A coupled quadrilateral grid level set projection method applied to ink jet simulation
Journal of Computational Physics
A study of numerical methods for the level set approach
Applied Numerical Mathematics
IEEE Transactions on Visualization and Computer Graphics
A second order discontinuous Galerkin fast sweeping method for Eikonal equations
Journal of Computational Physics
MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
International Journal of Robotics Research
A Fast Marching Method for Hamilton-Jacobi Equations Modeling Monotone Front Propagations
Journal of Scientific Computing
Adaptation of Eikonal Equation over Weighted Graph
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Journal of Computational Physics
Combining area patrol, perimeter surveillance, and target tracking using ordered upwind methods
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Toward model free atmospheric sensing by aerial robot networks in strong wind fields
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
FIMH'07 Proceedings of the 4th international conference on Functional imaging and modeling of the heart
Efficient Beltrami flow using a short time kernel
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
Towards an identification of tumor growth parameters from time series of images
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
A segmentation framework for abdominal organs from CT scans
Artificial Intelligence in Medicine
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Geodesic Methods in Computer Vision and Graphics
Foundations and Trends® in Computer Graphics and Vision
Some Improvements for the Fast Sweeping Method
SIAM Journal on Scientific Computing
A 2D moving grid geometric deformable model
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Uniformly Accurate Discontinuous Galerkin Fast Sweeping Methods for Eikonal Equations
SIAM Journal on Scientific Computing
A Third Order Accurate Fast Marching Method for the Eikonal Equation in Two Dimensions
SIAM Journal on Scientific Computing
MICCAI'05 Proceedings of the 8th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
A toolbox of hamilton-jacobi solvers for analysis of nondeterministic continuous and hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Fast marching method for generic shape from shading
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Dual loops meshing: quality quad layouts on manifolds
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Analysis and applications of the Voronoi Implicit Interface Method
Journal of Computational Physics
Fast Two-scale Methods for Eikonal Equations
SIAM Journal on Scientific Computing
An attribute weighted distance transform
Pattern Recognition Letters
A uniformly second order fast sweeping method for eikonal equations
Journal of Computational Physics
A gradient augmented level set method for unstructured grids
Journal of Computational Physics
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We develop a family of fast methods for approximating the solutions to a wide class of static Hamilton--Jacobi PDEs; these fast methods include both semi-Lagrangian and fully Eulerian versions. Numerical solutions to these problems are typically obtained by solving large systems of coupled nonlinear discretized equations. Our techniques, which we refer to as "Ordered Upwind Methods" (OUMs), use partial information about the characteristic directions to decouple these nonlinear systems, greatly reducing the computational labor. Our techniques are considered in the context of control-theoretic and front-propagation problems.We begin by discussing existing OUMs, focusing on those designed for isotropic problems. We then introduce a new class of OUMs which decouple systems for general (anisotropic) problems. We prove convergence of one such scheme to the viscosity solution of the corresponding Hamilton--Jacobi PDE. Next, we introduce a set of finite-differences methods based on an analysis of the role played by anisotropy in the context of front propagation and optimal trajectory problems.The performance of the methods is analyzed, and computational experiments are performed using test problems from computational geometry and seismology.