A reformulated convex and selective variational image segmentation model and its fast multilevel algorithm

Selective image segmentation is the task of extracting one object of interest among many others in an image based on minimal user input. Two-phase segmentation models cannot guarantee to locate this object, while multiphase models are more likely to classify this object with another features in the image. Several selective models were proposed recently and they would find local minimizers (sensitive to initialization) because non-convex minimization functionals are involved. Recently, Spencer-Chen (CMS 2015) has successfully proposed a convex selective variational image segmentation model (named CDSS), allowing a global minimizer to be found independently of initialization. However, their algorithm is sensitive to the regularization parameter µ and the area parameter θ due to nonlinearity in the functional and additionally it is only effective for images of moderate size. In order to process images of large size associated with high resolution, urgent need exists in developing fast iterative solvers. In this paper, a stabilized variant of CDSS model through primal-dual formulation is proposed and an optimization based multilevel algorithm for the new model is introduced. Numerical results show that the new model is less sensitive to parameter µ and θ compared to the original CDSS model and the multilevel algorithm produces quality segmentation in optimal computational time.