The Resource Mathematical tools for shape analysis and description, Silvia Biasotti, Bianca Falcidieno, Daniela Giorgi, and Michela Spagnuolo, (electronic book)
Mathematical tools for shape analysis and description, Silvia Biasotti, Bianca Falcidieno, Daniela Giorgi, and Michela Spagnuolo, (electronic book)
Resource Information
The item Mathematical tools for shape analysis and description, Silvia Biasotti, Bianca Falcidieno, Daniela Giorgi, and Michela Spagnuolo, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Sydney Jones Library, University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Mathematical tools for shape analysis and description, Silvia Biasotti, Bianca Falcidieno, Daniela Giorgi, and Michela Spagnuolo, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Sydney Jones Library, University of Liverpool.
This item is available to borrow from 1 library branch.
- 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 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
- Language
- eng
- Extent
- 1 PDF (xiv, 124 pages)
- 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 Gromov-Hausdorff measure -- 6.2.4 Natural pseudo-distance --
- 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 3-manifolds -- 9.3 Concepts in action --
- 10. Morse and Morse-Smale 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 man-made 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
- Isbn
- 9781627053648
- Label
- Mathematical tools for shape analysis and description
- Title
- Mathematical tools for shape analysis and description
- Statement of responsibility
- Silvia Biasotti, Bianca Falcidieno, Daniela Giorgi, and Michela Spagnuolo
- Language
- eng
- 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 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
- Cataloging source
- CaBNVSL
- http://library.link/vocab/creatorName
- Biasotti, Silvia
- Dewey number
- 006.6
- Illustrations
- illustrations
- Index
- no index present
- LC call number
- TA1637.5
- LC item number
- .B525 2014
- Literary form
- non fiction
- Nature of contents
-
- dictionaries
- abstracts summaries
- bibliography
- http://library.link/vocab/relatedWorkOrContributorName
-
- Falcidieno, B.
- Giorgi, Daniela
- Spagnuolo, Michela.
- http://library.link/vocab/subjectName
-
- Image processing
- Shapes
- Form perception
- Image analysis
- Three-dimensional imaging
- Target audience
-
- adult
- specialized
- Label
- Mathematical tools for shape analysis and description, Silvia Biasotti, Bianca Falcidieno, Daniela Giorgi, and Michela Spagnuolo, (electronic book)
- Bibliography note
- Includes bibliographical references (pages 103-121)
- Color
- multicolored
- 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 Gromov-Hausdorff measure -- 6.2.4 Natural pseudo-distance --
- 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 3-manifolds -- 9.3 Concepts in action --
- 10. Morse and Morse-Smale 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 man-made 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
- Control code
- 201407CGR016
- Dimensions
- unknown
- Extent
- 1 PDF (xiv, 124 pages)
- File format
- multiple file formats
- Form of item
- online
- Isbn
- 9781627053648
- Other control number
- 10.2200/S00588ED1V01Y201407CGR016
- Other physical details
- illustrations.
- Reformatting quality
- access
- Specific material designation
- remote
- System details
- System requirements: Adobe Acrobat Reader
- Label
- Mathematical tools for shape analysis and description, Silvia Biasotti, Bianca Falcidieno, Daniela Giorgi, and Michela Spagnuolo, (electronic book)
- Bibliography note
- Includes bibliographical references (pages 103-121)
- Color
- multicolored
- 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 Gromov-Hausdorff measure -- 6.2.4 Natural pseudo-distance --
- 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 3-manifolds -- 9.3 Concepts in action --
- 10. Morse and Morse-Smale 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 man-made 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
- Control code
- 201407CGR016
- Dimensions
- unknown
- Extent
- 1 PDF (xiv, 124 pages)
- File format
- multiple file formats
- Form of item
- online
- Isbn
- 9781627053648
- Other control number
- 10.2200/S00588ED1V01Y201407CGR016
- Other physical details
- illustrations.
- Reformatting quality
- access
- Specific material designation
- remote
- System details
- System requirements: Adobe Acrobat Reader
Subject
- Three-dimensional imaging -- Mathematics
- Form perception -- Mathematics
- Image analysis -- Mathematics
- Image processing -- Digital techniques | Mathematics
- Shapes -- Mathematics
Member of
- Synthesis lectures in computer graphics and animation, 16
- Online access with purchase: Morgan & Claypool (Synthesis Collection Five)
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Mathematical-tools-for-shape-analysis-and/ZRiSg5Fs4Tk/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Mathematical-tools-for-shape-analysis-and/ZRiSg5Fs4Tk/">Mathematical tools for shape analysis and description, Silvia Biasotti, Bianca Falcidieno, Daniela Giorgi, and Michela Spagnuolo, (electronic book)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">Sydney Jones Library, University of Liverpool</a></span></span></span></span></div>
