  Image segmentation is an important median level vision topic. Accurate and
efficient multiphase segmentation for images with intensity inhomogeneity is
still a great challenge. We present a new two-stage multiphase segmentation
method trying to tackle this, where the key is to compute an inhomogeneity-free
approximate image. For this, we propose to use a new non-Lipschitz variational
decomposition model in the first stage. The minimization problem is solved by
an iterative support shrinking algorithm, with a global convergence guarantee
and a lower bound theory of the image gradient of the iterative sequence. The
latter indicates that the generated approximate image (inhomogeneity-corrected
component) is with very neat edges and suitable for the following thresholding
operation. In the second stage, the segmentation is done by applying a
widely-used simple thresholding technique to the piecewise constant
approximation. Numerical experiments indicate good convergence properties and
effectiveness of our method in multiphase segmentation for either clean or
noisy homogeneous and inhomogeneous images. Both visual and quantitative
comparisons with some state-of-the-art approaches demonstrate the performance
advantages of our non-Lipschitz based method.
