Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
A fast level set method for propagating interfaces
Journal of Computational Physics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A variational level set approach to multiphase motion
Journal of Computational Physics
Diffeomorphisms Groups and Pattern Matching in Image Analysis
International Journal of Computer Vision
Variational problems on flows of diffeomorphisms for image matching
Quarterly of Applied Mathematics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
Motion of curves in three spatial dimensions using a level set approach
Journal of Computational Physics
Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method
Journal of Computational Physics
Transport and diffusion of material quantities on propagating interfaces via level set methods
Journal of Computational Physics
A Level-Set Based Approach to Image Registration
MMBIA '00 Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis
An Eulerian Formulation for Solving Partial Differential Equations Along a Moving Interface
Journal of Scientific Computing
Journal of Computational Physics
An Improvement of a Recent Eulerian Method for Solving PDEs on General Geometries
Journal of Scientific Computing
A Lagrangian-Eulerian shell-fluid coupling algorithm based on level sets
Computers and Structures
EURASIP Journal on Advances in Signal Processing - Special issue on recent advances in biometric systems: a signal processing perspective
A new level-set based approach to shape and topology optimization under geometric uncertainty
Structural and Multidisciplinary Optimization
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Tracking level set representation driven by a stochastic dynamics
Proceedings of the 7th international conference on Curves and Surfaces
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In this paper, we propose a completely Eulerian approach to maintain a point correspondence during a level set evolution. Our work is in the spirit of some recent methods (D. Adalsteinsson, J. Sethian, Transport and diffusion of material quantities on propagating interfaces via level set methods, Journal of Computational Physics 185(1) (2003) 271-288; J.-J. Xu, H.-K. Zhao, An Eulerian formulation for solving partial differential equations along a moving interface, Journal of Scientific Computing 19 (2003) 573-594) for handling interfacial data on moving level set interfaces. Our approach maintains an explicit backward correspondence from the evolving interface to the initial one, by advecting the initial point coordinates with the same velocity as the level set function. It leads to a system of coupled Eulerian partial differential equations. We describe in detail a robust numerical implementation of our approach, in accordance with the narrow band methodology. We show in a variety of numerical experiments that it can handle both normal and tangential velocities, large deformations, shocks, rarefactions and topological changes. The possible applications of our approach include scientific visualization, computer graphics and image processing.