An Introduction to Laplacian Spectral Distances and Kernels : Theory, Computation, and Applications
Patanè, Giuseppe, 1974-
An Introduction to Laplacian Spectral Distances and Kernels : Theory, Computation, and Applications by Giuseppe Patanè - 1st edition 2017 - 1 recurso en línea (XX, 120 páginas) - Synthesis Lectures on Visual Computing: Computer Graphics Animation Computational Photography and Imaging 2469-4223 .
List 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.
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.
9783031025938
10.1007/978-3-031-02593-8 doi
Geometría--Proceso de datos
Gráficos de ordenador--Matemáticas
Funciones armónicas
QA448.D38 / 2017 EB
An Introduction to Laplacian Spectral Distances and Kernels : Theory, Computation, and Applications by Giuseppe Patanè - 1st edition 2017 - 1 recurso en línea (XX, 120 páginas) - Synthesis Lectures on Visual Computing: Computer Graphics Animation Computational Photography and Imaging 2469-4223 .
List 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.
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.
9783031025938
10.1007/978-3-031-02593-8 doi
Geometría--Proceso de datos
Gráficos de ordenador--Matemáticas
Funciones armónicas
QA448.D38 / 2017 EB