“An Introduction to Laplacian Spectral Kernels and Distances: Theory, Computation, and Applications” by Patane

  • ©Giuseppe Patane

Conference:


Entry Number: 03

Title:

    An Introduction to Laplacian Spectral Kernels and Distances: Theory, Computation, and Applications

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Abstract:


    Prerequisites
    Familiarity with linear algebra, discrete geometry processing, and computer graphics.

    Who Should Attend
    Graduate students and researchers interested in numerical geometry processing and spectral shape analysis.

    Level
    Intermediate

    Description
    This course explains the properties, discretization, computation, and main applications of the Laplace-Beltrami operator; the associated differential equations (harmonic equation, Laplacian eigenproblem, diffusion, and wave equations); the Laplacian spectral kernels; and distances (commute-time, biharmonic, wave, diffusion distances). While previous work has focused mainly on specific applications of theses topics on surface meshes, the course proposes a general approach that enables review of the Laplacian kernels and distances on surfaces and volumes, and for any choice of the Laplacian weights. Because it discusses all the reviewed numerical schemes for computation of the Laplacian spectral kernels and distances in terms of robustness, approximation accuracy, and computational cost, it supports selection of the most appropriate method with respect to shape representation, computational resources, and target applications.


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