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020 _a9783031025938
_9978-3-031-02593-8
024 7 _a10.1007/978-3-031-02593-8
_2doi
050 4 _aQA1-939
072 7 _aPB
_2bicssc
072 7 _aMAT000000
_2bisacsh
072 7 _aPB
_2thema
082 0 4 _a510
_223
100 1 _aPatanè, Giuseppe.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981560
245 1 3 _aAn Introduction to Laplacian Spectral Distances and Kernels
_h[electronic resource] :
_bTheory, Computation, and Applications /
_cby Giuseppe Patanè.
250 _a1st ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXX, 120 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSynthesis Lectures on Visual Computing: Computer Graphics, Animation, Computational Photography and Imaging,
_x2469-4223
505 0 _aList of Figures -- List of Tables -- Preface -- Acknowledgments -- Laplace Beltrami Operator -- Heat and Wave Equations -- Laplacian Spectral Distances -- Discrete Spectral Distances -- Applications -- Conclusions -- Bibliography -- Author's Biography.
520 _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.
650 0 _aMathematics.
_911584
650 0 _aImage processing
_xDigital techniques.
_94145
650 0 _aComputer vision.
_981561
650 1 4 _aMathematics.
_911584
650 2 4 _aComputer Imaging, Vision, Pattern Recognition and Graphics.
_931569
710 2 _aSpringerLink (Online service)
_981562
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031014659
776 0 8 _iPrinted edition:
_z9783031037214
830 0 _aSynthesis Lectures on Visual Computing: Computer Graphics, Animation, Computational Photography and Imaging,
_x2469-4223
_981563
856 4 0 _uhttps://doi.org/10.1007/978-3-031-02593-8
912 _aZDB-2-SXSC
942 _cEBK
999 _c85198
_d85198