Color image segmentation by the vector-valued Allen-Cahn phase-field model: a multigrid solution

David A Kay, Alessandro Tomasi
IEEE Transactions on Image Processing: a Publication of the IEEE Signal Processing Society 2009, 18 (10): 2330-9
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.

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