Image Selective Segmentation Based On Variational Partial Differential Equations

Selective segmentation refers to the local segmentation of a single object of interest in an image in some way,which is the premise and basis of efficient and accurate analysis of medical images.Selective segmentation based on medical images plays a very important role in disease focus identification,early diagnosis,treatment plan planning,and intraoperative navigation.This paper studies image selective segmentation methods based on partial differential equations.The main research contents and innovations are as follows:(1)A fast algorithm for numerically solving the selective segmentation RCI model is studied.The existing algorithm for solving the RCI model is the additive operator splitting method,which has high computational cost and slow solution speed.By using the knowledge of geometric measure theory,we construct the convex relaxation model of RCI model.Furthermore,a fast algorithm is designed for solving the relaxed model by using alternating direction multiplier method(ADMM).Numerical experiments show that the designed algorithm not only improves the segmentation speed,but also has higher segmentation accuracy.(2)A Retinex-based selective model is proposed for segmenting inhomogeneous images.By employing the Retinex theory to decouple the input inhomogeneous image into illumination bias and reflective parts,then we introduce the priori regularization of these two parts in the proposed model for selective segmentation.Then an alternating minimization algorithm is established to numerically solve the model.Finally,numerical experimental results are given to show the effectiveness of the proposed method and the established algorithm.(3)A convex formulation of the model is presented and the existence of the solutions to the proposed model is proved.Furthermore,the equivalence between the solutions of the proposed model and its convex relaxation is given in this paper.