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 variational level set approach to multiphase motion
Journal of Computational Physics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Review
A PDE-based fast local level set method
Journal of Computational Physics
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Journal of Computational Physics
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Journal of Computational Physics
Geometric Level Set Methods in Imaging,Vision,and Graphics
Geometric Level Set Methods in Imaging,Vision,and Graphics
Journal of Computational Physics
Level Set Evolution without Re-Initialization: A New Variational Formulation
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
A New Total Variation Method for Multiplicative Noise Removal
SIAM Journal on Imaging Sciences
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
An efficient local Chan-Vese model for image segmentation
Pattern Recognition
Variational piecewise constant level set methods for shape optimization of a two-density drum
Journal of Computational Physics
Multiplicative noise removal using variable splitting and constrained optimization
IEEE Transactions on Image Processing
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
A binary level set model and some applications to Mumford-Shah image segmentation
IEEE Transactions on Image Processing
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Interface evolution problems are often solved elegantly by the level set method, which generally requires the time-consuming reinitialization process. In order to avoid reinitialization, we reformulate the variational model as a constrained optimization problem. Then we present an augmented Lagrangian method and a projection Lagrangian method to solve the constrained model and propose two gradient-type algorithms. For the augmented Lagrangian method, we employ the Uzawa scheme to update the Lagrange multiplier. For the projection Lagrangian method, we use the variable splitting technique and get an explicit expression for the Lagrange multiplier. We apply the two approaches to the Chan-Vese model and obtain two efficient alternating iterative algorithms based on the semi-implicit additive operator splitting scheme. Numerical results on various synthetic and real images are provided to compare our methods with two others, which demonstrate effectiveness and efficiency of our algorithms.