A novel image segmentation model with an edge weighting function

A variational model for image segmentation consists of a data term and a regularization term. Usually, the data term is chosen as squared $\text{ L }_{2}$ norm, and the regularization term is determined by the prior assumption. In this paper, we present a novel model in the framework of MAP (maximum a posteriori). A new iteratively reweighted $\text{ L }_{2}$ norm is used in the data term, which shares the advantages of $\text{ L }_{2}$ and mixed $\text{ L }_{21}$ norm. An edge weighting function is addressed in the regularization term, which enforces the ability to reduce the outlier effects and preserve edges. An improved region-based graph cuts algorithm is proposed to solve this model efficiently. Numerical experiments show our method can get better segmentation results, especially in terms of removing outliers and preserving edges.