A Three-Stage Variational Image Segmentation via Scalar Auxiliary Variable Algorithm

In the modern information society, image has become an important carrier of information, and there are a lot of information transmitted in the form of image on the network. As a basic and important task in the field of computer vision, image segmentation has broad application prospects in many fields. In this paper, a three-stage image segmentation model is proposed. The first stage in our framework is to perform a dimension lifting method. An intensity inhomogeneity image is added as an additional channel, which results in a vector-valued image. In the second stage, a convex variant of the Mumford–Shah model is applied to each channel of the vector-valued image to obtain a smooth approximation. We use the scalar auxiliary variable (SAV) algorithm to solve this model and prove that the SAV for solving this convex model has the unconditional stability. In the last stage, we apply a thresholding method to the smoothed vector-valued image to get the final segmentation. Finally, the performance and advantages of the model are verified by numerical experiments compared with other models.