000 06678nam a2200913 i 4500
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
020 _z9781627053631
_qprint
024 7 _a10.2200/S00588ED1V01Y201407CGR016
_2doi
035 _a(CaBNVSL)swl00403922
035 _a(OCoLC)890973864
040 _aCaBNVSL
_beng
_erda
_cCaBNVSL
_dCaBNVSL
050 4 _aTA1637.5
_b.B525 2014
082 0 4 _a006.6
_223
090 _a
_bMoCl
_e201407CGR016
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.
300 _a1 PDF (xiv, 124 pages) :
_billustrations.
336 _atext
_2rdacontent
337 _aelectronic
_2isbdmedia
338 _aonline resource
_2rdacarrier
490 1 _aSynthesis lectures on computer graphics and animation,
_x1933-9003 ;
_v# 16
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.
650 0 _aShapes
_xMathematics.
650 0 _aForm perception
_xMathematics.
650 0 _aImage analysis
_xMathematics.
650 0 _aThree-dimensional imaging
_xMathematics.
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.
700 1 _aGiorgi, Daniela
_c(Mathematician),
_eauthor.
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