经典数学丛书（影印版）：图像分析中的模型和逆问题

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