PDE and Level Sets
PDE and Level Sets

Author: Swamy Laxminarayan

Publisher: Springer Science & Business Media

Published: 2006-04-11

Total Pages: 446

ISBN-13: 0306479303

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PDE & Level Sets: Algorithmic Approaches to Static & Motion Imagery is specially dedicated to the segmentation of complex shapes from the field of imaging sciences using level sets and PDEs. It covers the fundamentals of level sets, different kinds of concepts of both geodesic curvature flows and planar flows, as well as the power of incorporation of regional-statistics in level set framework. In covering this material, this book presents segmentation of object-in-motion imagery based on level sets in eigen analysis framework, while also presenting classical problems of boundary completion in cognitive images, like the pop-up of subjective contours in the famous triangle of Kanizsa using surface evolution framework, or the mean curvature evolution of a graph with respect to the Riemannian metric induced by the image. All results are presented for modal completion of cognitive objects with missing boundaries.

Level Set Methods and Fast Marching Methods
Level Set Methods and Fast Marching Methods

Author: J. A. Sethian

Publisher: Cambridge University Press

Published: 1999-06-13

Total Pages: 404

ISBN-13: 9780521645577

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This new edition of Professor Sethian's successful text provides an introduction to level set methods and fast marching methods, which are powerful numerical techniques for analyzing and computing interface motion in a host of settings. They rely on a fundamental shift in how one views moving boundaries; rethinking the natural geometric Lagrangian perspective and exchanging it for an Eulerian, initial value partial differential equation perspective. For this edition, the collection of applications provided in the text has been expanded, including examples from physics, chemistry, fluid mechanics, combustion, image processing, material science, fabrication of microelectronic components, computer vision, computer-aided design, and optimal control theory. This book will be a useful resource for mathematicians, applied scientists, practising engineers, computer graphic artists, and anyone interested in the evolution of boundaries and interfaces.

Geometry of PDEs and Related Problems
Geometry of PDEs and Related Problems

Author: Xavier Cabré

Publisher: Springer

Published: 2018-10-03

Total Pages: 207

ISBN-13: 3319951866

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The aim of this book is to present different aspects of the deep interplay between Partial Differential Equations and Geometry. It gives an overview of some of the themes of recent research in the field and their mutual links, describing the main underlying ideas, and providing up-to-date references. Collecting together the lecture notes of the five mini-courses given at the CIME Summer School held in Cetraro (Cosenza, Italy) in the week of June 19–23, 2017, the volume presents a friendly introduction to a broad spectrum of up-to-date and hot topics in the study of PDEs, describing the state-of-the-art in the subject. It also gives further details on the main ideas of the proofs, their technical difficulties, and their possible extension to other contexts. Aiming to be a primary source for researchers in the field, the book will attract potential readers from several areas of mathematics.

Partial Differential Equations
Partial Differential Equations

Author: Walter A. Strauss

Publisher: John Wiley & Sons

Published: 2007-12-21

Total Pages: 467

ISBN-13: 0470054565

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Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Level Set Methods and Dynamic Implicit Surfaces
Level Set Methods and Dynamic Implicit Surfaces

Author: Stanley Osher

Publisher: Springer Science & Business Media

Published: 2006-04-06

Total Pages: 292

ISBN-13: 0387227466

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Very hot area with a wide range of applications; Gives complete numerical analysis and recipes, which will enable readers to quickly apply the techniques to real problems; Includes two new techniques pioneered by Osher and Fedkiw; Osher and Fedkiw are internationally well-known researchers in this area

Recent Advances in Scientific Computing and Partial Differential Equations
Recent Advances in Scientific Computing and Partial Differential Equations

Author: S.-Y. Cheng

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 234

ISBN-13: 0821831550

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The volume is from the proceedings of the international conference held in celebration of Stanley Osher's sixtieth birthday. It presents recent developments and exciting new directions in scientific computing and partial differential equations for time dependent problems and its interplay with other fields, such as image processing, computer vision and graphics. Over the past decade, there have been very rapid developments in the field. This volume emphasizes the strong interaction of advanced mathematics with real-world applications and algorithms. The book is suitable for graduate students and research mathematicians interested in scientific computing and partial differential equations.

Geometric Level Set Methods in Imaging, Vision, and Graphics
Geometric Level Set Methods in Imaging, Vision, and Graphics

Author: Stanley Osher

Publisher: Springer Science & Business Media

Published: 2007-05-08

Total Pages: 523

ISBN-13: 0387218106

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Here is, for the first time, a book that clearly explains and applies new level set methods to problems and applications in computer vision, graphics, and imaging. It is an essential compilation of survey chapters from the leading researchers in the field. The applications of the methods are emphasized.

Future Visions on Biomedicine and Bioinformatics 2
Future Visions on Biomedicine and Bioinformatics 2

Author: Lodewijk Bos

Publisher: Springer Science & Business Media

Published: 2011-07-11

Total Pages: 108

ISBN-13: 3642195547

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Swamy Laxminarayan was an outstanding researcher active in many diverse fields of science and technology. He was one of the most prominent biomedical scientists and his ideas influenced the Biomedical Technology substantially. This book tries to provide an overview on the multiple achievements of Swamy Laxminarayan. It presents a collection of his most outstanding publications and an overview on his outstanding life. This Volume is the second part of the liber amicorum in Memory of Swamy Laxminarayan.

Biomedical Image Analysis and Machine Learning Technologies: Applications and Techniques
Biomedical Image Analysis and Machine Learning Technologies: Applications and Techniques

Author: Gonzalez, Fabio A.

Publisher: IGI Global

Published: 2009-12-31

Total Pages: 390

ISBN-13: 1605669571

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Medical images are at the base of many routine clinical decisions and their influence continues to increase in many fields of medicine. Since the last decade, computers have become an invaluable tool for supporting medical image acquisition, processing, organization and analysis. Biomedical Image Analysis and Machine Learning Technologies: Applications and Techniques provides a panorama of the current boundary between biomedical complexity coming from the medical image context and the multiple techniques which have been used for solving many of these problems. This innovative publication serves as a leading industry reference as well as a source of creative ideas for applications of medical issues.