图像分析中的模型和逆问题

作者简介

Inthelastdecadeofthepastcenturlrwewitnessedanexceptionalparticipationofmathematiciansinthedevelopmentofdigitalimageprocessingasascience.Thesecontributionshavefoundanaturalplaceatthelowlevelofprocessing，withtheadventofmathematicalmorphology，differentialequations，Markovrandomfields，andwavelettheory.Theyarealsoreflectedintheincreasinglyimportantrolemodelinghasplayedinsolvingcomplexproblems.

Althoughmodelingisoftenahiddenstageofthesolution，thebenefitsofcorrectlymodelinganimageprocessingproblemarehuge.Modelingistheveryplacewhere"sensitivity"stealsaleadover"geometry"，toputitinPascal'swords，Correct modeling introduces information that can not be expressed by data ordeduced by equations，but refiects the subtle dependency or causality between the ingredients.Modeling has more to do withpotsandpansthanrecipesandspices，todrawouttheculinarymetaphor.BernardChalmond'sworkismainlydedicatedtomodelingissues.Itdoesnotfullycoverthisfield，sinceitismostlyconcernedwithtwotypesofmodel:Bayesianmodelsissuedfromprobabilitytheoryandenergy-basedmodelsderivedfromphysicsandmechanics.Withinthescopeofthesemodels，thebookdeeplyexploresthevariousconsequencesofthechoiceofamodel;itcomparestheirhypotheses，discussestheirmerits，explorestheirvalidity，andsuggestspossiblefieldsofapplication.

Thisbookfulfillsaneedinthefieldofcomputerscienceresearchandeducation.Itisnotintendedforprofessionalmathematicians，butitundoubtedlydealswithappliedmathematics.

书籍目录

ForewordbyHenriMaitre

Acknowledgments

ListofFigures

NotationandSymbols

1Introduction

1.1AboutModeling

1.1.1BayesianApproach

1.1.2InverseProblem

1.1.3Energy-BasedFormulation

1.1.4Models

1.2StructureoftheBook

ⅠSplineModels

2NonparametricSplineModels

2.1Definition

2.2Optimiation

2.2.1BendingSpline

2.2.2SplineUnderTension

2.2.3Robustness

2.3BayesianInterpretation

2.4ChoiceofR,egularizationParameter

2.5ApproximationUsingaSurface

2.5.1L-SplineSurface

2.5.2QuadraticEnergy

2.5.3FiniteElementOptimization

3ParametricSplineModels

3.1RepresentationonaBasisofB-Splines

3.1.1ApproximationSpline

3.1.2ConstructionofB-Splines

3.2Extensions

3.2.1MultidimensionalCase

3.2.2Heteroscedasticity

3.3High-DimensionalSplines

3.3.1RevealingDirections

3.3.2ProjectionPursuitRegression

4Auto-AssociativeModels

4.1AnalysisofMultidimensionalData

4.1.1AClassicalApproach

4.1.2TowardanAlternativeApproach

4.2Auto-AssociativeCompositeModels

4.2.1ModelandAlgorithm

4.2.2Properties..,

4.3ProjectionPursuitandSplineSmoothing

4.3.1Projectionlndex

4.3.2SplineSmoothing

4.4Illustration

ⅡMarkovModels

5FundamentalAspects

5.1Definitions

5.1.1FiniteMarkovFields

5.1.2GibbsFields

5.2Markov-GibbsEquivalence

5.3Examples

5.3.1BendingEnergy

5.3.2BernoulliEnergy

5.3.3GaussianEnergy

5.4ConsistencyProblem

..

ⅢModelinginAction

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