Open Daily: 10am - 10pm | Alley door pickup 10am - 7pm 3038 Hennepin Ave Minneapolis, MN
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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
An Introduction to Laplacian Spectral Distances and Kernels: Theory, Computation, and Applications

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

Patanè, Giuseppe

Paperback

Series: Synthesis Lectures on Visual Computing: Computer Graphics, A

General ComputersGeneral MathematicsGeometry

ISBN10: 3031014650
ISBN13: 9783031014659
Publisher: Springer Nature
Published: Jul 5 2017
Pages: 120
Weight: 0.56
Height: 0.30 Width: 7.50 Depth: 9.25
Language: English

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.

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