图像分析中的模型和逆问题 英文影印版
作者：（法）查蒙德 著
出版时间：2014年版
丛编项： 经典数学丛书
内容简介　Inthelastdecadeofthepastcenturlrwewitnessedanexceptionalparticipationofmathematiciansinthedevelopmentofdigitalimageprocessingasascience.Thesecontributionshavefoundanaturalplaceatthelowlevelofprocessing，withtheadventofmathematicalmorphology，differentialequations，Markovrandomfields，andwavelettheory.Theyarealsoreflectedintheincreasinglyimportantrolemodelinghasplayedinsolvingcomplexproblems.Althoughmodelingisoftenahiddenstageofthesolution，thebenefitsofcorrectlymodelinganimageprocessingproblemarehuge.Modelingistheveryplacewhere"sensitivity"stealsaleadover"geometry"，toputitinPascal'swords，Correctmodelingintroducesinformationthatcannotbeexpressedbydataordeducedbyequations，butrefiectsthesubtledependencyorcausalitybetweentheingredients.Modelinghasmoretodowithpotsandpansthanrecipesandspices，todrawouttheculinarymetaphor.BernardChalmond'sworkismainlydedicatedtomodelingissues.Itdoesnotfullycoverthisfield，sinceitismostlyconcernedwithtwotypesofmodel：Bayesianmodelsissuedfromprobabilitytheoryandenergy-basedmodelsderivedfromphysicsandmechanics.Withinthescopeofthesemodels，thebookdeeplyexploresthevariousconsequencesofthechoiceofamodel;itcomparestheirhypotheses，discussestheirmerits，explorestheirvalidity，andsuggestspossiblefieldsofapplication.Thisbookfulfillsaneedinthefieldofcomputerscienceresearchandeducation.Itisnotintendedforprofessionalmathematicians，butitundoubtedlydealswithappliedmathematics.
目录
Foreword by Henri Maitre
Acknowledgments
List of Figures
Notation and Symbols
1 Introduction
1.1 About Modeling
1.1.1 Bayesian Approach
1.1.2 Inverse Problem
1.1.3 Energy-Based Formulation
1.1.4 Models
1.2 Structure of the Book
Ⅰ Spline Models
2 Nonparametric Spline Models
2.1 Definition
2.2 Optimiation
2.2.1 Bending Spline
2.2.2 Spline Under Tension
2.2.3 Robustness
2.3 Bayesian Interpretation
2.4 Choice of R,egularization Parameter
2.5 Approximation Using a Surface
2.5.1 L-Spline Surface
2.5.2 Quadratic Energy
2.5.3 Finite Element Optimization
3 Parametric Spline Models
3.1 Representation on a Basis of B-Splines
3.1.1 Approximation Spline
3.1.2 Construction of B-Splines
3.2 Extensions
3.2.1 Multidimensional Case
3.2.2 Heteroscedasticity
3.3 High-Dimensional Splines
3.3.1 Revealing Directions
3.3.2 Projection Pursuit Regression
4 Auto-Associative Models
4.1 Analysis of Multidimensional Data
4.1.1 A Classical Approach
4.1.2 Toward an Alternative Approach
4.2 Auto-Associative Composite Models
4.2.1 Model and Algorithm
4.2.2 Properties.. ,
4.3 Projection Pursuit and Spline Smoothing
4.3.1 Projectionlndex
4.3.2 Spline Smoothing
4.4 Illustration
Ⅱ Markov Models
5 Fundamental Aspects
5.1 Definitions
5.1.1 Finite Markov Fields
5.1.2 Gibbs Fields
5.2 Markov-Gibbs Equivalence
5.3 Examples
5.3.1 Bending Energy
5.3.2 Bernoulli Energy
5.3.3 Gaussian Energy
5.4 Consistency Problem
……
Ⅲ Modeling in Action