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图像处理中的数学问题-第2版

作者：（法）奥伯特著

出版社：世界图书出版公司

出版年：2009-10-01

评分：5分

ISBN：9787510005381

所属分类：教辅教材

书刊介绍

图像处理中的数学问题-第2版内容简介

简介《图像处理中的数学问题(第2版)(英文版)》由世界图书出版公司出版。

图像处理中的数学问题-第2版本书特色

《图像处理中的数学问题(第2版)(英文版)》由世界图书出版公司出版。

图像处理中的数学问题-第2版目录

foreword
preface to the second edition
preface to the first edition
guide to the main mathematical concepts and
their application
notation and symbols
1introduction
1.1the image society
1.2what is a digital image?
1.3about partial differential equations (pdes)
1.4detailed plan
2mathematical preliminaries
how to read this chapter
2.1the direct method in the calculus of variations...
2.1.1topologies on banach spaces
2.1.2convexity and lower semicontinuity .
2.1.3relaxation
2.1.4about f-convergence
2.2the space of functions of bounded variation
2.2.1basic definitions on measures
2.2.2definition of bv(ft)
2.2.3properties of bv(f~)
2.2.4convex functions of measures
2.3viscosity solutions in pdes
2.3.1about the eikonal equation
2.3.2definition of viscosity solutions
2.3.3about the existence
2.3.4about the uniqueness
2.4elements of differential geometry: curvature
2.4.1parametrized curves
2.4.2curves as isolevel of a function u
2.4.3images as surfaces
2.5other classical results used in this book
2.5.1inequalities
2.5.2calculus facts
2.5.3about convolution and smoothing
2.5.4uniform convergence
2.5.5dominated convergence theorem
2.5.6well-posed problems
3image restoration
how to read this chapter
3.1image degradation
3.2the energy method
3.2.1an inverse problem
3.2.2regularization of the problem
3.2.3existence and uniqueness of a solution for the minimization problem
3.2.4toward the numerical approximation
the projection approach
the half-quadratic minimization approach
3.2.5some invariances and the role of a
3.2.6some remarks on the nonconvex case
3.3pde-based methods
3.3.1smoothing pdes
the heat equation
nonlinear diffusion
the alvarez-guichard-lions-morel
scale space theory
weickert's approach
surface based approaches
3.3.2smoothing-enhancing pdes
the perona and malik model
……
4the segmentation problem
5other challenging applications
a introduction to finite difference methods
b experiment yourself!
references
index

图像处理中的数学问题-第2版节选

《图像处理中的数学问题(第2版)(英文版)》内容简介：Introduction、The Image Society、What Is a Digital Image、About Partial Differential Equations（PDEs）、Detailed Plan、Mathematical Preliminaries、How to Read This Chapter、The Direct Method in the Calculus of Vgriations、Topologies on Banach Spaces、Convexity and Lower Semicontinuity、Rclaxation、Aboutr-Convergence、The Space of Functions of Bounded Variation、Basic Definitions on Measures、Definition ofBV（Ω）、Properties ofBV（Ω）、Convex Functions of Measures、Viscosity Solutions in PDEs等等。

图像处理中的数学问题-第2版相关资料

插图：The message we wish to convey iS that the intuition that lcads to certain formulations and the underlying theoretical study are often complementary．Developing a theoretical justification of a problem is not simply“art for art's sake．”In particular，a deep understanding of the theoretical difficulties may lead to the development of suitable numerical schemes or different models．This book iS concerned with the mathematical study of certain image processing problems．Thus we target two audiences：The first iS the mathematical community．and we show the contribution of mathematics to this domain by studying classical and challenging problems that come from computer vision．It is also the occasion to highlight some difficult and unsolved theoretical questions．The second is the computer vision community：we present a clear． selLC0ntained．and global overview of the mathematics involved for the problems of image restoration，image segmentation，sequence analysis，and image classification．We hope that this work will serve as a useful source of reference and inspiration for fellow researchers in applied mathematics and computer vision， as well as being a basis for advanced courses within these fields．This book iS divided into seven main parts．Chapter 1 introduces the subject and gives a detailed plan of the book．In Chapter 2，most of the mathematical notions used therein are recalled in an educative fashion and illustrated in detail．In Chapters 3 and 4 we examine how PDES and variational methods can be Successfully applied in the restoration and segmentation of one image．Chapter 5 is more applied，and some challenging computer vision problems are described，such as inpainting，sequence analysis，classification or vector-valued image processing．Since the final goal of any approach is to compute a numerical solution，we propose an introduction to the method of fini