Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Machine Vision and Applications
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
International Journal of Computer Vision
Physica D
Motion of curves in three spatial dimensions using a level set approach
Journal of Computational Physics
Motion of curves constrained on surfaces using a level-set approach
Journal of Computational Physics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Using the Vector Distance Functions to Evolve Manifolds of Arbitrary Codimension
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
A Lagrangian particle level set method
Journal of Computational Physics
Reconstructing Open Surfaces from Image Data
International Journal of Computer Vision
Geometric Partial Differential Equations and Image Analysis
Geometric Partial Differential Equations and Image Analysis
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
A second order accurate level set method on non-graded adaptive cartesian grids
Journal of Computational Physics
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
A grid based particle method for moving interface problems
Journal of Computational Physics
Global minimization of the active contour model with TV-Inpainting and two-phase denoising
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Journal of Computational Physics
Robust edge detection using mumford-shah model and binary level set method
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Curvature minimization for surface reconstruction with features
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Journal of Scientific Computing
Hi-index | 31.46 |
We propose a new numerical method for modeling motion of open curves in two dimensions and open surfaces in three dimensions. Following the grid based particle method we proposed in [S. Leung, H.K. Zhao, A grid based particle method for moving interface problems. J. Comput. Phys. 228 (2009) 2993-3024], we represent the open curve or the open surface by meshless Lagrangian particles sampled according to an underlying fixed Eulerian mesh. The underlying grid is used to provide a quasi-uniform sampling and neighboring information for meshless particles. The key idea in the current paper is to represent and to track end-points of the open curve and boundary-points of the open surface explicitly and consistently with interior particles. We apply our algorithms to several applications including spiral crystal growth modeling and image segmentation using active contours.