图像处理中的数学问题（第2版）（英文版）

图书标准信息

• 作者 [法]奥伯特 著
• 出版社 世界图书出版公司
• 出版时间 2009-10
• 版次 1
• ISBN 9787510005381
• 定价 45.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 377页
• 正文语种 英语

【内容简介】

Introduction、TheImageSociety、WhatIsaDigitalImage、AboutPartialDifferentialEquations（PDEs）、DetailedPlan、MathematicalPreliminaries、HowtoReadThisChapter、TheDirectMethodintheCalculusofVgriations、TopologiesonBanachSpaces、ConvexityandLowerSemicontinuity、Rclaxation、Aboutr-Convergence、TheSpaceofFunctionsofBoundedVariation、BasicDefinitionsonMeasures、DefinitionofBV（Ω）、PropertiesofBV（Ω）、ConvexFunctionsofMeasures、ViscositySolutionsinPDEs等等。

【目录】

Foreword
PrefacetotheSecondEdition
PrefacetotheFirstEdition
GuidetotheMainMathematicalConceptsand
TheirApplication
NotationandSymbols
1Introduction
1.1TheImageSociety
1.2WhatIsaDigitalImage7
1.3AboutPartialDifferentialEquations（PDEs）
1.4DetailedPlan

2MathematicalPreliminaries
HowtoReadThisChapter.
2.1TheDirectMethodintheCalculusofVgriations
2.1.1TopologiesonBanachSpaces
2.1.2ConvexityandLowerSemicontinuity
2.1.3Rclaxat.ion
2.1.4Aboutr-Convergence
2.2TheSpaceofFunctionsofBoundedVariation
2.2.1BasicDefinitionsonMeasures
2.2.2DefinitionofBV（Ω）
2.2.3PropertiesofBV（Ω）
2.2.4ConvexFunctionsofMeasures
2.3ViscositySolutionsinPDEs
2.3.1AbouttheEikonalEquation
2.3.2DefinitionofViscositySolutions
2.3.3AbouttheExistence
2.3.4AbouttheUniqueness
2.4ElementsofDifferentialGeometry：Curvature
2.4.1ParametrizedCurves
2.4.2CurvesaSIsolevelofaFunctionu
2.4.3ImagesaSSurfaces
2.50therClassicalResultsUsedinThisBook
2.5.1Inequalities
2.5.2CalculusFacts
2.5.3AboutConvolutionandSmoothing
2.5.4UniformConvergence
2.5.5DominatedConvergence了heorem
2.5.6Well-PosedProblems

3ImageRestorationHowtoReadThisChapter
3.1ImageDegradation
3.2TheEnergyMethod
3.2.1AnInverseProblem
3.2.2RegularizationoftheProblem
3.2.3ExistenceandUniquenessofaSolutionfortheMinimizationProblem
3.2.4TowardtheNumericalApproximation
TheProjectionApproach
TheHalf-QuadraticMinimizationApproach
3.2.5SomeInvariancesandtheRoleof
3.2.6SomeRemarksontheNonconvexCaSe
3.3PDE-BaSedMethods
3.3.1SmoothingPDEs
TheHeatEquation
NonlinearDiRusion
TheAlvarez-Guichard-Lions-Morel
ScaleSpaceTheory
WeickertsApproach
SurfaceBasedApproaches
3.3.2Smoothing-EnhancingPDEs
ThePeronaandMalikModel
RegutarizationofthePeronaandMalikModel：CatteetaL
3.3.3EnhancingPDEs
TheOsherandRudinShockFilters
ACaseStudy：ConstructionofaSolutionbytheMethodofCharacteristics
CommentsontheShock-FilterEquation
3.3.4NeighborbOOdFilters，NonlocalMeansAlgorithm，andPDEs
NeighborhoodFilters
HowtoSuppresstheStaircaseEffect？
NonlocalMeansFilter（NL-Means）

4TheSegmentationProblem
HowtoReadThisChapter
4.1DefinitionandObjectives
4.2TheMumfordandShahFunctional
4.2.1AMinimizationProblem
4.2.2TheMathematicalFrameworkfortheExistenceofaSolution
4.2.3RegularityoftheEdgeSet
4.2.4ApproximationsoftheMumfordandShahFunctional
4.2.5ExperimentalResults
4.3GeodesicActiveContoursandtheLevel.SetMethod
4.3.1TheKass-Witkin-Terzopoulosmodel
4.3.2TheGeodesicActiveContoursModel
4.3.3TheLevel-SetMethod
4.3.4TheReinitializationEquation
CharaCterizationoftheDistanceFunction
ExistenceandUniqueness
4.3.5ExperimentalResults
4.3.6AboutSomeRecentAdvances
GlobalStoppingCriterion
TowardMoreGeneralShapeRepresentation

5OtherChallengingAppliCations
HowtoReadThisChapter
5.1ReinventingSomeImagePartsbyInpainting
5.1.1IntroduCtion
5.1.2VariationalModels
TheMasnouandMorelApproach
TheBallesteretal.Approach
TheChanandShenTotalVariationMinimization
Approach
5.1.3PDE-BasedApproaches
TheBertalmioeta1.Approach
TheChanandShenCurvature-DrivenDiffusionApproach
5.1.4Discussion
5.2DecomposinganImageintoGeometryandTexture
5.2.1Introduction
5.2.2ASpaceforModelingOscillatingPatterns
5.2.3Meyer’SModel.
5.2.4AnAlgorithmtoSolveMeyer’SModel
PriorNumericalC：ontribution
TheAujoleta1.Approach
StudyoftheAsymptoticCase
BacktoMeyersModel
5.2.5ExperimentalResults
DenoisingCapabilities
DealingWithTexture
5.2.6AboutSomeRecentAdvances
5.3SequenceAnalysis
5.3.1Introduction
5.3.2TheOpticalFlow：AnApparentMotion
TheOpticalFlowConstraint（OFC）
SolvingtheApertureProblem
OverviewofaDiscontinuity.Preserving
VariationalApproach
AlternativestotheOFC
5.3.3SequenceSegmentation
Introduction
AVriationalFormulation
MathematicalStudyoftheTime-SampledEnergy
Experiments
5.3.4SequenceRestoration
PrinciplesofVideoInpainting
TotalVariation（tV）MinimizationApproach
MotionCompensated（MC）Inpainting
5.4ImageClassification
5.4.1Introduction
5.4.2ALevel-SetApproachforImageClassification
5.4.3AVariationalModelforImageClassificationandRestoration
5.5Vector-ValuedImages
5.5.1Introduction
5.5.2AnFXtendedNbtionofGrudieut
AIntroductiontoFiniteDigerenceMethods
BExperimentYourself！
References
Index