An Introduction to Laplacian Spectral Distances and Kernels

An Introduction to Laplacian Spectral Distances and Kernels
Author :
Publisher : Morgan & Claypool Publishers
Total Pages : 141
Release :
ISBN-10 : 9781681731407
ISBN-13 : 1681731401
Rating : 4/5 (07 Downloads)

Book Synopsis An Introduction to Laplacian Spectral Distances and Kernels by : Giuseppe Patanè

Download or read book An Introduction to Laplacian Spectral Distances and Kernels written by Giuseppe Patanè and published by Morgan & Claypool Publishers. This book was released on 2017-07-05 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 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.


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