• 经典数学丛书(影印版):图像分析中的模型和逆问题
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经典数学丛书(影印版):图像分析中的模型和逆问题

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作者[法]查蒙德(Chalmond B.) 著

出版社世界图书出版公司

出版时间2014-11

版次1

印数1千册

装帧平装

上书时间2021-11-20

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图书标准信息
  • 作者 [法]查蒙德(Chalmond B.) 著
  • 出版社 世界图书出版公司
  • 出版时间 2014-11
  • 版次 1
  • ISBN 9787510070198
  • 定价 59.00元
  • 装帧 平装
  • 开本 24开
  • 纸张 胶版纸
  • 页数 309页
  • 正文语种 英语
  • 丛书 经典数学丛书
【内容简介】
  Inthelastdecadeofthepastcenturlrwewitnessedanexceptionalparticipationofmathematiciansinthedevelopmentofdigitalimageprocessingasascience.Thesecontributionshavefoundanaturalplaceatthelowlevelofprocessing,withtheadventofmathematicalmorphology,differentialequations,Markovrandomfields,andwavelettheory.Theyarealsoreflectedintheincreasinglyimportantrolemodelinghasplayedinsolvingcomplexproblems.
  Althoughmodelingisoftenahiddenstageofthesolution,thebenefitsofcorrectlymodelinganimageprocessingproblemarehuge.Modelingistheveryplacewhere"sensitivity"stealsaleadover"geometry",toputitinPascal'swords,Correctmodelingintroducesinformationthatcannotbeexpressedbydataordeducedbyequations,butrefiectsthesubtledependencyorcausalitybetweentheingredients.Modelinghasmoretodowithpotsandpansthanrecipesandspices,todrawouttheculinarymetaphor.BernardChalmond'sworkismainlydedicatedtomodelingissues.Itdoesnotfullycoverthisfield,sinceitismostlyconcernedwithtwotypesofmodel:Bayesianmodelsissuedfromprobabilitytheoryandenergy-basedmodelsderivedfromphysicsandmechanics.Withinthescopeofthesemodels,thebookdeeplyexploresthevariousconsequencesofthechoiceofamodel;itcomparestheirhypotheses,discussestheirmerits,explorestheirvalidity,andsuggestspossiblefieldsofapplication.
  Thisbookfulfillsaneedinthefieldofcomputerscienceresearchandeducation.Itisnotintendedforprofessionalmathematicians,butitundoubtedlydealswithappliedmathematics.
【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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