Image segmentation is to separate the image domain into local regions. Implicit active contour models via the level-set method can provide smooth and closed contours. The major category is based on the Mumford-Shah image component decomposition model. Approximating the image domain by a set of homogeneous regions, segmentation based on the piecewise constant (PC) models fail in intensity inhomogeneous images. Requiring intensity smoothness in local regions, segmentation based on the piecewise smooth (PS)
models can perform better for intensity inhomogeneity than those PC based. Existing PS-based techniques are inefficient and not robust to complicate intensity scenarios with noise. Here we introduce a new functional model by decomposing an image into three parts: PS components, PC components and noise components. We convexify the decomposition model by incorporating with relaxation techniques and optimize
the PS components over the whole image domain. New numerical algorithms are also proposed to implement the above approaches efficiently. Numerical validation experiments show that the proposed approaches can achieve much faster, more robust and more accurate image segmentation than existing arts.