A case study of a two-stage image segmentation algorithm

Mumford-Shah (MS) model has attracted considerable research interests in the past decades. It is a classical and important approach for image segmentation. In a recent work, as an extension to MS model, Cai et al. proposed a two-stage image segmentation method. In the first stage of this method, a convex variant of MS model is developed. Then, after finding the unique minimizer of this new model, in the second stage, image segmentation is conducted by automatically thresholding. Compared with MS model, the new model is convex and computationally efficient. In this paper, as a further study, the theoretical aspect of Cai et al.’s method is emphasized and some primary results are obtained.