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Image segmentation is an important median level vision topic. Accurate andefficient multiphase segmentation for images with intensity inhomogeneity isstill a great challenge. We present a new two-stage multiphase segmentationmethod trying to tackle this, where the key is to compute an inhomogeneity-freeapproximate image. For this, we propose to use a new non-Lipschitz variationaldecomposition model in the first stage. The minimization problem is solved byan iterative support shrinking algorithm, with a global convergence guaranteeand a lower bound theory of the image gradient of the iterative sequence. Thelatter indicates that the generated approximate image (inhomogeneity-correctedcomponent) is with very neat edges and suitable for the following thresholdingoperation. In the second stage, the segmentation is done by applying awidely-used simple thresholding technique to the piecewise constantapproximation. Numerical experiments indicate good convergence properties andeffectiveness of our method in multiphase segmentation for either clean ornoisy homogeneous and inhomogeneous images. Both visual and quantitativecomparisons with some state-of-the-art approaches demonstrate the performanceadvantages of our non-Lipschitz based method.

Effective two-stage image segmentation: a new non-Lipschitz decomposition approach with convergent algorithm