An Introduction to Laplacian Spectral Distances and Kernels : Theory, Computation, and Applications / by Giuseppe Patanè.

Format:

Book

Author/Creator:

Patanè, Giuseppe., Author.

Series:

Synthesis Lectures on Visual Computing: Computer Graphics, Animation, Computational Photography and Imaging, 2469-4223

Language:

English

Subjects (All):

Mathematics.

Image processing—Digital techniques.

Computer vision.

Computer Imaging, Vision, Pattern Recognition and Graphics.

Local Subjects:

Mathematics.

Computer Imaging, Vision, Pattern Recognition and Graphics.

Physical Description:

1 online resource (XX, 120 p.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

Summary:

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.

Contents:

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.

ISBN:

9783031025938

3031025938