Riemannian Fast-Marching on Cartesian Grids, Using Voronoi's First Reduction of Quadratic Forms
From MaRDI portal
Publication:5244392
DOI10.1137/17M1127466zbMath1447.65114OpenAlexW2923052940WikidataQ115246943 ScholiaQ115246943MaRDI QIDQ5244392
Publication date: 21 November 2019
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/17m1127466
Riemannian metriceikonal equationsub-Riemannian metricfast-marching methodVoronoi reductionRander metric
Dynamic programming in optimal control and differential games (49L20) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for boundary value problems involving PDEs (65N06) Existence theories for optimal control problems involving partial differential equations (49J20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Boundary value problems for nonlinear first-order PDEs (35F30)
Related Items
Monotone discretization of the Monge–Ampère equation of optimal transport, A linear finite-difference scheme for approximating randers distances on cartesian grids, Single pass computation of first seismic wave travel time in three dimensional heterogeneous media with general anisotropy, Monotone and Second Order Consistent Scheme for the Two Dimensional Pucci Equation, Second order monotone finite differences discretization of linear anisotropic differential operators
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Geodesic distance and curves through isotropic and anisotropic heat equations on images and surfaces
- Convergence rate for the ordered upwind method
- A fast marching method for Hamilton-Jacobi equations modeling monotone front propagations
- A numerical approach to the infinite horizon problem of deterministic control theory
- Zermelo navigation on Riemannian manifolds
- Optimal paths for variants of the 2D and 3D Reeds-Shepp car with applications in image analysis
- Fast sweeping methods for factored anisotropic eikonal equations: multiplicative and additive factors
- Global minimum for a Finsler elastica minimal path approach
- Sparse non-negative stencils for anisotropic diffusion
- An ordered upwind method with precomputed stencil and monotone node acceptance for solving static convex Hamilton-Jacobi equations
- Corner cases, singularities, and dynamic factoring
- Weighted distance maps computation on parametric three-dimensional manifolds
- Efficient fast marching with Finsler metrics
- An $\cal O(N)$ Level Set Method for Eikonal Equations
- A PDE Approach to Data-Driven Sub-Riemannian Geodesics in $SE$(2)
- Minimal Stencils for Discretizations of Anisotropic PDEs Preserving Causality or the Maximum Principle
- An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton–Jacobi Equations and Applications
- Can Local Single-Pass Methods Solve Any Stationary Hamilton--Jacobi--Bellman Equation?
- Anisotropic Fast-Marching on Cartesian Grids Using Lattice Basis Reduction
- Geodesic Methods in Computer Vision and Graphics
- A Level Set Formulation for the Solution of the Dirichlet Problem for Hamilton–Jacobi Equations
- Label-Setting Methods for Multimode Stochastic Shortest Path Problems on Graphs
- Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations
- Classification of eight-dimensional perfect forms
- On Deterministic Control Problems: An Approximation Procedure for the Optimal Cost I. The Stationary Problem
- Viscosity Solutions of Hamilton-Jacobi Equations
- Low-dimensional lattices. III. Perfect forms
- Computing geodesic paths on manifolds
- Low-dimensional lattices. VI. Voronoi reduction of three-dimensional lattices
- A Viscosity Solutions Approach to Shape-From-Shading
- Ordered Upwind Methods for Static Hamilton--Jacobi Equations: Theory and Algorithms
- Fast Sweeping Algorithms for a Class of Hamilton--Jacobi Equations
- Ordered upwind methods for static Hamilton–Jacobi equations
- A fast sweeping method for Eikonal equations
- Efficient algorithms for globally optimal trajectories
- A fast marching level set method for monotonically advancing fronts.
- Convergent Filtered Schemes for the Monge--Ampère Partial Differential Equation
- A fast algorithm for the two dimensional HJB equation of stochastic control
- Algorithmic Number Theory
- Convergent Difference Schemes for Degenerate Elliptic and Parabolic Equations: Hamilton--Jacobi Equations and Free Boundary Problems
- Diffusion processes in a small time interval
- Monotone and consistent discretization of the Monge-Ampère operator
- On an Asymmetrical Metric in the Four-Space of General Relativity
- Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
