Statistics And Analysis Of Shapes

Author : Anuj Srivastava
Publisher : Springer
ISBN 13 : 1493940201
Total Pages : 447 pages
Book Rating : 4.02/5 ( download)

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Download or read book Functional and Shape Data Analysis written by Anuj Srivastava and published by Springer. This book was released on 2016-10-03 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Ian L. Dryden
Publisher : John Wiley & Sons
ISBN 13 : 1119072506
Total Pages : 496 pages
Book Rating : 4.08/5 ( download)

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Download or read book Statistical Shape Analysis written by Ian L. Dryden and published by John Wiley & Sons. This book was released on 2016-06-28 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Statistical 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 .

Author : Hamid Krim
Publisher : Springer Science & Business Media
ISBN 13 : 0817644814
Total Pages : 396 pages
Book Rating : 4.19/5 ( download)

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Download or read book Statistics and Analysis of Shapes written by Hamid Krim and published by Springer Science & Business Media. This book was released on 2007-12-31 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Christopher G. Small
Publisher : Springer Science & Business Media
ISBN 13 : 1461240328
Total Pages : 237 pages
Book Rating : 4.27/5 ( download)

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Download or read book The Statistical Theory of Shape written by Christopher G. Small and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Ian L. Dryden
Publisher : John Wiley & Sons
ISBN 13 : 0470699620
Total Pages : 516 pages
Book Rating : 4.21/5 ( download)

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Download or read book Statistical Shape Analysis written by Ian L. Dryden and published by John Wiley & Sons. This book was released on 2016-09-06 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Subhash R Lele
Publisher : CRC Press
ISBN 13 : 9780367397630
Total Pages : 328 pages
Book Rating : 4.33/5 ( download)

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Download or read book An Invariant Approach to Statistical Analysis of Shapes written by Subhash R Lele and published by CRC Press. This book was released on 2019-08-30 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 succeed, it needs techniques that not only satisfy mathematical and statistical rigor but also attend to the scientific issues. An Invariant Approach to the Statistical Analysis of Shapes results from a long and fruitful collaboration between a mathematical statistician and a biologist. Together they have developed a methodology that addresses the importance of scientific relevance, biological variability, and invariance of the statistical and scientific inferences with respect to the arbitrary choice of the coordinate system. They present the history and foundations of morphometrics, discuss the various kinds of data used in the analysis of form, and provide justification for choosing landmark coordinates as a preferred data type. They describe the statistical models used to represent intra-population variability of landmark data and show that arbitrary translation, rotation, and reflection of the objects introduce infinitely many nuisance parameters. The most fundamental part of morphometrics-comparison of forms-receives in-depth treatment, as does the study of growth and growth patterns, classification, clustering, and asymmetry. Morphometrics has only recently begun to consider the invariance principle and its implications for the study of biological form. With the advantage of dual perspectives, An Invariant Approach to the Statistical Analysis of Shapes stands as a unique and important work that brings a decade's worth of innovative methods, observations, and insights to an audience of both statisticians and biologists.

Author : D. G. Kendall
Publisher : John Wiley & Sons
ISBN 13 : 0470317841
Total Pages : 318 pages
Book Rating : 4.46/5 ( download)

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Download or read book Shape and Shape Theory written by D. G. Kendall and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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/

Author : LUIGI SALMASO
Publisher : Springer Science & Business Media
ISBN 13 : 1461481635
Total Pages : 105 pages
Book Rating : 4.38/5 ( download)

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Download or read book Permutation Tests in Shape Analysis written by LUIGI SALMASO and published by Springer Science & Business Media. This book was released on 2013-09-06 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical shape analysis is a geometrical analysis from a set of shapes in which statistics are measured to describe geometrical properties from similar shapes or different groups, for instance, the difference between male and female Gorilla skull shapes, normal and pathological bone shapes, etc. Some of the important aspects of shape analysis are to obtain a measure of distance between shapes, to estimate average shapes from a (possibly random) sample and to estimate shape variability in a sample[1]. One of the main methods used is principal component analysis. Specific applications of shape analysis may be found in archaeology, architecture, biology, geography, geology, agriculture, genetics, medical imaging, security applications such as face recognition, entertainment industry (movies, games), computer-aided design and manufacturing. This is a proposal for a new Brief on statistical shape analysis and the various new parametric and non-parametric methods utilized to facilitate shape analysis. ​ ​

Author : Subhash R. Lele
Publisher : CRC Press
ISBN 13 : 1420036173
Total Pages : 323 pages
Book Rating : 4.76/5 ( download)

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Download or read book An Invariant Approach to Statistical Analysis of Shapes written by Subhash R. Lele and published by CRC Press. This book was released on 2001-01-19 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : M. C. Delfour
Publisher : SIAM
ISBN 13 : 0898719364
Total Pages : 637 pages
Book Rating : 4.69/5 ( download)

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Download or read book Shapes and Geometries written by M. C. Delfour and published by SIAM. This book was released on 2011-01-01 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.