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

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FMX Conference

Courses

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

Sunday, 30 July, 10:45 am - 12:15 pm, Los Angeles Convention Center, Los Angeles Convention Center - Room 402AB

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.

Level

Intermediate

Prerequisites

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

Intended Audience

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

Instructor(s)

Giuseppe Patane
L'istituto di Matematica Applicata e Tecnologie Informatiche