Fast reaction, slow diffusion, and curve shortening
SIAM Journal on Applied Mathematics
Weakly differentiable functions
Weakly differentiable functions
Visual reconstruction with discontinuities using variational methods
Image and Vision Computing
Front interaction and nonhomogeneous equilibria for tristable reaction-diffusion equations
SIAM Journal on Applied Mathematics
Motion of multiple junctions: a level set approach
Journal of Computational Physics
A variational level set approach to multiphase motion
Journal of Computational Physics
Efficient algorithms for diffusion-generated motion by mean curvature
Journal of Computational Physics
A Variational Model for Image Classification and Restoration
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Level Set Model for Image Classification
International Journal of Computer Vision
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A phase field approach in the numerical study of the elastic bending energy for vesicle membranes
Journal of Computational Physics
Nonlinear diffusion filtering on extended neighborhood
Applied Numerical Mathematics
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Piecewise constant level set methods and image segmentation
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
A semi-implicit level set method for structural shape and topology optimization
Journal of Computational Physics
Design of piezoelectric actuators using a multiphase level set method of piecewise constants
Journal of Computational Physics
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
A Statistical Overlap Prior for Variational Image Segmentation
International Journal of Computer Vision
Variational piecewise constant level set methods for shape optimization of a two-density drum
Journal of Computational Physics
Effective level set image segmentation with a kernel induced data term
IEEE Transactions on Image Processing
Multiphase image segmentation using a phase-field model
Computers & Mathematics with Applications
Piecewise constant level set method for structural topology optimization with MBO type of projection
Structural and Multidisciplinary Optimization
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
Adaptive wavelet collocation methods for image segmentation using TV---Allen---Cahn type models
Advances in Computational Mathematics
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In this work, we are trying to propose fast algorithms for Mumford-Shah image segmentation using some recently proposed piecewise constant level set methods (PCLSM). Two variants of the PCLSM will be considered in this work. The first variant, which we call the binary level set method, needs a level set function which only takes values 卤1 to identify the regions. The second variant only needs to use one piecewise constant level set function to identify arbitrary number of regions. For the Mumford-Shah image segmentation model with these new level set methods, one needs to minimize some smooth energy functionals under some constrains. A penalty method will be used to deal with the constraint. AOS (additive operator splitting) and MOS (multiplicative operator splitting) schemes will be used to solve the Euler-Lagrange equations for the minimization problems. By doing this, we obtain some algorithms which are essentially applying the MBO scheme for our segmentation models. Advantages and disadvantages are discussed for the proposed schemes.