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Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. Gilles Aubert, Pierre Kornprobst (auth.) Partial differential equations and variational methods were introduced into image processing about 15 years ago, and intensive research has been carried out since then.

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Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, Second Edition (Applied Mathematical Sciences) Gilles Aubert, Pierre Kornprobst. The updated 2nd edition of this book presents a variety of image analysis applications, reviews their precise mathematics and shows how to discretize them. For the mathematical community, the book shows the contribution of mathematics to this domain, and highlights unsolved theoretical questions.

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Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)

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Partial differential equations (PDEs) have been successful for solving many problems in image processing and computer vision. However, designing PDEs usually requires high mathematical skills and good insight to the problems. In this paper, we propose a framework for learning a system of PDEs from real data. Compared to the traditional approaches to designing PDEs, […]

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For the mathematical community, the book shows the contribution of mathematics to this domain, and highlights unsolved theoretical questions. For the computer vision community, it presents a clear, self-contained and global overview of the mathematics involved in image procesing problems.

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In this paper,we describe some central mathematical problems in medical imaging.The subject has been undergoing rapid changes driven by better hardware and software.Much of the software is based on novel methods utilizing geometric partial differential equations in conjunction with standard signal/image processing techniques as well as

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Mathematical problems in image processing : partial differemial equations and file calculus of variations / Gilles Aubcrt. Pierre Komprobst. p. cm. -- (Applied mathematical sciences : 147) Includes bibliographical references and index. ISBN 11-387-95326-4/alk. paper) I. Image processing--Mathematics. I. Kornprobst, Pierre. ll. Title. Ill. Applied

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mathematical and engineering problems connected with image processing in general and medical imaging in particular. These include image smoothing, registration, and segmentation (see Sections 5.1, 5.2, and 5.3). We show how geometric partial diﬀerential equations and variational methods may be used to address some of these

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The mathematical models have been increasingly used in some traditional engineering fields, such as image processing and analysis and computer vision, over the past three decades. So, since the 1980s, the partial differential equations (PDEs) have been successfully used for solving numerous image processing and computer vision tasks.

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Partial differential equations and variational methods were introduced into image processing about 15 years ago, and intensive research has been carried out since then. The main goal of this work is to present the variety of image analysis applications and the precise mathematics involved. It is intended for two audiences.

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The second is the computer vision community, to present a clear, self-contained, and global overview of the mathematics involved in image processing problems. The book is divided into five main parts. Chapter 1 is a detailed overview. Chapter 2 describes and illustrates most of the mathematical notions found throughout the work.

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