Format:
1 Online-Ressource (xiv, 124 Seiten)
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Illustrationen
Edition:
Also available in print
ISBN:
1627053646
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9781627053648
Series Statement:
Synthesis lectures on computer graphics and animation #16
Content:
This book is a guide for researchers and practitioners to the new frontiers of 3D shape analysis and the complex mathematical tools most methods rely on. The target reader includes students, researchers and professionals with an undergraduate mathematics background, who wish to understand the mathematics behind shape analysis. The authors begin with a quick review of basic concepts in geometry, topology, differential geometry, and proceed to advanced notions of algebraic topology, always keeping an eye on the application of the theory, through examples of shape analysis methods such as 3D segmentation, correspondence, and retrieval. A number of research solutions in the field come from advances in pure and applied mathematics, as well as from the re-reading of classical theories and their adaptation to the discrete setting. In a world where disciplines (fortunately) have blurred boundaries, the authors believe that this guide will help to bridge the distance between theory and practice
Content:
1. About this book -- 1.1 Shape and shape analysis -- 1.2 Why math for 3D shape analysis? -- 1.3 What this book is and what it is not -- 1.4 Expected readers -- 1.5 How this book is organized --
Content:
10. Morse and Morse-Smale complexes -- 10.1 Basic concepts -- 10.2 Concepts in action --
Content:
11. Topological persistence -- 11.1 Basic concepts -- 11.2 Persistence diagrams -- 11.3 Persistence spaces -- 11.4 Concepts in action --
Content:
12. Beyond geometry and topology -- 12.1 3D textured shape retrieval -- 12.2 Qualitative organization of collections of 3D models -- 12.3 Recognition of functional parts of man-made objects --
Content:
13. Resources -- 13.1 Software -- 13.2 3D datasets and benchmarks -- 13.2.1 3D datasets -- 13.2.2 Benchmarks and contests -- Bibliography -- Authors' biographies
Content:
2. 3D shape analysis in a nutshell -- 2.1 3D shape analysis: problems and solutions -- 2.2 Applications --
Content:
3. Geometry, topology, and shape representation -- 3.1 Metric and metric spaces -- 3.2 Geodesic distance -- 3.3 Topological spaces -- 3.4 Continuous and smooth functions between topological spaces -- 3.5 Manifolds -- 3.6 Charts -- 3.7 Smooth manifold -- 3.8 Orientability -- 3.9 Tangent space -- 3.10 Riemannian manifold --
Content:
4. Differential geometry and shape analysis -- 4.1 Geodesic distances on surfaces -- 4.1.1 Computing geodesics on meshes -- 4.1.2 Concepts in action -- 4.2 Curvature on surfaces -- 4.2.1 Computing curvature on meshes -- 4.2.2 Concepts in action --
Content:
5. Spectral methods for shape analysis -- 5.1 Laplace operators -- 5.1.1 Concepts in action -- 5.2 Heat equation -- 5.2.1 Concepts in action --
Content:
6. Maps and distances between spaces -- 6.1 Space transformations -- 6.1.1 Isometries -- 6.1.2 Affine transformations -- 6.1.3 Mobius transformation -- 6.1.4 Concepts in action -- 6.2 Distances between spaces -- 6.2.1 Hausdorff metric -- 6.2.2 Bottleneck distance -- 6.2.3 Gromov-Hausdorff measure -- 6.2.4 Natural pseudo-distance --
Content:
7. Algebraic topology and topology invariants -- 7.1 Cell decompositions -- 7.1.1 Concepts in action -- 7.2 Homology -- 7.2.1 Concepts in action --
Content:
8. Differential topology and shape analysis -- 8.1 Critical points and Morse functions -- 8.1.1 Integral lines -- 8.1.2 Concepts in action -- 8.2 Topological analysis through (lower) level sets -- 8.3 Homology of manifolds --
Content:
9. Reeb graphs -- 9.1 Reeb graph definition -- 9.2 Reeb graphs on 2- and 3-manifolds -- 9.3 Concepts in action --
Note:
Abstract freely available; full-text restricted to subscribers or individual document purchasers
,
Includes bibliographical references (pages 103-121)
,
1. About this book1.1 Shape and shape analysis -- 1.2 Why math for 3D shape analysis? -- 1.3 What this book is and what it is not -- 1.4 Expected readers -- 1.5 How this book is organized
,
10. Morse and Morse-Smale complexes10.1 Basic concepts -- 10.2 Concepts in action
,
11. Topological persistence11.1 Basic concepts -- 11.2 Persistence diagrams -- 11.3 Persistence spaces -- 11.4 Concepts in action
,
12. Beyond geometry and topology12.1 3D textured shape retrieval -- 12.2 Qualitative organization of collections of 3D models -- 12.3 Recognition of functional parts of man-made objects
,
13. Resources13.1 Software -- 13.2 3D datasets and benchmarks -- 13.2.1 3D datasets -- 13.2.2 Benchmarks and contests -- Bibliography -- Authors' biographies.
,
2. 3D shape analysis in a nutshell2.1 3D shape analysis: problems and solutions -- 2.2 Applications
,
3. Geometry, topology, and shape representation3.1 Metric and metric spaces -- 3.2 Geodesic distance -- 3.3 Topological spaces -- 3.4 Continuous and smooth functions between topological spaces -- 3.5 Manifolds -- 3.6 Charts -- 3.7 Smooth manifold -- 3.8 Orientability -- 3.9 Tangent space -- 3.10 Riemannian manifold
,
4. Differential geometry and shape analysis4.1 Geodesic distances on surfaces -- 4.1.1 Computing geodesics on meshes -- 4.1.2 Concepts in action -- 4.2 Curvature on surfaces -- 4.2.1 Computing curvature on meshes -- 4.2.2 Concepts in action
,
5. Spectral methods for shape analysis5.1 Laplace operators -- 5.1.1 Concepts in action -- 5.2 Heat equation -- 5.2.1 Concepts in action
,
6. Maps and distances between spaces6.1 Space transformations -- 6.1.1 Isometries -- 6.1.2 Affine transformations -- 6.1.3 Mobius transformation -- 6.1.4 Concepts in action -- 6.2 Distances between spaces -- 6.2.1 Hausdorff metric -- 6.2.2 Bottleneck distance -- 6.2.3 Gromov-Hausdorff measure -- 6.2.4 Natural pseudo-distance
,
7. Algebraic topology and topology invariants7.1 Cell decompositions -- 7.1.1 Concepts in action -- 7.2 Homology -- 7.2.1 Concepts in action
,
8. Differential topology and shape analysis8.1 Critical points and Morse functions -- 8.1.1 Integral lines -- 8.1.2 Concepts in action -- 8.2 Topological analysis through (lower) level sets -- 8.3 Homology of manifolds
,
9. Reeb graphs9.1 Reeb graph definition -- 9.2 Reeb graphs on 2- and 3-manifolds -- 9.3 Concepts in action
,
Also available in print.
,
System requirements: Adobe Acrobat Reader.
,
Mode of access: World Wide Web.
Additional Edition:
ISBN 1627053638
Additional Edition:
ISBN 9781627053631
Additional Edition:
Print version Mathematical tools for shape analysis and description
Language:
English
DOI:
10.2200/S00588ED1V01Y201407CGR016
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