Label Function Enhancement Method For Multi-phase Image Segmentation Variational Mode

The variational model of multiphase image segmentation is a typical multi-variable optimization problem.Its nonlinear,nonconvex,and nonsmooth characteristics lead to prominent local extremum problems.Its result depends on initial conditions and penalty parameters,which is difficult to apply in practice.The original problem can be theoretically transformed into a global convex optimization problem through box function,generalized co-area formula,and layer cake formula.However,with the increase of the number of phases,the dimension of box function increases sharply,resulting in complex calculation and low efficiency.To solve the above problems,a multiphase image segmentation model that divides multiple regions by a scalar multi-label function-the LLT model is improved.The main innovations are as follows:1.A convex optimization method of LLT model based on a label function is proposed.In the process of alternately optimizing the variational model of image segmentation,the subproblem of parameter estimation is completed first.Then,aiming at the related subproblem of label function,based on the idea of Cartesian flow and calibration theory,functional lifting method is used to lift the discrete label function to a binary super level set function.Finally,the convex optimization method of the subproblem is designed by convex relaxation technique of binary label function to improve local extremum problem of the whole model.2.An vector LLT model based on two label functions is proposed,and its convex optimization method is designed.With the increase of the number of phases in the multiphase image,the number of labels increase,and the computational efficiency of image segmentation gradually decrease.Therefore,the LLT model based on two label functions is designed.According to different label functions,the corresponding convex optimization method of multiple label functions is designed to find the global optimum.3.The primal dual algorithm is designed for the proposed model.In order to improve the computational efficiency,the subproblem is transformed into a minimax optimization problem by introducing dual variables,and the calculation is simplified by primal dual algorithm and projection algorithm.To reduce the number of iterations,the acceleration term is introduced in the calculation.Finally,segmentation experiments of multiple multiphase gray and color images are carried out,and the results show that the energy minimum of proposed model is much smaller than the direct calculation result of original model;the improved method hardly depends on settings of initial level set and selection of experimental parameters;the proposed algorithm greatly reduces the overall number of iterations and has high computational efficiency.