Statistical Shape Analysis
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Statistical Shape Analysis
Author | : Ian L. Dryden,Kanti V. Mardia |
Publsiher | : John Wiley & Sons |
Total Pages | : 496 |
Release | : 2016-06-28 |
Genre | : Mathematics |
ISBN | : 9781119072508 |
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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 .
Statistical Shape and Deformation Analysis
Author | : Guoyan Zheng,Shuo Li,Gabor Szekely |
Publsiher | : Academic Press |
Total Pages | : 508 |
Release | : 2017-03-23 |
Genre | : Computers |
ISBN | : 9780128104941 |
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Statistical Shape and Deformation Analysis: Methods, Implementation and Applications contributes enormously to solving different problems in patient care and physical anthropology, ranging from improved automatic registration and segmentation in medical image computing to the study of genetics, evolution and comparative form in physical anthropology and biology. This book gives a clear description of the concepts, methods, algorithms and techniques developed over the last three decades that is followed by examples of their implementation using open source software. Applications of statistical shape and deformation analysis are given for a wide variety of fields, including biometry, anthropology, medical image analysis and clinical practice. Presents an accessible introduction to the basic concepts, methods, algorithms and techniques in statistical shape and deformation analysis Includes implementation examples using open source software Covers real-life applications of statistical shape and deformation analysis methods
The Statistical Theory of Shape
Author | : Christopher G. Small |
Publsiher | : Springer Science & Business Media |
Total Pages | : 237 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9781461240327 |
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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.
Statistical Shape Analysis
Author | : Ian L. Dryden,Kanti V. Mardia |
Publsiher | : Wiley-Blackwell |
Total Pages | : 398 |
Release | : 1998-09-16 |
Genre | : Mathematics |
ISBN | : UOM:39015048515913 |
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Thos book involves methods for the geometrical study of random objects where location, rotation and scale information.
Functional and Shape Data Analysis
Author | : Anuj Srivastava,Eric P. Klassen |
Publsiher | : Springer |
Total Pages | : 447 |
Release | : 2016-10-03 |
Genre | : Mathematics |
ISBN | : 9781493940202 |
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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 Models of Shape
Author | : Rhodri Davies,Carole Twining,Chris Taylor |
Publsiher | : Springer Science & Business Media |
Total Pages | : 309 |
Release | : 2008-12-15 |
Genre | : Computers |
ISBN | : 9781848001381 |
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The goal of image interpretation is to convert raw image data into me- ingful information. Images are often interpreted manually. In medicine, for example, a radiologist looks at a medical image, interprets it, and tra- lates the data into a clinically useful form. Manual image interpretation is, however, a time-consuming, error-prone, and subjective process that often requires specialist knowledge. Automated methods that promise fast and - jective image interpretation have therefore stirred up much interest and have become a signi?cant area of research activity. Early work on automated interpretation used low-level operations such as edge detection and region growing to label objects in images. These can p- ducereasonableresultsonsimpleimages,butthepresenceofnoise,occlusion, andstructuralcomplexity oftenleadstoerroneouslabelling. Furthermore,- belling an object is often only the ?rst step of the interpretation process. In order to perform higher-level analysis, a priori information must be incor- rated into the interpretation process. A convenient way of achieving this is to use a ?exible model to encode information such as the expected size, shape, appearance, and position of objects in an image. The use of ?exible models was popularized by the active contour model, or ‘snake’ [98]. A snake deforms so as to match image evidence (e.g., edges) whilst ensuring that it satis?es structural constraints. However, a snake lacks speci?city as it has little knowledge of the domain, limiting its value in image interpretation.
Statistical Shape Analysis
Author | : Ian L. Dryden,Kanti V. Mardia |
Publsiher | : John Wiley & Sons |
Total Pages | : 516 |
Release | : 2016-09-06 |
Genre | : Mathematics |
ISBN | : 9780470699621 |
Download Statistical Shape Analysis Book in PDF, Epub and Kindle
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.
Parametric and Nonparametric Inference for Statistical Dynamic Shape Analysis with Applications
Author | : Chiara Brombin,Luigi Salmaso,Lara Fontanella,Luigi Ippoliti,Caterina Fusilli |
Publsiher | : Springer |
Total Pages | : 115 |
Release | : 2016-02-19 |
Genre | : Mathematics |
ISBN | : 3319263102 |
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This book considers specific inferential issues arising from the analysis of dynamic shapes with the attempt to solve the problems at hand using probability models and nonparametric tests. The models are simple to understand and interpret and provide a useful tool to describe the global dynamics of the landmark configurations. However, because of the non-Euclidean nature of shape spaces, distributions in shape spaces are not straightforward to obtain. The book explores the use of the Gaussian distribution in the configuration space, with similarity transformations integrated out. Specifically, it works with the offset-normal shape distribution as a probability model for statistical inference on a sample of a temporal sequence of landmark configurations. This enables inference for Gaussian processes from configurations onto the shape space. The book is divided in two parts, with the first three chapters covering material on the offset-normal shape distribution, and the remaining chapters covering the theory of NonParametric Combination (NPC) tests. The chapters offer a collection of applications which are bound together by the theme of this book. They refer to the analysis of data from the FG-NET (Face and Gesture Recognition Research Network) database with facial expressions. For these data, it may be desirable to provide a description of the dynamics of the expressions, or testing whether there is a difference between the dynamics of two facial expressions or testing which of the landmarks are more informative in explaining the pattern of an expression.