Efficient Algorithms for Diffusion-Generated Motion by Mean Curvature
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Summary
This work proposes a new, spectral discretization of diffusion-generated methods which obtains greatly improved efficiency over the usual finite difference approach, by integrating Fourier modes exactly and by neglecting the contributions of rapidly decaying solution transients.
- Type
- article
- Published
- 1998-08-10
- Cited by
- 297
- References
- 75
- OpenAlex
- https://openalex.org/W1996075842
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:120523528
Keywords
Discretization, Curvature, Sharpening, Finite difference, Quadrature (astronomy)
References
- High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
- Chebyshev & Fourier Spectral Methods
- Three-phase boundary motions under constant velocities.
- Flow by mean curvature of convex surfaces into spheres
- Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature
- MATLAB : high-performance numeric computation and visualization software : エクスターナルインタフェースガイド
- The heat equation shrinking convex plane curves
- Maple V Language Reference Manual
- Applications of spatial data structures - computer graphics, image processing, and GIS
- Reaction-diffusion processes and evolution to harmonic maps
- The Surface Evolver
- A Simple Proof of Convergence for an Approximation Scheme for Computing Motions by Mean Curvature
- Multilevel computations of integral transforms and particle interactions with oscillatory kernels
- A Fast Level Set Method for Propagating Interfaces
- Finding half boundaries and junctions in images
- Fast reaction, slow diffusion, and curve shortening
- Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
- Computation of Self-Similar Solutions for Mean Curvature Flow
- On the Fast Fourier Transform of Functions with Singularities
- Implicit-Explicit Methods for Time-Dependent PDE''s
Cited by
- Edge Aware Anisotropic Diffusion for 3D Scalar Data
- Image Completion Using a Diffusion Driven Mean Curvature Flowin A Sub-Riemannian Space
- A Remark on the Discrete Deterministic Game Approach for Curvature Flow Equations
- Convergence of the thresholding scheme for multi-phase mean-curvature flow
- On geometric variational models for inpainting surface holes
- Modélisation numérique de la dynamique des globules rouges par la méthode des fonctions de niveau
- Edge aware anisotropic diffusion for 3D scalar data on regular lattices
- On a minimizing movement for diffusion-generated interfacial motions (The latest developments in theory and application on scientific computation)
- Curvature flows with junctions as model for capillary flows in complicated domains
- Numerical Methods for Evolutionary Differential Equations
- Graph Based Models for Unsupervised High Dimensional Data Clustering and Network Analysis
- A variational method for diffusion-generated area-preserving interface motion
- An Improved Level Set Method With Two Step Splitting Evolution
- A Simple Scheme for Volume-Preserving Motion by Mean Curvature
- Affine Morphological Multiscale Analysis of Corners and Multiple Junctions
- Geometric curve evolution and image processing
- Multi-class Graph Mumford-Shah Model for Plume Detection Using the MBO scheme
- Modeling Shape, Appearance and Self-Occlusions for Articulated Object Tracking
- Study of Image Local Scale Structure Using Nonlinear Diffusion
- Multi-scale representation and recognition of three dimensional surfaces using geometric invariants
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