Statistical Shape And Deformation Analysis
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Statistical Shape And Deformation Analysis
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Author : Guoyan Zheng
language : en
Publisher: Academic Press
Release Date : 2017-03-23
Statistical Shape And Deformation Analysis written by Guoyan Zheng and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-23 with Computers categories.
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
Statistical Shape Analysis
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Author : Ian L. Dryden
language : en
Publisher: Wiley-Blackwell
Release Date : 1998-09-16
Statistical Shape Analysis written by Ian L. Dryden and has been published by Wiley-Blackwell this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-16 with Mathematics categories.
Thos book involves methods for the geometrical study of random objects where location, rotation and scale information.
Statistical Shape Analysis
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Author : Ian L. Dryden
language : en
Publisher: John Wiley & Sons
Release Date : 2016-06-28
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 2016-06-28 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. 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 .
Permutation Tests In Shape Analysis
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Author : LUIGI SALMASO
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-06
Permutation Tests In Shape Analysis written by LUIGI SALMASO 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 2013-09-06 with Mathematics categories.
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.
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.
Elastic Shape Analysis Of Three Dimensional Objects
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Author : Ian H. Jermyn
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2017-09-15
Elastic Shape Analysis Of Three Dimensional Objects written by Ian H. Jermyn and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-15 with Computers categories.
Statistical analysis of shapes of 3D objects is an important problem with a wide range of applications. This analysis is difficult for many reasons, including the fact that objects differ in both geometry and topology. In this manuscript, we narrow the problem by focusing on objects with fixed topology, say objects that are diffeomorphic to unit spheres, and develop tools for analyzing their geometries. The main challenges in this problem are to register points across objects and to perform analysis while being invariant to certain shape-preserving transformations. We develop a comprehensive framework for analyzing shapes of spherical objects, i.e., objects that are embeddings of a unit sphere in R, including tools for: quantifying shape differences, optimally deforming shapes into each other, summarizing shape samples, extracting principal modes of shape variability, and modeling shape variability associated with populations. An important strength of this framework is that it is elastic: it performs alignment, registration, and comparison in a single unified framework, while being invariant to shape-preserving transformations. The approach is essentially Riemannian in the following sense. We specify natural mathematical representations of surfaces of interest, and impose Riemannian metrics that are invariant to the actions of the shape-preserving transformations. In particular, they are invariant to reparameterizations of surfaces. While these metrics are too complicated to allow broad usage in practical applications, we introduce a novel representation, termed square-root normal fields (SRNFs), that transform a particular invariant elastic metric into the standard L2 metric. As a result, one can use standard techniques from functional data analysis for registering, comparing, and summarizing shapes. Specifically, this results in: pairwise registration of surfaces; computation of geodesic paths encoding optimal deformations; computation of Karcher means and covariances under the shape metric; tangent Principal Component Analysis (PCA) and extraction of dominant modes of variability; and finally, modeling of shape variability using wrapped normal densities. These ideas are demonstrated using two case studies: the analysis of surfaces denoting human bodies in terms of shape and pose variability; and the clustering and classification of the shapes of subcortical brain structures for use in medical diagnosis. This book develops these ideas without assuming advanced knowledge in differential geometry and statistics. We summarize some basic tools from differential geometry in the appendices, and introduce additional concepts and terminology as needed in the individual chapters.
Shape Analysis In Medical Image Analysis
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Author : Shuo Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-28
Shape Analysis In Medical Image Analysis written by Shuo Li 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 2014-01-28 with Technology & Engineering categories.
This book contains thirteen contributions from invited experts of international recognition addressing important issues in shape analysis in medical image analysis, including techniques for image segmentation, registration, modelling and classification and applications in biology, as well as in cardiac, brain, spine, chest, lung and clinical practice. This volume treats topics such as for example, anatomic and functional shape representation and matching; shape-based medical image segmentation; shape registration; statistical shape analysis; shape deformation; shape-based abnormity detection; shape tracking and longitudinal shape analysis; machine learning for shape modeling and analysis; shape-based computer-aided-diagnosis; shape-based medical navigation; benchmark and validation of shape representation, analysis and modeling algorithms. This work will be of interest to researchers, students and manufacturers in the fields of artificial intelligence, bioengineering, biomechanics, computational mechanics, computational vision, computer sciences, human motion, mathematics, medical imaging, medicine, pattern recognition and physics.
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.
Morphometrics With R
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Author : Julien Claude
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-15
Morphometrics With R written by Julien Claude 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 2008-12-15 with Science categories.
This book aims to explain how to use R to perform morphometrics. Morpho- tric analysis is the study of shape and size variations and covariations and their covariations with other variables. Morphometrics is thus deeply rooted within stat- tical sciences. While most applications concern biology, morphometrics is becoming common tools used in archeological, palaeontological, geographical, or medicine disciplines. Since the recent formalizations of some of the ideas of predecessors, such as D’arcy Thompson, and thanks to the development of computer techno- gies and new ways for appraising shape changes and variation, morphometrics have undergone, and are still undergoing, a revolution. Most techniques dealing with s- tistical shape analysis have been developed in the last three decades, and the number of publications using morphometrics is increasing rapidly. However, the majority of these methods cannot be implemented in available software and therefore prosp- tive students often need to acquire detailed knowledge in informatics and statistics before applying them to their data. With acceleration in the accumulation of me- ods accompanying the emerging science of statistical shape analysis, it is becoming important to use tools that allow some autonomy. R easily helps ful?ll this need. Risalanguage andenvironment forstatisticalcomputingandgraphics. Although there is an increasing number of computer applications that perform morphometrics, using R has several advantages that confer to users considerable power and possible new horizons in a world that requires rapid adaptability.
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.