A binary level set variational model with L1 data term for image segmentation

In this paper, we propose a variational model in binary level set framework for segmenting two-phase images with impulse noise. In this model, the contour is implicitly represented by the discontinuity of a binary level set function instead of the zero-level set. The energy functional consists of three terms, i.e., the data term that is defined by L1-norm metric, the regularization term that is defined by Dirichlet energy of level set function, and the penalty term that punishes the deviation of level set function from binary function. We design a three-step time-splitting scheme to solve the gradient descent flow of the proposed model efficiently, in which the flow equation is divided into three differential equations that are solved sequentially and alternatively until convergence. We present some experimental results that are performed on simulated and real images, which demonstrate that our model is very robust to impulse noise and has the best performance compared with five relevant models.