Generic Model Variational Level Set Method And Fast Projection Algorithm Based On

Image segmentation is a basic problem of computer vision. Variational level set method has been extensively applied to image segmentation due to its adaptive capability of topological structure, unified expression of2D and3D segmentation result, and integrated capacity of multiple models and so forth. This thesis focuses on the generalized variational level set models for two-phase and multiphase images segmentation. For multiphase segmentation, different region partition strategies and their corresponding characteristic functions are designed, and they are respectively using n level set functions to segment n regions, n-1level set functions to segment n regions, n level set functions to segment2n regions, and1multilayer level set function to segment n regions. Based on piecewise constant assumption, piecewise smooth assumption, texture assumption, discontinuous optical flow assumption, and different noise distribution assumption, two-phase and multiphase segmentation models for two-dimensional and three-dimensional images are presented under this variational level set theoretical framework. In order to avoid complicated and tedious re-initialization problem and meanwhile improve the computational efficiency, through introducing split auxiliary variable, Bregman iterative parameter, Lagrangian multiplier, and dual variable, four fast projection methods are proposed respectively, i.e. split Bregman projection method (SBPM), augmented Lagrangian projection method (ALPM), dual split Bregman projection method (DSBPM), and dual augmented Lagrangian projection method (DALPM). Finally, numerical experiments are presented to validate the effectiveness and efficiency of proposed models and algorthims.