Research And Improvement Of ADMM Algorithm Of Variational Level Set Model For Two-phase/multiphase Image Segmentation

Image segmentation is a core component in image analysis and computer vision.It is widely applied medical imaging,remote sensing imaging,intelligence traffic,biology molecular imaging,and so on.Variational image segmentation models based on variational level set method provide a unified framework for multiphase image segmentation,the investigations of their fast algorithms have received more and more attentions recent years.The Chan-Vese model under the variational level set framework for two-phase image segmentation is fundamental to multiphase variational image segmentation,its fast algorithms can be extended to variational models for multiphase image segmentation also.In this thesis,some dual variables are introduced to transform the Chan-Vese model into continuous maximum flow problem which is a typical graph-cut problem,it is then solved under the framework of ADMM(Alternating Direction Method of Multipliers)by introducing Lagrange multipliers with high computation efficiency and good robust property.The Chung-Vese model under variational level set framework for multiphase image segmentation is the best model in this area thanks to its region partition scheme using only one level set function,but its classical gradient descent method is slow to solve.In this thesis,a symmetric expression is proposed taking into account the domain of the level set function to circumvent the original complex characteristic functions.Based on the new scheme for region division,a concise ADMM projection algorithm is proposed by introducing some auxiliary variables and Lagrange multipliers,leading to high computational efficiency and robustness without re-initialization of the level set function.Finally,some numerical examples are given for two-phase and multiphase image segmentation to demonstrate the merits of the proposed algorithms over the previous ones.