图像处理中的数学问题-第2版

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