1653046783

Ricci Flow for Shape Analysis and Surface Registration : Theories, Algorithms and Applications / by Wei Zeng, Xianfeng David Gu

Englisch

New York, NY : Springer New York, 2013

Online-Ressource (XI, 139 p. 69 illus., 49 illus. in color, online resource)

Description based upon print version of record

Druckausg.: Ricci flow for shape analysis and surface registration. - New York, NY [u.a.] : Springer, 2013. - XI, 139 S.

978-1-4614-8781-4

Weitere Ausgaben: 978-1-4614-8780-7 (Druckausgabe)

DOI: 10.1007/978-1-4614-8781-4

Preface; Contents; 1 Introduction; 1.1 Manifold and Riemannian Metric; 1.2 Ricci Flow; 1.3 Mappings Among Manifolds; Homeomorphism; Diffeomorphism; Isometric Mapping; Conformal Mapping; Area Preserving Mapping; Rigid Motion; 1.4 Shape Space; 1.5 Mapping Space; 1.6 Computational Frameworks; 1.6.1 Surface Classification; Homeomorphism Group; Conformal Transformation Group; Isometry Group; Rigid Motion Group; 1.6.2 Shape Comparison; 1.6.3 Surface Registration; 2 Surface Topology and Geometry; 2.1 Surface Topology; 2.1.1 Fundamental Group; 2.1.2 Covering Space; 2.2 Surface Differential Geometry

2.2.1 Movable Frame Method2.2.2 First and Second Fundamental Forms; 2.2.3 Curves on Surfaces; 2.3 Conformal Metric Deformation; 2.3.1 Isothermal Coordinates; 2.3.2 Gauss Curvature Under Conformal Deformation; 2.3.3 Geodesic Curvature Under Conformal Deformation; 2.4 Surface Ricci Flow; References; 3 Riemann Surface; 3.1 Conformal Structure; 3.2 Teichmüller Space; 3.3 Conformal Module; 3.3.1 Topological Sphere; 3.3.2 Topological Quadrilateral; 3.3.3 Topological Annulus; 3.3.4 Topological Disk; 3.3.5 Topological Multiply Connected Annulus; 3.3.6 Topological Torus

3.3.7 Genus One Surface with Boundaries3.3.8 High Genus Closed Surface; Fuchs Group; Poincaré Model; Fricke Coordinates; 3.3.9 High Genus Surface with Boundaries; 3.4 Quasi-Conformal Mapping; 3.4.1 Measurable Riemann Mapping; 3.4.2 Existence of Isothermal Coordinates; 3.4.3 Conformal Surface Representation; 3.4.4 Diffeomorphism Space and Beltrami Holomorphic Flow; 3.4.5 Teichmüller Map and Teichmüller Distance; 3.5 Harmonic Maps; 3.5.1 Topological Disk; 3.5.2 Genus Zero Closed Surface; 3.5.3 High Genus Closed Surface; 3.5.4 Teichmüller Space Representation; References

4 Discrete Surface Ricci Flow4.1 Discrete Surface; 4.1.1 Simplicial Complex; 4.1.2 Discrete Riemannian Metric and Curvature; 4.1.3 Discrete Gauss-Bonnet Theorem; 4.2 Euclidean Discrete Surface Ricci Flow; 4.2.1 Thurston's Intuition; 4.2.2 Discrete Conformal Metric Deformation; 4.2.3 Euclidean Derivative Cosine Law; 4.2.4 Discrete Ricci Energy; 4.2.5 Global Rigidity; Legendre Transformation; 4.2.6 Convergence Analysis; 4.2.7 Unified Euclidean Discrete Surface Ricci Flow; Generalized Schemes; Unified Theorems; Geometric Interpretation of Ricci Energy; 4.3 Hyperbolic Discrete Surface Ricci Flow

4.3.1 Hyperbolic Derivative Cosine Law4.3.2 Thurston's Circle Packing; 4.3.3 Discrete Hyperbolic Ricci Energy; 4.3.4 Generalized Schemes; Further Readings; References; 5 Algorithms and Applications; 5.1 Discrete Surface Ricci Flow Algorithm; 5.2 Registration and Tracking; Typical Types of Mappings; Common Framework; 5.2.1 Isometric and Conformal Mapping; Application; 5.2.2 Harmonic Mapping; Topological Disks; Topological Spheres; Topological Tori; High Genus Closed Surfaces; Surfaces with Boundaries; Application; 5.2.3 Quasi-Conformal Mapping; Solving Beltrami Equation

Optimization in Mapping Space

*Ricci-Fluss / Riemannsche Fläche

*Computer vision ; Computer science -- Mathematics ; Discrete groups ; Mathematics ; Geometry ; Optical data processing. ; Computer mathematics. ; Convex geometry . ; Discrete geometry. ; Mathematics ; Computer vision ; Computer science -- Mathematics ; Geometry ; Discrete groups

Klassifikation der Library of Congress: QA440-699

Dewey Dezimal-Klassifikation: 516; ; 516.362;

Dewey Dezimal-Klassifikation: 516

Regensburger Verbund-Klassifikation: SK 370: SA-SP Mathematik / SK Monografien / Differentialgeometrie, Tensoranalysis

Book Industry Communication: PBM

bisacsh: MAT012000

Mathematics Subject Classification: *53-02

Mathematics Subject Classification: 53A05

Mathematics Subject Classification: 53C44

Mathematics Subject Classification: 57N25

Mathematics Subject Classification: 54C56

Mathematics Subject Classification: 52B70

1. Introduction -- 2. Computational -- 3. Computational Geometry -- 4. Differential Geometry of Surface -- 5. Riemann Surface -- 6. Ricci Flow -- 7. Topological Algorithms -- 8. Harmonic Maps -- 9. Discrete Ricci Flow -- 10. Shape Analysis -- 11. Surface Diffeomorphism -- 12. Medical Imaging Applications -- 13. Computer Vision Applications -- 14. Computer Graphics Applications -- 15. Network Applications. .

Ricci Flow for Shape Analysis and Surface Registration introduces the beautiful and profound Ricci flow theory in a discrete setting. By using basic tools in linear algebra and multivariate calculus, readers can deduce all the major theorems in surface Ricci flow by themselves. The authors adapt the Ricci flow theory to practical computational algorithms, apply Ricci flow for shape analysis and surface registration, and demonstrate the power of Ricci flow in many applications in medical imaging, computer graphics, computer vision and wireless sensor network. Due to minimal pre-requisites, this book is accessible to engineers and medical experts, including educators, researchers, students and industry engineers who have an interest in solving real problems related to shape analysis and surface registration. .

https://zbmath.org/?q=an:1292.53004 [Zentralblatt MATH]

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https://doi.org/10.1007/978-1-4614-8781-4 [E-books (Springer)]