內容簡介
圖像處理與分析Variational,PDE,Wavelet,and Stochastic Methodsis systematic and well organized,The authors first investigate the geometric,functional,and atomic structures of images and then rigorously develop and analyzes ever alimage processors.
The book is comprehensive and integrative, covering the four most powerful classes of mathematical tools in contemporary image analysis and processing while exploring the irintrinsic connection sand integration.
The material is balanced in theory and computation, following a solid theoretic alanalysis of model building and performance with computational implementation and numerical examples.
This book is written for graduate students and researcher sinapplied mathematics, computerscience, electrical engineering, and other disciplines who are interested in problems in imaging and computervision.
It can beused as a reference by scientists with specific tasks in image processing, as well as by researcher swith a general interest in finding out about the latest advances.
目錄
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.andFatemi'sTVDenoisingModel
4.5.5ComputationalApproachestoTVDenoising
4.5.6DualityfortheTVDenoisingModel
4.5.7SolutionStructuresoftheTVDenoisingModel
4.6DenoisingviaNonlinearDiffusionandScale-SpaceTheory
4.6.1PeronaandMalik'sNonlinearDiffusionModel
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
6.1.4Shannon'sSamplingTheorem
6.1.5RadialBasisFunctionsandThin-PlateSplines
6.2ChallengesandGuidelinesfor2-DImageInpainting
6.2.1MainChallengesforImageInpainting
6.2.2GeneralGuidelinesforImageInpainting
6.3InpaintingofSobolevImages:Green'sFormulae
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
6.8ImageInpaintingviaEuler'sElasticasandCurvatures
6.8.1InpaintingBasedontheElasticaImageModel
6.8.2InpaintingviaMumford-Shah-EulerImageModel
6.9InpaintingofMeyer'sTexture
6.10ImageInpaintingwithMissingWaveletCoefficients
6.11PDEInpainting:Transport.Diffusion.andNavier-Stokes
6.11.1SecondOrderInterpolationModels
6.11.2AThirdOrderPDEInpaintingModelandNavier-Stokes
……
7ImageSegmentation
Bibliography
Index
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