ImageProcessingandAnalysis：Variational，PDE，Wavelet，andStochasticMethodsissystematicandwellorganized，Theauthorsfirstinvestigatethegeometric，functional，andatomicstructuresofimagesandthenrigorouslydevelopandanalyzeseveralimageprocessors.Thebookiscomprehensiveandintegrative，coveringthefourmostpowerfulclassesofmathematicaltoolsincontemporaryimageanalysisandprocessingwhileexploringtheirintrinsicconnectionsandintegration.Thematerialisbalancedintheoryandcomputation，followingasolidtheoreticalanalysisofmodelbuildingandperformancewithcomputationalimplementationandnumericalexamples.　　Thisbookiswrittenforgraduatestudentsandresearchersinappliedmathematics，computerscience，electricalengineering，andotherdisciplineswhoareinterestedinproblemsinimagingandcomputervision.Itcanbeusedasareferencebyscientistswithspecifictasksinimageprocessing，aswellasbyresearcherswithageneralinterestinfindingoutaboutthelatestadvances. ListofFiguresPreface1Introduction1.1DawningoftheEraofImagingSciences1.1.1ImageAcquisition1.1.2ImageProcessing1.1.3ImageInterpretationandVisualIntelligence1.2ImageProcessingbyExamples1.2.1ImageContrastEnhancement1.2.2ImageDenoisirg1.2.3ImageDeblurring1.2.4ImageInpainting1.2.5ImageSegmentation1.3AnOverviewofMethodologiesinImageProcessing1.3.1MorphologicalApproach1.3.2FourierandSpectralAnalysis1.3.3WaveletandSpace-ScaleAnalysis1.3.4StochasticModeling1.3.5VariaticnalMethods1.3.6PartialDifferentialEquations（PDEs）1.3.7DifferentApproachesAreIntrinsicallyInterconnected1.4OrganizationoftheBook1.5HowtoReadtheBcok2SomeModernImageAnalysisTools2.1GeometryofCurvesandSurfaces2.1.IGeometryofCurves2.1.2GeometryofSurfacesinThreeDimensions2.1.3HausdorffMeasuresandDimensions2.2FunctionswithBoundedVariations2.2.1TotalVariatienasaRadonMeasure2.2.2BasicPropertiesofBVFunctions2.2.3TheCo-AreaFormula2.3ElementsofThermodynamicsandStatisticalMechanics2.3.1EssentialsofThermodynamics2.3.2EntropyandPotentials2.3.3StatisticalMechanicsofEnsembles2.4BayesianStatisticalInference2.4.1ImageProcessingorVisualPerceptionasInference2.4.2BayesianInference：BiasDuetoPriorKnowledge2.4.3BayesianMethodinImageProcessing2.5LinearandNonlinearFilteringandDiffusion2.5.1PointSpreadingandMarkovTransition2.5.2LinearFilteringandDiffusion2.5.3NonlinearFilteringandDiffusion2.6WaveletsandMultiresolutionAnalysis2.6.1QuestforNewImageAnalysisTools2.6.2EarlyEdgeTheoryandMarr’sWavelets2.6.3WindowedFrequencyAnalysisandGaborWavelets2.6.4Frequency-WindowCoupling：Malvar-WilsonWavelets2.6.5TheFrameworkofMultiresolutionAnalysis（MRA）2.6.6FastImageAnalysisandSynthesisviaFilterBanks3ImageModelingandRepresentation3.1ModelingandRepresentation：What，Why，andHow3.2DeterministicImageModels3.2.1ImagesasDistributions（GeneralizedFunctions）3.2.2LpImages3.2.3SobolevImagesHn（Ω）3.2.4BVImages3.3WaveletsandMultiscaleRepresentation3.3.1Constructionof2-DWavelets3.3.2WaveletResponsestoTypicalImageFeatures3.3.3BesovImagesandSparseWaveletRepresentation3.4LatticeandRandomFieldRepr