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Geometric Partial Differential Equations and Image Analysis

2001-01-01 Law
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Release : 2001-01-01
Genre : Law
Kind : eBook
Book Rating : 758/5 ( reviews)

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Book Synopsis Geometric Partial Differential Equations and Image Analysis by : Guillermo Sapiro

Download or read book Geometric Partial Differential Equations and Image Analysis written by Guillermo Sapiro. This book was released on 2001-01-01. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. This research area brings a number of new concepts into the field, providing a very fundamental and formal approach to image processing. State-of-the-art practical results in a large number of real problems are achieved with the techniques described in this book. Applications covered include image segmentation, shape analysis, image enhancement, and tracking. This book will be a useful resource for researchers and practitioners. It is intended to provide information for people investigating new solutions to image processing problems as well as for people searching for existent advanced solutions.

Geometric Curve Evolution and Image Processing

2003-02-27 Mathematics
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Release : 2003-02-27
Genre : Mathematics
Kind : eBook
Book Rating : 028/5 ( reviews)

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Book Synopsis Geometric Curve Evolution and Image Processing by : Frédéric Cao

Download or read book Geometric Curve Evolution and Image Processing written by Frédéric Cao. This book was released on 2003-02-27. Available in PDF, EPUB and Kindle. Book excerpt: In image processing, "motions by curvature" provide an efficient way to smooth curves representing the boundaries of objects. In such a motion, each point of the curve moves, at any instant, with a normal velocity equal to a function of the curvature at this point. This book is a rigorous and self-contained exposition of the techniques of "motion by curvature". The approach is axiomatic and formulated in terms of geometric invariance with respect to the position of the observer. This is translated into mathematical terms, and the author develops the approach of Olver, Sapiro and Tannenbaum, which classifies all curve evolution equations. He then draws a complete parallel with another axiomatic approach using level-set methods: this leads to generalized curvature motions. Finally, novel, and very accurate, numerical schemes are proposed allowing one to compute the solution of highly degenerate evolution equations in a completely invariant way. The convergence of this scheme is also proved.

Geometric Partial Differential Equations and Image Analysis

2006-02-13 Mathematics
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Release : 2006-02-13
Genre : Mathematics
Kind : eBook
Book Rating : 514/5 ( reviews)

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Book Synopsis Geometric Partial Differential Equations and Image Analysis by : Guillermo Sapiro

Download or read book Geometric Partial Differential Equations and Image Analysis written by Guillermo Sapiro. This book was released on 2006-02-13. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. This research area brings a number of new concepts into the field, providing a very fundamental and formal approach to image processing. State-of-the-art practical results in a large number of real problems are achieved with the techniques described in this book. Applications covered include image segmentation, shape analysis, image enhancement, and tracking. This book will be a useful resource for researchers and practitioners. It is intended to provide information for people investigating new solutions to image processing problems as well as for people searching for existent advanced solutions.

Geometric Analysis and Nonlinear Partial Differential Equations

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 272/5 ( reviews)

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Book Synopsis Geometric Analysis and Nonlinear Partial Differential Equations by : Stefan Hildebrandt

Download or read book Geometric Analysis and Nonlinear Partial Differential Equations written by Stefan Hildebrandt. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods or more general significance. " We think that many, if not all, papers of this book are written in this spirit and will give the reader access to an important branch of analysis by exhibiting interest ing problems worth to be studied. Most of the collected articles have an extensive introductory part describing the history of the presented problems as well as the state of the art and offer a well chosen guide to the literature. This way the papers became lengthier than customary these days, but the level of presentation is such that an advanced graduate student should find the various articles both readable and stimulating.

Geometric Partial Differential Equations - Part I

2020-01-14 Mathematics
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Release : 2020-01-14
Genre : Mathematics
Kind : eBook
Book Rating : 045/5 ( reviews)

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Book Synopsis Geometric Partial Differential Equations - Part I by :

Download or read book Geometric Partial Differential Equations - Part I written by . This book was released on 2020-01-14. Available in PDF, EPUB and Kindle. Book excerpt: Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering. About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimization Each chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further reading The authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs

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