国外数学名著系列（续一）38：图像处理与分析

图书标准信息

• 作者 [美]陈繁昌 著
• 出版社 科学出版社
• 出版时间 2009-01
• 版次 1
• ISBN 9787030234858
• 定价 88.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 400页
• 字数 504千字
• 正文语种 英语

【内容简介】

　　ImageProcessingandAnalysis：Variational，PDE，Wavelet，andStochasticMethodsissystematicandwellorganized，Theauthorsfirstinvestigatethegeometric，functional，andatomicstructuresofimagesandthenrigorouslydevelopandanalyzeseveralimageprocessors.Thebookiscomprehensiveandintegrative，coveringthefourmostpowerfulclassesofmathematicaltoolsincontemporaryimageanalysisandprocessingwhileexploringtheirintrinsicconnectionsandintegration.Thematerialisbalancedintheoryandcomputation，followingasolidtheoreticalanalysisofmodelbuildingandperformancewithcomputationalimplementationandnumericalexamples.
　　Thisbookiswrittenforgraduatestudentsandresearchersinappliedmathematics，computerscience，electricalengineering，andotherdisciplineswhoareinterestedinproblemsinimagingandcomputervision.Itcanbeusedasareferencebyscientistswithspecifictasksinimageprocessing，aswellasbyresearcherswithageneralinterestinfindingoutaboutthelatestadvances.

【目录】

ListofFigures
Preface
1Introduction
1.1DawningoftheEraofImagingSciences
1.1.1ImageAcquisition
1.1.2ImageProcessing
1.1.3ImageInterpretationandVisualIntelligence

1.2ImageProcessingbyExamples
1.2.1ImageContrastEnhancement
1.2.2ImageDenoisirg
1.2.3ImageDeblurring
1.2.4ImageInpainting
1.2.5ImageSegmentation

1.3AnOverviewofMethodologiesinImageProcessing
1.3.1MorphologicalApproach
1.3.2FourierandSpectralAnalysis
1.3.3WaveletandSpace-ScaleAnalysis
1.3.4StochasticModeling
1.3.5VariaticnalMethods
1.3.6PartialDifferentialEquations（PDEs）
1.3.7DifferentApproachesAreIntrinsicallyInterconnected

1.4OrganizationoftheBook
1.5HowtoReadtheBcok

2SomeModernImageAnalysisTools
2.1GeometryofCurvesandSurfaces
2.1.IGeometryofCurves
2.1.2GeometryofSurfacesinThreeDimensions
2.1.3HausdorffMeasuresandDimensions

2.2FunctionswithBoundedVariations
2.2.1TotalVariatienasaRadonMeasure
2.2.2BasicPropertiesofBVFunctions
2.2.3TheCo-AreaFormula

2.3ElementsofThermodynamicsandStatisticalMechanics
2.3.1EssentialsofThermodynamics
2.3.2EntropyandPotentials
2.3.3StatisticalMechanicsofEnsembles

2.4BayesianStatisticalInference
2.4.1ImageProcessingorVisualPerceptionasInference
2.4.2BayesianInference：BiasDuetoPriorKnowledge
2.4.3BayesianMethodinImageProcessing

2.5LinearandNonlinearFilteringandDiffusion
2.5.1PointSpreadingandMarkovTransition
2.5.2LinearFilteringandDiffusion
2.5.3NonlinearFilteringandDiffusion

2.6WaveletsandMultiresolutionAnalysis
2.6.1QuestforNewImageAnalysisTools
2.6.2EarlyEdgeTheoryandMarr’sWavelets
2.6.3WindowedFrequencyAnalysisandGaborWavelets
2.6.4Frequency-WindowCoupling：Malvar-WilsonWavelets
2.6.5TheFrameworkofMultiresolutionAnalysis（MRA）
2.6.6FastImageAnalysisandSynthesisviaFilterBanks

3ImageModelingandRepresentation
3.1ModelingandRepresentation：What，Why，andHow
3.2DeterministicImageModels
3.2.1ImagesasDistributions（GeneralizedFunctions）
3.2.2LpImages
3.2.3SobolevImagesHn（Ω）
3.2.4BVImages

3.3WaveletsandMultiscaleRepresentation
3.3.1Constructionof2-DWavelets
3.3.2WaveletResponsestoTypicalImageFeatures
3.3.3BesovImagesandSparseWaveletRepresentation

3.4LatticeandRandomFieldRepresentation
3.4.1NaturalImagesofMotherNature
3.4.2ImagesasEnsemblesandDistributions
3.4.3ImagesasGibbs’Ensembles
3.4.4ImagesasMarkovRandomFields
3.4.5VisualFiltersandFilterBanks
3.4.6Entropy-BasedLearningofImagePatterns

3.5Level-SetRepresentation
3.5.1ClassicalLevelSets
3.5.2CumulativeLevelSets
3.5.3Level-SetSynthesis
3.5.4AnExample：LevelSetsofPiecewiseConstantImages
3.5.5HighOrderRegularityofLevelSets
3.5.6StatisticsofLevelSetsofNaturalImages

3.6TheMumford-ShahFreeBoundaryImageModel
3.6.1PiecewiseConstant1-DImages：AnalysisandSynthesis
3.6.2PiecewiseSmooth1-DImages：FirstOrderRepresentation
3.6.3PiecewiseSmoothI-DImages：PoissonRepresentation
3.6.4PiecewiseSmooth2-DImages
3.6.5TheMumford-ShahModel
3.6.6TheRoleofSpecialBVImages

4ImageDenoising
4.1Noise：Origins.Physics.andModels
4.l.1OriginsandPhysicsofNoise
4.1.2ABriefOverviewof1-DStochasticSignals
4.1.3StochasticModelsofNoises
4.1.4AnalogWhiteNoisesasRandomGeneralizedFunctions
4.1.5RandomSignalsfromStochasticDifferentialEquations
4.l.62-DStochasticSpatialSignals：RandomFields

4.2LinearDenoising：LowpassFiltering
4.2.1Signalvs.Noise
4.2.2DenoisingviaLinearFiltersandDiffusion

4.3Data-DrivenOptimalFiltering：WienerFilters
4.4WaveletShrinkageDenoising
4.4.1Shrinkage：Quasi-statisticalEstimationofSingletons
4.4.2Shrinkage：VariationalEstimationofSingletons
4.4.3DenoisingviaShrinkingNoisyWaveletComponents
4.4.4VariationalDenoisingofNoisyBesovImages

4.5VariationalDenoisingBasedonBVImageModel
4.5.1TV.RobustStatistics.andMedian
4.5.2TheRoleofTVandBVImageModel
4.5.3BiasedIteratedMedianFiltering
4.5.4Rudin.Osher.andFatemisTVDenoisingModel
4.5.5ComputationalApproachestoTVDenoising
4.5.6DualityfortheTVDenoisingModel
4.5.7SolutionStructuresoftheTVDenoisingModel

4.6DenoisingviaNonlinearDiffusionandScale-SpaceTheory
4.6.1PeronaandMaliksNonlinearDiffusionModel
4.6.2AxiomaticScale-SpaceTheory

4.7DenoisingSalt-and-PepperNoise
4.8MultichannelTVDenoising
4.8.1VariationalTVDenoisingofMultichannelImages
4.8.2ThreeVersionsofTV[u]

5ImageDeblurring
5.1Blur：PhysicalOriginsandMathematicalModels
5.1.1PhysicalOrigins
5.1.2MathematicalModelsofBlurs
5.1.3Linearvs.NonlinearBlurs

5.2Ill-posednessandRegularization
5.3DeblurringwithWienerFilters
5.3.1IntuitiononFilter-BasedDeblurring
5.3.2WienerFiltering

5.4DeblurringofBVImageswithKnownPSF
5.4.1TheVariationalModel
5.4.2ExistenceandUniqueness
5.4.3Computation

5.5VariationalBlindDeblurringwithUnknownPSF
5.5.1ParametricBlindDeblurring
5.5.2Parametric-Field-BasedBlindDeblurring
5.5.3NonparametricBlindDeblurring

6ImageInpainting
6.1ABriefReviewonClassicalInterpolationSchemes
6.1.1PolynomialInterpolation
6.1.2TrigonometricPolynomialInterpolation
6.1.3SplineInterpolation
6.1.4ShannonsSamplingTheorem
6.1.5RadialBasisFunctionsandThin-PlateSplines

6.2ChallengesandGuidelinesfor2-DImageInpainting
6.2.1MainChallengesforImageInpainting
6.2.2GeneralGuidelinesforImageInpainting

6.3InpaintingofSobolevImages：GreensFormulae
6.4GeometricModelingofCurvesandImages
6.4.1GeometricCurveModels
6.4.22-.3-PointAccumulativeEnergies.Length.andCurvature.
6.4.3ImageModelsviaFunctionalizingCurveModels
6.4.4ImageModelswithEmbeddedEdgeModels

6.5InpaintingBVImages(viatheTVRadonMeasure)
6.5.1FormulationoftheTVInpaintingModel
6.5.2JustificationofTVInpaintingbyVisualPerception
6.5.3ComputationofTVlnpainting
6.5.4DigitalZoomingBasedonTVInpainting
6.5.5Edge-BasedImageCodingviaInpainting
6.5.6MoreExamplesandApplicationsofTVInpainting

6.6ErrorAnalysisforImageInpainting
6.7InpaintingPiecewiseSmoothImagesviaMumfordandShah
6.8ImageInpaintingviaEulersElasticasandCurvatures
6.8.1InpaintingBasedontheElasticaImageModel
6.8.2InpaintingviaMumford-Shah-EulerImageModel

6.9InpaintingofMeyersTexture
6.10ImageInpaintingwithMissingWaveletCoefficients
6.11PDEInpainting：Transport.Diffusion.andNavier-Stokes
6.11.1SecondOrderInterpolationModels
6.11.2AThirdOrderPDEInpaintingModelandNavier-Stokes
……
7ImageSegmentation
Bibliography
Index