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.
作者简介
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.
目录
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 Morphology 2.5 Euclidean and affine Curve Evolution and Shape Analysis 2.6 Euclidean and Affine Surface Evolution 2.7 Area-and Volume-Preserving 3D Flows 2.8 Calssification of Invariant Geometric Flows Exercises 3 Geodesic Curves and Minimal Surfaces 3.1 Basic Two-Dimensional Derivation 3.2 Three-Dimensional Derivation 3.3 Geodesics in Vector-Valued Images 3.4 Finding the Minimal Geodesic 3.5 Affine Invariant Active Contours 3.6 Additional Extensions and Moditications 3.7 Tracking and Morphing Active Contours 3.8 Stereo Appendix A Appendix B Exercises 4 Geometric Diffusion of Scalar Images 4.1 Gaussian Filitering and Linear Scale Spaces 4.2 Edge-Stopping Diffusion 4.3 Directional Diffusion 4.4 Introducing Prior Knowledge 4.5 Some Order in the PDE Jungle 5 Geometric Diffusion of Vector-Valude Images 6 Diffusion on Nonflat Manifolds 7 Contrast Enhancement 8 Additional Theories and Applications Bibliography Index
