几何偏微分方程和图象分析

图书标准信息

• 作者 G.Sapiro 著
• 出版社 世界图书出版公司
• 出版时间 2003-09
• 版次 1
• ISBN 9787506259415
• 定价 88.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 385页

【内容简介】

　　Thisbookisanintroductiontotheuseofgeometricpartialdifferentialequations(PDEs)inimageprocessingandcomputervision.Thisrelativelynewresearchareabringsanumberofnewconceptsintothefield，providing，amongotherthings，averyfundamentalandformalapproachtoimageprocessing.State-of-the-artpracticalresultsinproblemssuchasimagesegmentation，stereo，imageenhancement，distancecomputations，andobjecttrackinghavebeenobtainedwithalgorithmsbasedonPDEsformulations.

【作者简介】

　　GuillermoDapiroisaProfessorofElectricalandComputerEngineeringattheUniversityofMinnesota,whereheworksondifferentialgeometryandgeometricpartialdifferentialequation,bothintheoryandapplicationsincomputervision,imageanalysis,andcomputergraphic.

【目录】

Listoffigures
Preface
Acknowledgments
Introduction
1BasicMathematicalBackground
1.1PlanarDifferentialGeometry
1.2AffineDifferentialGeometry
1.3CartanMovingFrames
1.4SpaceCurves
1.5Three-DimensionalDifferentialGeometry
1.6DiscreteDifferentialGeometry
1.7DifferentialInvariantsandLieGroupTheory
1.8BasicConceptsofPartialDifferentialEquations
1.9CalculusofVariationsandGradientDescentFlows
1.10NumericalAnalysis

Exercises
2GeometricCurveandSurfaceEvolution
2.1BasicConcepts
2.2LevelSetsandImplicitRepresentations
2.3VariationalLevelSets
2.4ContinuousMathematicalMorphology
2.5EuclideanandaffineCurveEvolutionandShapeAnalysis
2.6EuclideanandAffineSurfaceEvolution
2.7Area-andVolume-Preserving3DFlows
2.8CalssificationofInvariantGeometricFlows

Exercises
3GeodesicCurvesandMinimalSurfaces
3.1BasicTwo-DimensionalDerivation
3.2Three-DimensionalDerivation
3.3GeodesicsinVector-ValuedImages
3.4FindingtheMinimalGeodesic
3.5AffineInvariantActiveContours
3.6AdditionalExtensionsandModitications
3.7TrackingandMorphingActiveContours
3.8Stereo
AppendixA
AppendixB

Exercises
4GeometricDiffusionofScalarImages
4.1GaussianFiliteringandLinearScaleSpaces
4.2Edge-StoppingDiffusion
4.3DirectionalDiffusion
4.4IntroducingPriorKnowledge
4.5SomeOrderinthePDEJungle
5GeometricDiffusionofVector-ValudeImages
6DiffusiononNonflatManifolds
7ContrastEnhancement
8AdditionalTheoriesandApplications
Bibliography
Index