment error. In such cases the variation in shape can often be the subject of statistical analysis. The last decade has seen a considerable growth in interest in the statis tical theory of shape. This has been the result of a synthesis of a number of different areas and a recognition that there is considerable common ground among these areas in their study of shape variation. Despite this synthesis of disciplines, there are several different schools of statistical shape analysis. One of these, the Kendall school of shape analysis, uses a variety of mathe matical tools from differential geometry and probability, and is the subject of this book. The book does not assume a particularly strong background by the reader in these subjects, and so a brief introduction is provided to each of these topics. Anyone who is unfamiliar with this material is advised to consult a more complete reference. As the literature on these subjects is vast, the introductory sections can be used as a brief guide to the literature.

Statistics And Analysis Of Shapes

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Author : Hamid Krim
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-31

Statistics And Analysis Of Shapes written by Hamid Krim and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-31 with Mathematics categories.

The subject of pattern analysis and recognition pervades many aspects of our daily lives, including user authentication in banking, object retrieval from databases in the consumer sector, and the omnipresent surveillance and security measures around sensitive areas. Shape analysis, a fundamental building block in many approaches to these applications, is also used in statistics, biomedical applications (Magnetic Resonance Imaging), and many other related disciplines. With contributions from some of the leading experts and pioneers in the field, this self-contained, unified volume is the first comprehensive treatment of theory, methods, and algorithms available in a single resource. Developments are discussed from a rapidly increasing number of research papers in diverse fields, including the mathematical and physical sciences, engineering, and medicine.

Functional And Shape Data Analysis

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Author : Anuj Srivastava
language : en
Publisher: Springer
Release Date : 2016-10-03

Functional And Shape Data Analysis written by Anuj Srivastava and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-03 with Mathematics categories.

This textbook for courses on function data analysis and shape data analysis describes how to define, compare, and mathematically represent shapes, with a focus on statistical modeling and inference. It is aimed at graduate students in analysis in statistics, engineering, applied mathematics, neuroscience, biology, bioinformatics, and other related areas. The interdisciplinary nature of the broad range of ideas covered—from introductory theory to algorithmic implementations and some statistical case studies—is meant to familiarize graduate students with an array of tools that are relevant in developing computational solutions for shape and related analyses. These tools, gleaned from geometry, algebra, statistics, and computational science, are traditionally scattered across different courses, departments, and disciplines; Functional and Shape Data Analysis offers a unified, comprehensive solution by integrating the registration problem into shape analysis, better preparing graduate students for handling future scientific challenges. Recently, a data-driven and application-oriented focus on shape analysis has been trending. This text offers a self-contained treatment of this new generation of methods in shape analysis of curves. Its main focus is shape analysis of functions and curves—in one, two, and higher dimensions—both closed and open. It develops elegant Riemannian frameworks that provide both quantification of shape differences and registration of curves at the same time. Additionally, these methods are used for statistically summarizing given curve data, performing dimension reduction, and modeling observed variability. It is recommended that the reader have a background in calculus, linear algebra, numerical analysis, and computation.

Statistical Shape Analysis

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Author : Ian L. Dryden
language : en
Publisher: John Wiley & Sons
Release Date : 2016-07-08

Statistical Shape Analysis written by Ian L. Dryden and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-08 with Mathematics categories.

A thoroughly revised and updated edition of this introduction to modern statistical methods for shape analysis Shape analysis is an important tool in the many disciplines where objects are compared using geometrical features. Examples include comparing brain shape in schizophrenia; investigating protein molecules in bioinformatics; and describing growth of organisms in biology. This book is a significant update of the highly-regarded Statistical Shape Analysis by the same authors. The new edition lays the foundations of landmark shape analysis, including geometrical concepts and statistical techniques, and extends to include analysis of curves, surfaces, images and other types of object data. Key definitions and concepts are discussed throughout, and the relative merits of different approaches are presented. The authors have included substantial new material on recent statistical developments and offer numerous examples throughout the text. Concepts are introduced in an accessible manner, while retaining sufficient detail for more specialist statisticians to appreciate the challenges and opportunities of this new field. Computer code has been included for instructional use, along with exercises to enable readers to implement the applications themselves in R and to follow the key ideas by hands-on analysis. Offers a detailed yet accessible treatment of statistical methods for shape analysis Includes numerous examples and applications from many disciplines Provides R code for implementing the examples Covers a wide variety of recent developments in shape analysis Shape Analysis, with Applications in R will offer a valuable introduction to this fast-moving research area for statisticians and other applied scientists working in diverse areas, including archaeology, bioinformatics, biology, chemistry, computer science, medicine, morphometics and image analysis.

An Invariant Approach To Statistical Analysis Of Shapes

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Author : Subhash R. Lele
language : en
Publisher: CRC Press
Release Date : 2001-01-19

An Invariant Approach To Statistical Analysis Of Shapes written by Subhash R. Lele and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-19 with Mathematics categories.

Natural scientists perceive and classify organisms primarily on the basis of their appearance and structure- their form , defined as that characteristic remaining invariant after translation, rotation, and possibly reflection of the object. The quantitative study of form and form change comprises the field of morphometrics. For morphometrics to suc

Shape And Shape Theory

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Author : D. G. Kendall
language : en
Publisher: John Wiley & Sons
Release Date : 2009-09-25

Shape And Shape Theory written by D. G. Kendall and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-25 with Mathematics categories.

Shape and Shape Theory D. G. Kendall Churchill College, University of Cambridge, UK D. Barden Girton College, University of Cambridge, UK T. K. Carne King's College, University of Cambridge, UK H. Le University of Nottingham, UK The statistical theory of shape is a relatively new topic and is generating a great deal of interest and comment by statisticians, engineers and computer scientists. Mathematically, 'shape' is the geometrical information required to describe an object when location, scale and rotational effects are removed. The theory was pioneered by Professor David Kendall to solve practical problems concerning shape. This text presents an elegant account of the theory of shape that has evolved from Kendall's work. Features include: * A comprehensive account of Kendall's shape spaces * A variety of topological and geometric invariants of these spaces * Emphasis on the mathematical aspects of shape analysis * Coverage of the mathematical issues for a wide range of applications The early chapters provide all the necessary background information, including the history and applications of shape theory. The authors then go on to analyse the topic, in brilliant detail, in a variety of different shape spaces. Kendall's own procedures for visualising distributions of shapes and shape processes are covered at length. Implications from other branches of mathematics are explored, along with more advanced applications, incorporating statistics and stochastic analysis. Applied statisticians, applied mathematicians, engineers and computer scientists working and researching in the fields of archaeology, astronomy, biology, geography and physical chemistry will find this book of great benefit. The theories presented are used today in a wide range of subjects from archaeology through to physics, and will provide fascinating reading to anyone engaged in such research. Visit our web page! http://www.wiley.com/

Fractals Random Shapes And Point Fields

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Author : Dietrich Stoyan
language : en
Publisher:
Release Date : 1994-10-20

Fractals Random Shapes And Point Fields written by Dietrich Stoyan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-20 with Mathematics categories.

There has been an increasing interest in the statistical analysis of geometric objects and structures in many branches of science and engineering in recent years. The aim of this book is to present these statistical methods for practical use by non-mathematicians by outlining the mathematical ideas rather than concentrating on detailed proofs. The clarity of exposition ensures that the book will be a valuable resource for researchers and practitioners in many scientific disciplines who wish to use these methods in their work. In particular, the book is suited to materials scientists, geologists, environmental scientists, and biologists.

Statistical Shape Analysis

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Author : Ian L. Dryden
language : en
Publisher: John Wiley & Sons
Release Date : 2016-09-06

Shapes And Diffeomorphisms

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Author : Laurent Younes
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-17

Shapes And Diffeomorphisms written by Laurent Younes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-17 with Mathematics categories.

Shapes are complex objects to apprehend, as mathematical entities, in terms that also are suitable for computerized analysis and interpretation. This volume provides the background that is required for this purpose, including different approaches that can be used to model shapes, and algorithms that are available to analyze them. It explores, in particular, the interesting connections between shapes and the objects that naturally act on them, diffeomorphisms. The book is, as far as possible, self-contained, with an appendix that describes a series of classical topics in mathematics (Hilbert spaces, differential equations, Riemannian manifolds) and sections that represent the state of the art in the analysis of shapes and their deformations. A direct application of what is presented in the book is a branch of the computerized analysis of medical images, called computational anatomy.

Riemannian Geometric Statistics In Medical Image Analysis

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Author : Xavier Pennec
language : en
Publisher: Academic Press
Release Date : 2019-09-04

Riemannian Geometric Statistics In Medical Image Analysis written by Xavier Pennec and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-04 with Computers categories.

Over the past 15 years, there has been a growing need in the medical image computing community for principled methods to process nonlinear geometric data. Riemannian geometry has emerged as one of the most powerful mathematical and computational frameworks for analyzing such data. Riemannian Geometric Statistics in Medical Image Analysis is a complete reference on statistics on Riemannian manifolds and more general nonlinear spaces with applications in medical image analysis. It provides an introduction to the core methodology followed by a presentation of state-of-the-art methods. Beyond medical image computing, the methods described in this book may also apply to other domains such as signal processing, computer vision, geometric deep learning, and other domains where statistics on geometric features appear. As such, the presented core methodology takes its place in the field of geometric statistics, the statistical analysis of data being elements of nonlinear geometric spaces. The foundational material and the advanced techniques presented in the later parts of the book can be useful in domains outside medical imaging and present important applications of geometric statistics methodology Content includes: The foundations of Riemannian geometric methods for statistics on manifolds with emphasis on concepts rather than on proofs Applications of statistics on manifolds and shape spaces in medical image computing Diffeomorphic deformations and their applications As the methods described apply to domains such as signal processing (radar signal processing and brain computer interaction), computer vision (object and face recognition), and other domains where statistics of geometric features appear, this book is suitable for researchers and graduate students in medical imaging, engineering and computer science.

Statistics And Analysis Of Shapes

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