几何偏微分方程和图像分析

1 (p1): 1 Basic Mathematical Background
2 (p1-1): 1.1．Planar Differential Geometry
7 (p1-2): 1.2．Affine Differential Geometry
12 (p1-3): 1.3．Cartan Moving Frames
15 (p1-4): 1.4．Space Curves
17 (p1-5): 1.5．Three-Dimensional Differential Geometry
20 (p1-6): 1.6．Discrete Differential Geometry
22 (p1-7): 1.7．Differential Invariants and Lie Group Theory
45 (p1-8): 1.8．Basic Concepts of Partial Differential Equations
57 (p1-9): 1.9．Calculus of Variations and Gradient Descent Flows
61 (p1-10): 1.10．Numerical Analysis
69 (p1-11): Exercises
71 (p2): 2 Geometric Curve and Surface Evolution
71 (p2-1): 2.1．Basic Concepts
74 (p2-2): 2.2．Level Sets and Implicit Representations
91 (p2-3): 2.3．Variational Level Sets
92 (p2-4): 2.4．Continuous Mathematical Morphology
99 (p2-5): 2.5．Euclidean and Affine Curve Evolution and Shape Analysis
129 (p2-6): 2.6．Euclidean and Affine Surface Evolution
131 (p2-7): 2.7．Area-and Volume-Preserving 3D Flows
134 (p2-8): 2.8．Classification of Invariant Geometric Flows
142 (p2-9): Exercises
143 (p3): 3 Geodesic Curves and Minimal Surfaces
143 (p3-1): 3.1．Basic Two-Dimensional Derivation
165 (p3-2): 3.2．Three-Dimensional Derivation
182 (p3-3): 3.3．Geodesics in Vector-Valued Images
191 (p3-4): 3.4．Finding the Minimal Geodesic
197 (p3-5): 3.5．Affine Invariant Active Contours
205 (p3-6): 3.6．Additional Extensions and Modifications
207 (p3-7): 3.7．Tracking and Morphing Active Contours
215 (p3-8): 3.8．Stereo
217 (p3-9): Appendix A
218 (p3-10): Appendix B
220 (p3-11): Exercises
221 (p4): 4 Geometric Diffusion of Scalar Images
221 (p4-1): 4.1．Gaussian Filtering and Linear Scale Spaces
223 (p4-2): 4.2．Edge-Stopping Diffusion
241 (p4-3): 4.3．Directional Diffusion
248 (p4-4): 4.4．Introducing Prior Knowledge
260 (p4-5): 4.5．Some Order in the PDE Jungle
265 (p4-6): Exercises
267 (p5): 5 Geometric Diffusion of Vector-Valued Images
267 (p5-1): 5.1．Directional Diffusion of Multivalued Images
269 (p5-2): 5.2．Vectorial Median Filter
281 (p5-3): 5.3．Color…