Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Variational methods in image segmentation
Variational methods in image segmentation
International Journal of Computer Vision
SIAM Review
Multigrid
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Efficient segmentation based on Eikonal and diffusion equations
International Journal of Computer Mathematics - Computer Vision and Pattern Recognition
Unsupervised hierarchical image segmentation with level set and additive operator splitting
Pattern Recognition Letters
A fast multigrid implicit algorithm for the evolution of geodesic active contours
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Snakes, shapes, and gradient vector flow
IEEE Transactions on Image Processing
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Multigrid Geometric Active Contour Models
IEEE Transactions on Image Processing
Discrete optimization of the multiphase piecewise constant mumford-shah functional
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
A robust multigrid approach for variational image registration models
Journal of Computational and Applied Mathematics
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In this paper, we present two related multigrid algorithms for multiphase image segmentation. Algorithm I solves the model by Vese-Chan. We first generalize our recently developed multigrid method to this multiphase segmentation model (MG1); we also give a local Fourier analysis for the local smoother which leads to a new and more effective smoother. Although MG1 is found many magnitudes faster than the fast method of additive operator splitting (AOS), both algorithms are not robust with regard to the initial guess. To overcome this dependence on the initial guess, we consider a hierarchical segmentation model which achieves multiphase segmentation by repeated use of the Chan-Vese two-phase model; our Algorithm II solves this model by a multigrid algorithm (MG2). Numerical experiments show that both algorithms are efficient and in particular MG2 is more robust than MG1 with respect to initial guesses. AMS subject classifications: 68U10, 65F10, 65K10.