| This book is an introduction to the use of geometric partial differential equations (PDEs) in image processing and computer vision. This relatively new research area brings a number of new concepts into the field, providing, among other things, a very fundamental and formal approach to image processing. State-of-the-art practical results in problems such as image segmentation, stereo, image enhancement, distance computations, and object tracking have been obtained with algorithms based on PDE's formulations. 此书为英文版！ |
| GuillermoDapiroisaProfessorofElectricalandComputerEngineeringattheUniversityofMinnesota,whereheworksondifferentialgeometryandgeometricpartialdifferentialequation,bothintheoryandapplicationsincomputervision,imageanalysis,andcomputergraphic. |
| 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 |
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