Global minimum for a variant Mumford–Shah model with application to medical image segmentation

Traditional level set-based active contour models/snakes are widely applied to medical image segmentation. The main problems faced by those traditional models are that they cannot find the global minimum of the energy functionals and hardly handle the intensity inhomogeneities which often occur in medical images. In order to overcome the drawbacks mentioned above, we make use of a global minimisation framework and the dual formulation of the total variation (TV) norm to solve a global variant Mumford–Shah energy with bias field estimator. Furthermore, we utilise a new method to compute the bias field estimator by the Gaussian kernel function, which can ensure the bias field estimator to keep smooth in the whole image domain. Finally, through the dual projection method of the weighted TV norm, we can find the global minimum of the variant Mumford–Shah energy with bias field estimator rather than the local one. Experimental results demonstrate that our method can obtain the desired results both in synthetic and medical images