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Shapes and Diffeomorphisms

2010-05-17 Mathematics
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Release : 2010-05-17
Genre : Mathematics
Kind : eBook
Book Rating : 555/5 ( reviews)

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Book Synopsis Shapes and Diffeomorphisms by : Laurent Younes

Download or read book Shapes and Diffeomorphisms written by Laurent Younes. This book was released on 2010-05-17. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Shapes and Diffeomorphisms

2019-05-17 Mathematics
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Release : 2019-05-17
Genre : Mathematics
Kind : eBook
Book Rating : 964/5 ( reviews)

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Book Synopsis Shapes and Diffeomorphisms by : Laurent Younes

Download or read book Shapes and Diffeomorphisms written by Laurent Younes. This book was released on 2019-05-17. Available in PDF, EPUB and Kindle. Book excerpt: This book covers mathematical foundations and methods for the computerized analysis of shapes, providing the requisite background in geometry and functional analysis and introducing various algorithms and approaches to shape modeling, with a special focus on the interesting connections between shapes and their transformations by diffeomorphisms. A direct application is to computational anatomy, for which techniques such as large‒deformation diffeomorphic metric mapping and metamorphosis, among others, are presented. The appendices detail a series of classical topics (Hilbert spaces, differential equations, Riemannian manifolds, optimal control). The intended audience is applied mathematicians and mathematically inclined engineers interested in the topic of shape analysis and its possible applications in computer vision or medical imaging. The first part can be used for an advanced undergraduate course on differential geometry with a focus on applications while the later chapters are suitable for a graduate course on shape analysis through the action of diffeomorphisms. Several significant additions appear in the 2nd edition, most notably a new chapter on shape datasets, and a discussion of optimal control theory in an infinite-dimensional framework, which is then used to enrich the presentation of diffeomorphic matching.

Mathematics Of Shapes And Applications

2019-11-20 Mathematics
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Release : 2019-11-20
Genre : Mathematics
Kind : eBook
Book Rating : 149/5 ( reviews)

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Book Synopsis Mathematics Of Shapes And Applications by : Sergey Kushnarev

Download or read book Mathematics Of Shapes And Applications written by Sergey Kushnarev. This book was released on 2019-11-20. Available in PDF, EPUB and Kindle. Book excerpt: Understanding how a single shape can incur a complex range of transformations, while defining the same perceptually obvious figure, entails a rich and challenging collection of problems, at the interface between applied mathematics, statistics and computer science. The program on Mathematics of Shapes and Applications, was held at the Institute for Mathematical Sciences at the National University of Singapore in 2016. It provided discussions on theoretical developments and numerous applications in computer vision, object recognition and medical imaging.The analysis of shapes is an example of a mathematical problem directly connected with applications while offering deep open challenges to theoretical mathematicians. It has grown, over the past decades, into an interdisciplinary area in which researchers studying infinite-dimensional Riemannian manifolds (global analysis) interact with applied mathematicians, statisticians, computer scientists and biomedical engineers on a variety of problems involving shapes.The volume illustrates this wealth of subjects by providing new contributions on the metric structure of diffeomorphism groups and shape spaces, recent developments on deterministic and stochastic models of shape evolution, new computational methods manipulating shapes, and new statistical tools to analyze shape datasets. In addition to these contributions, applications of shape analysis to medical imaging and computational anatomy are discussed, leading, in particular, to improved understanding of the impact of cognitive diseases on the geometry of the brain.

Shapes and Geometries

2011-01-01 Mathematics
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Release : 2011-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 364/5 ( reviews)

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Book Synopsis Shapes and Geometries by : M. C. Delfour

Download or read book Shapes and Geometries written by M. C. Delfour. This book was released on 2011-01-01. 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.

Symmetry and Integration Methods for Differential Equations

2008-01-10 Mathematics
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Release : 2008-01-10
Genre : Mathematics
Kind : eBook
Book Rating : 499/5 ( reviews)

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Book Synopsis Symmetry and Integration Methods for Differential Equations by : George Bluman

Download or read book Symmetry and Integration Methods for Differential Equations written by George Bluman. This book was released on 2008-01-10. Available in PDF, EPUB and Kindle. Book excerpt: This text discusses Lie groups of transformations and basic symmetry methods for solving ordinary and partial differential equations. It places emphasis on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This new edition covers contact transformations, Lie-B cklund transformations, and adjoints and integrating factors for ODEs of arbitrary order.

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