000 06373nam a2200757 i 4500
001 7987902
003 IEEE
005 20200413152925.0
006 m eo d
007 cr cn |||m|||a
008 170721s2017 caua foab 000 0 eng d
020 _a9781681731407
_qebook
020 _z9781681731391
_qprint
024 7 _a10.2200/S00781ED1V01Y201705VCP029
_2doi
035 _a(CaBNVSL)swl00407638
035 _a(OCoLC)994268518
040 _aCaBNVSL
_beng
_erda
_cCaBNVSL
_dCaBNVSL
050 4 _aQA448.D38
_bP275 2017
082 0 4 _a516.00285
_223
100 1 _aPatanè, Giuseppe,
_d1974-,
_eauthor.
245 1 3 _aAn introduction to Laplacian spectral distances and kernels :
_btheory, computation, and applications /
_cGiuseppe Patanè.
264 1 _a[San Rafael, California] :
_bMorgan & Claypool,
_c2017.
300 _a1 PDF (xxv, 113 pages) :
_billustrations.
336 _atext
_2rdacontent
337 _aelectronic
_2isbdmedia
338 _aonline resource
_2rdacarrier
490 1 _aSynthesis lectures on visual computing,
_x2469-4223 ;
_v# 29
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 93-112).
505 0 _a1. Laplace-Beltrami operator -- 1.1 Discrete Laplacians and spectral properties -- 1.1.1 Laplacian on graphs, meshes, and volumes -- 1.1.2 Laplacian matrix of point sets -- 1.2 Harmonic equation -- 1.3 Laplacian eigenproblem -- 1.3.1 Discrete Laplacian eigenfunctions -- 1.3.2 Stability of the Laplacian spectrum --
505 8 _a2. Heat and wave equations -- 2.1 Heat equation -- 2.1.1 Heat equation on surfaces and volumes -- 2.1.2 Optimal time value of the heat kernel -- 2.1.3 Comparison of the heat kernel at different scales -- 2.2 Wave equation -- 2.3 Discrete heat equation and kernel -- 2.3.1 Properties of the heat kernel -- 2.3.2 Linear independence of the heat kernel at different points and scales -- 2.4 Computation of the discrete heat kernel -- 2.4.1 Linear approximation -- 2.4.2 Polynomial approximation -- 2.4.3 Rational approximation -- 2.4.4 Special case: heat equation on volumes -- 2.5 Discussion --
505 8 _a3. Laplacian spectral distances -- 3.1 Green kernel and linear operator -- 3.2 Laplacian spectral operator and kernel -- 3.2.1 Laplacian spectral kernel -- 3.2.2 Spectrum of the spectral operator -- 3.3 Laplacian spectral distances -- 3.3.1 Well-posedness of the spectral kernels and distances -- 3.3.2 Scale invariance and shape signatures -- 3.4 Main examples of spectral distances -- 3.4.1 Selection of the filter map -- 3.4.2 Diffusion distances -- 3.4.3 Commute-time and biharmonic distances -- 3.4.4 Geodesic and transportation distances via heat kernel -- 3.5 Spectrum-free approximation -- 3.5.1 Polynomial filter -- 3.5.2 Arbitrary filter: polynomial approximation -- 3.5.3 Arbitrary filter: rational approximation -- 3.5.4 Arbitrary filter: factorization of the rational approximation -- 3.5.5 Convergence and accuracy --
505 8 _a4. Discrete spectral distances -- 4.1 Discrete spectral kernels and distances -- 4.2 Native spectral spaces -- 4.3 Computation of the spectral distances -- 4.3.1 Truncated approximation -- 4.3.2 Spectrum-free approximation -- 4.3.3 A unified spectrum-free computation -- 4.4 Discussion --
505 8 _a5. Applications -- 5.1 Design of scalar functions with constrained critical points -- 5.2 Laplacian smoothing of scalar functions -- 5.2.1 Related work on smoothing -- 5.2.2 Unconstrained and constrained Laplacian smoothing of scalar functions --
505 8 _a6. Conclusions -- Bibliography -- Author's biography.
506 _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 _aIn geometry processing and shape analysis, several applications have been addressed through the properties of the Laplacian spectral kernels and distances, such as commute-time, biharmonic, diffusion, and wave distances. Within this context, this book is intended to provide a common background on the definition and computation of the Laplacian spectral kernels and distances for geometry processing and shape analysis. To this end, we define a unified representation of the isotropic and anisotropic discrete Laplacian operator on surfaces and volumes; then, we introduce the associated differential equations, i.e., the harmonic equation, the Laplacian eigenproblem, and the heat equation. Filtering the Laplacian spectrum, we introduce the Laplacian spectral distances, which generalize the commute-time, biharmonic, diffusion, and wave distances, and their discretization in terms of the Laplacian spectrum. As main applications, we discuss the design of smooth functions and the Laplacian smoothing of noisy scalar functions. All the reviewed numerical schemes are discussed and compared in terms of robustness, approximation accuracy, and computational cost, thus supporting the reader in the selection of the most appropriate with respect to shape representation, computational resources, and target application.
530 _aAlso available in print.
588 _aTitle from PDF title page (viewed on July 21, 2017).
650 0 _aGeometry
_xData processing.
650 0 _aShapes
_xComputer simulation
_xMathematics.
650 0 _aComputer graphics
_xMathematics.
650 0 _aLaplacian operator.
650 0 _aHarmonic functions.
653 _aLaplace-Beltrami operator
653 _aLaplacian spectrum
653 _aharmonic equation
653 _aLaplacian eigenproblem
653 _aheat equation
653 _adiffusion geometry
653 _aLaplacian spectral distance and kernels
653 _aspectral geometry processing
653 _ashape analysis
653 _anumerical analysis
655 0 _aElectronic books.
776 0 8 _iPrint version:
_z9781681731391
830 0 _aSynthesis digital library of engineering and computer science.
830 0 _aSynthesis lectures on visual computing ;
_v# 29.
_x2469-4223
856 4 2 _3Abstract with links to resource
_uhttp://ieeexplore.ieee.org/servlet/opac?bknumber=7987902
999 _c562274
_d562274