Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
IEEE Transactions on Image Processing
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Based on the expression of a open surface on which images are defined as intersection of zero level set of a signed distance function and a binary label function and by making use of concepts of intrinsic gradient and divergence, the partitioning strategy of regions on a surface via m binary label functions for 2m regions, a general varaitional model for multiphase image segmentation on an implicit open surface is proposed. Based on techniques of convex relaxation and thresholding, the gradient descent method, dual method, Split Bregman method, augmented Lagrange method are designed, where, the last three methods are fast ones. In order to improve its efficiency and make it implement easily, we propose another new method based on dual method without convex relaxation and thresholding of binary label functions, which is referred as direct dual method. Finally, numerical examples validate the model and its fast algorithms proposed in this paper.