Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Motion of multiple junctions: a level set approach
Journal of Computational Physics
Monotone multigrid methods for elliptic variational inequalities I
Numerische Mathematik
A variational level set approach to multiphase motion
Journal of Computational Physics
V-cycle Convergence with Unsymmetric Smoothers and Application to an Anisotropic Model Problem
SIAM Journal on Numerical Analysis
The method of subspace corrections
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Global and uniform convergence of subspace correction methods for some convex optimization problems
Mathematics of Computation
A level set algorithm for minimizing the Mumford-Shah functional in image processing
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Geometrical image segmentation by the Allen-Cahn equation
Applied Numerical Mathematics
Threshold dynamics for the piecewise constant Mumford-Shah functional
Journal of Computational Physics
Color image enhancement via chromaticity diffusion
IEEE Transactions on Image Processing
Preconditioning for Allen-Cahn variational inequalities with non-local constraints
Journal of Computational Physics
Journal of Visual Communication and Image Representation
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We present an efficient numerical solution of a PDE-driven model for color image segmentation and give numerical examples of the results. The method combines the vector-valued Allen-Cahn phase field equation with initial data fitting terms with prescribed interface width and fidelity constants. Efficient numerical solution is achieved using a multigrid splitting of a finite element space, thereby producing an efficient and robust method for the segmentation of large images. We also present the use of adaptive mesh refinement to further speed up the segmentation process.