Physical description 
1 PDF (xiv, 124 pages) : illustrations. 

polychrome rdacc 
Series 
Synthesis lectures on computer graphics and animation, 19339003 ; # 16.


Synthesis digital library of engineering and computer science.


Synthesis lectures in computer graphics and animation ; # 16. 19339003.

Notes 
Part of: Synthesis digital library of engineering and computer science. 
Bibliography 
Includes bibliographical references (pages 103121). 
Contents 
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  

2. 3D shape analysis in a nutshell  2.1 3D shape analysis: problems and solutions  2.2 Applications  

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  

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  

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  

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 GromovHausdorff measure  6.2.4 Natural pseudodistance  

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  

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  

9. Reeb graphs  9.1 Reeb graph definition  9.2 Reeb graphs on 2 and 3manifolds  9.3 Concepts in action  

10. Morse and MorseSmale complexes  10.1 Basic concepts  10.2 Concepts in action  

11. Topological persistence  11.1 Basic concepts  11.2 Persistence diagrams  11.3 Persistence spaces  11.4 Concepts in action  

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 manmade objects  

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. 
Restrictions 
Abstract freely available; fulltext restricted to subscribers or individual document purchasers. 
Summary 
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 rereading 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. 
Other formats 
Also available in print. 
System notes 
Mode of access: World Wide Web. 

System requirements: Adobe Acrobat Reader. 
Notes 
Title from PDF title page (viewed on September 18, 2014). 
Other author 
Falcidieno, B. (Bianca), author.


Giorgi, Daniela (Mathematician), author.


Spagnuolo, Michela, author.

Subject 
Image processing  Digital techniques  Mathematics.


Shapes  Mathematics.


Form perception  Mathematics.


Image analysis  Mathematics.


Threedimensional imaging  Mathematics.


computational topology. 

differential geometry. 

algebraic topology. 

spectral methods. 

shape invariants. 

distance measures. 

shape transformations. 

3D shape analysis. 

3D shape description. 

3D shape retrieval. 

Morse theory. 

topological persistence. 
Standard Number 
10.2200/S00588ED1V01Y201407CGR016 
ISBN 
9781627053648 (ebook) 

9781627053631 (print) 