多相图像分割的Split-Bregman方法及对偶方法

Split-Bregman Method and Dual Method for Multiphase Image Segmentation

变分水平集方法为多相图像分割提供了统一框架,但其能量泛函的局部极值问题和较低的计算效率制约着该类方法的应用,文中针对此问题提出一种改进模型和方法.首先将两相图像分割的全局凸优化模型推广到多相图像分割,建立了多相图像分割的交替凸优化变分模型,以改善传统模型的局部极值问题;然后提出了相应的快速Split-Bregman方法和对偶方法来提高计算效率,其中Split-Bregman方法通过引入辅助变量将凸松弛后的变分问题转化为简单的Poisson方程和精确的软阈值公式,对偶方法则通过引入对偶变量将该问题转化为对偶变量的半隐式迭代计算和主变量的精确计算公式.文中的改进模型适用于任意多相图像分割,且对二维和三维图像分割具有相同形式,可用于三维图像的多对象自动形状恢复.最后通过多个数值算例验证了文中方法的计算效率优于传统的方法.

The variational level set method can be used to design general frameworks for multiphase image segmentation,but its drawbacks of local minimization and low efficiency are two problems of their applications in different areas.In this work,firstly,the global convex minimization method for two-phase image segmentation is extended to variational multiphase image segmentation,which results in an alternating convex minimization problem.Secondly,the Split-Bregman method and dual method are designed for the proposed model to improve the computation efficiency.The Split-Bregman method is implemented by introducing auxiliary variables which transform the relaxed convex variational model into solving simple Poisson equations and exact soft thresholding formulation,the dual method is implemented by introducing dual variables which lead to semi-implicit iterative scheme of dual variables and exact formulation of primal variables.The proposed model can be used for image segmentation of any phase,is under the same formulation for both 2D and 3D image segmentation.It is suitable for 3D shape recovery from 3D images.Experiments demonstrate its high efficiency of our proposed model in comparison with the traditional methods