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Part of the book series: Synthesis Lectures on Visual Computing: Computer Graphics, Animation, Computational Photography and Imaging (SLVCCGACPI)
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About this book
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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Table of contents (6 chapters)
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Bibliographic Information
Book Title: An Introduction to Laplacian Spectral Distances and Kernels
Book Subtitle: Theory, Computation, and Applications
Authors: Giuseppe Patanè
Series Title: Synthesis Lectures on Visual Computing: Computer Graphics, Animation, Computational Photography and Imaging
DOI: https://doi.org/10.1007/978-3-031-02593-8
Publisher: Springer Cham
eBook Packages: Synthesis Collection of Technology (R0), eBColl Synthesis Collection 7
Copyright Information: Springer Nature Switzerland AG 2017
Softcover ISBN: 978-3-031-01465-9Published: 05 July 2017
eBook ISBN: 978-3-031-02593-8Published: 31 May 2022
Series ISSN: 2469-4215
Series E-ISSN: 2469-4223
Edition Number: 1
Number of Pages: XX, 120
Topics: Mathematics, general, Computer Imaging, Vision, Pattern Recognition and Graphics