Three-dimensional convex and selective variational image segmentation model

Selective image segmentation is a task of extracting one object of interest among many others in an image based on minimal user input. Several three-dimensional (3-D) selective models were proposed and they would find local minimizer because of their non-convex formulation, hence they are sensitive to initialization. This paper presents a new formulation for 3-D convex selective segmentation model. In order to solve the developed 3-D model, a projection algorithm is proposed. Numerical tests show that the proposed model is efiective in segmenting 3-D complex image structures and allowing a global minimizer to be found independently of initialization.