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