000 | 06678nam a2200913 i 4500 | ||
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001 | 6909386 | ||
003 | IEEE | ||
005 | 20200413152915.0 | ||
006 | m eo d | ||
007 | cr cn |||m|||a | ||
008 | 140918s2014 caua foab 000 0 eng d | ||
020 |
_a9781627053648 _qebook |
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020 |
_z9781627053631 _qprint |
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024 | 7 |
_a10.2200/S00588ED1V01Y201407CGR016 _2doi |
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035 | _a(CaBNVSL)swl00403922 | ||
035 | _a(OCoLC)890973864 | ||
040 |
_aCaBNVSL _beng _erda _cCaBNVSL _dCaBNVSL |
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050 | 4 |
_aTA1637.5 _b.B525 2014 |
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082 | 0 | 4 |
_a006.6 _223 |
090 |
_a _bMoCl _e201407CGR016 |
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100 | 1 |
_aBiasotti, Silvia., _eauthor. |
|
245 | 1 | 0 |
_aMathematical tools for shape analysis and description / _cSilvia Biasotti, Bianca Falcidieno, Daniela Giorgi, and Michela Spagnuolo. |
264 | 1 |
_aSan Rafael, California (1537 Fourth Street, San Rafael, CA 94901 USA) : _bMorgan & Claypool, _c2014. |
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300 |
_a1 PDF (xiv, 124 pages) : _billustrations. |
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336 |
_atext _2rdacontent |
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337 |
_aelectronic _2isbdmedia |
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338 |
_aonline resource _2rdacarrier |
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490 | 1 |
_aSynthesis lectures on computer graphics and animation, _x1933-9003 ; _v# 16 |
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538 | _aMode of access: World Wide Web. | ||
538 | _aSystem requirements: Adobe Acrobat Reader. | ||
500 | _aPart of: Synthesis digital library of engineering and computer science. | ||
504 | _aIncludes bibliographical references (pages 103-121). | ||
505 | 0 | _a1. 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 -- | |
505 | 8 | _a2. 3D shape analysis in a nutshell -- 2.1 3D shape analysis: problems and solutions -- 2.2 Applications -- | |
505 | 8 | _a3. 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 -- | |
505 | 8 | _a4. 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 -- | |
505 | 8 | _a5. 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 -- | |
505 | 8 | _a6. 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 -- | |
505 | 8 | _a7. Algebraic topology and topology invariants -- 7.1 Cell decompositions -- 7.1.1 Concepts in action -- 7.2 Homology -- 7.2.1 Concepts in action -- | |
505 | 8 | _a8. 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 -- | |
505 | 8 | _a9. Reeb graphs -- 9.1 Reeb graph definition -- 9.2 Reeb graphs on 2- and 3-manifolds -- 9.3 Concepts in action -- | |
505 | 8 | _a10. Morse and Morse-Smale complexes -- 10.1 Basic concepts -- 10.2 Concepts in action -- | |
505 | 8 | _a11. Topological persistence -- 11.1 Basic concepts -- 11.2 Persistence diagrams -- 11.3 Persistence spaces -- 11.4 Concepts in action -- | |
505 | 8 | _a12. 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 -- | |
505 | 8 | _a13. Resources -- 13.1 Software -- 13.2 3D datasets and benchmarks -- 13.2.1 3D datasets -- 13.2.2 Benchmarks and contests -- Bibliography -- Authors' biographies. | |
506 | 1 | _aAbstract freely available; full-text restricted to subscribers or individual document purchasers. | |
510 | 0 | _aCompendex | |
510 | 0 | _aINSPEC | |
510 | 0 | _aGoogle scholar | |
510 | 0 | _aGoogle book search | |
520 | 3 | _aThis 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. | |
530 | _aAlso available in print. | ||
588 | _aTitle from PDF title page (viewed on September 18, 2014). | ||
650 | 0 |
_aImage processing _xDigital techniques _xMathematics. |
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650 | 0 |
_aShapes _xMathematics. |
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650 | 0 |
_aForm perception _xMathematics. |
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650 | 0 |
_aImage analysis _xMathematics. |
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650 | 0 |
_aThree-dimensional imaging _xMathematics. |
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653 | _acomputational topology | ||
653 | _adifferential geometry | ||
653 | _aalgebraic topology | ||
653 | _aspectral methods | ||
653 | _ashape invariants | ||
653 | _adistance measures | ||
653 | _ashape transformations | ||
653 | _a3D shape analysis | ||
653 | _a3D shape description | ||
653 | _a3D shape retrieval | ||
653 | _aMorse theory | ||
653 | _atopological persistence | ||
700 | 1 |
_aFalcidieno, B. _q(Bianca), _eauthor. |
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700 | 1 |
_aGiorgi, Daniela _c(Mathematician), _eauthor. |
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700 | 1 |
_aSpagnuolo, Michela., _eauthor. |
|
776 | 0 | 8 |
_iPrint version: _z9781627053631 |
830 | 0 | _aSynthesis digital library of engineering and computer science. | |
830 | 0 |
_aSynthesis lectures in computer graphics and animation ; _v# 16. _x1933-9003 |
|
856 | 4 | 0 |
_3Abstract with links to full text _uhttp://dx.doi.org/10.2200/S00588ED1V01Y201407CGR016 |
856 | 4 | 2 |
_3Abstract with links to resource _uhttp://ieeexplore.ieee.org/servlet/opac?bknumber=6909386 |
999 |
_c562086 _d562086 |