几何偏微分方程和图象分析
2003-9
世界图书出版公司
G.Sapiro
385
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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 PDEs formulations.
Guillermo Dapiro is a Professor of Electrical and Computer Engineering at the University of Minnesota, where he works on differential geometry and geometric partial differential equation, both in theory and applications in computer vision, image analysis, and computer graphic.
List of figures Preface Acknowledgments Introduction 1 Basic Mathematical Background 1.1 Planar Differential Geometry 1.2 Affine Differential Geometry 1.3 Cartan Moving Frames 1.4 Space Curves 1.5 Three-Dimensional Differential Geometry 1.6 Discrete Differential Geometry 1.7 Differential Invariants and Lie Group Theory 1.8 Basic Concepts of Partial Differential Equations 1.9 Calculus of Variations and Gradient Descent Flows 1.10 Numerical Analysis Exercises 2 Geometric Curve and Surface Evolution 2.1 Basic Concepts 2.2 Level Sets and Implicit Representations 2.3 Variational Level Sets 2.4 Continuous Mathematical Morphology2.5 Euclidean and affine Curve Evolution and Shape Analysis2.6 Euclidean and Affine Surface Evolution2.7 Area-and Volume-Preserving 3D Flows2.8 Calssification of Invariant Geometric Flows Exercises 3 Geodesic Curves and Minimal Surfaces3.1 Basic Two-Dimensional Derivation3.2 Three-Dimensional Derivation3.3 Geodesics in Vector-Valued Images3.4 Finding the Minimal Geodesic3.5 Affine Invariant Active Contours3.6 Additional Extensions and Moditications3.7 Tracking and Morphing Active Contours3.8 StereoAppendix AAppendix B Exercises 4 Geometric Diffusion of Scalar Images4.1 Gaussian Filitering and Linear Scale Spaces4.2 Edge-Stopping Diffusion4.3 Directional Diffusion4.4 Introducing Prior Knowledge4.5 Some Order in the PDE Jungle5 Geometric Diffusion of Vector-Valude Images6 Diffusion on Nonflat Manifolds7 Contrast Enhancement8 Additional Theories and ApplicationsBibliographyIndex
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.
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