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几何偏微分方程和图像分析PDF|Epub|txt|kindle电子书版本网盘下载

Sapiro，G.编著
出版社：北京;西安：世界图书出版公司
ISBN：7506259419
出版时间：2003
标注页数：385页
文件大小：55MB
文件页数：409页
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图书目录

1 Basic Mathematical Background1

1.1．Planar Differential Geometry2

1.2．Affine Differential Geometry7

1.3．Cartan Moving Frames12

1.4．Space Curves15

1.5．Three-Dimensional Differential Geometry17

1.6．Discrete Differential Geometry20

1.7．Differential Invariants and Lie Group Theory22

1.8．Basic Concepts of Partial Differential Equations45

1.9．Calculus of Variations and Gradient Descent Flows57

1.10．Numerical Analysis61

Exercises69

2 Geometric Curve and Surface Evolution71

2.1．Basic Concepts71

2.2．Level Sets and Implicit Representations74

2.3．Variational Level Sets91

2.4．Continuous Mathematical Morphology92

2.5．Euclidean and Affine Curve Evolution and Shape Analysis99

2.6．Euclidean and Affine Surface Evolution129

2.7．Area-and Volume-Preserving 3D Flows131

2.8．Classification of Invariant Geometric Flows134

Exercises142

3 Geodesic Curves and Minimal Surfaces143

3.1．Basic Two-Dimensional Derivation143

3.2．Three-Dimensional Derivation165

3.3．Geodesics in Vector-Valued Images182

3.4．Finding the Minimal Geodesic191

3.5．Affine Invariant Active Contours197

3.6．Additional Extensions and Modifications205

3.7．Tracking and Morphing Active Contours207

3.8．Stereo215

Appendix A217

Appendix B218

Exercises220

4 Geometric Diffusion of Scalar Images221

4.1．Gaussian Filtering and Linear Scale Spaces221

4.2．Edge-Stopping Diffusion223

4.3．Directional Diffusion241

4.4．Introducing Prior Knowledge248

4.5．Some Order in the PDE Jungle260

Exercises265

5 Geometric Diffusion of Vector-Valued Images267

5.1．Directional Diffusion of Multivalued Images267

5.2．Vectorial Median Filter269

5.3．Color Self-Snakes281

Exercises283

6 Diffusion on Nonflat Manifolds284

6.1．The General Problem287

6.2．Isotropic Diffusion290

6.3．Anisotropic Diffusion292

6.4．Examples293

6.5．Vector Probability Diffusion298

Appendix304

Exercises305

7 Contrast Enhancement307

7.1．Global PDE-Based Approach310

7.2．Shape-Preserving Contrast Enhancement325

Exercises337

8 Additional Theories and Applications338

8.1 Interpolation338

8.2．Image Repair:Inpainting343

8.3．Shape from Shading355

8.4．Blind Deconvolution357

Exercises358

Bibliography359

Index381