隐式曲面多相图像分割的变分水平集方法

Variational Level Set Methods for Multiphase Image Segmentation on Implicit Surfaces

基于隐式曲面的水平集表达、隐式曲面上的内蕴梯度概念和图像分割的标记函数方法,建立了隐式曲面上多相图像分割的水平集模型,并设计了相应的Split Bregman方法.首先,将分段常值与光滑平面图像两相分割的Chan-Vese模型推广到隐式曲面上图像分割的变分水平集模型,并根据图像分割的二值标记函数和凸松弛的概念将该模型转化为全局凸优化的极值问题;然后借助n-1个水平集函数划分n个区域的区域特征函数,将隐式曲面上两相图像分割变分模型推广到了多相图像分割,并利用凸优化方法将该模型的变分问题松弛为一系列凸子优化过程.通过引进辅助变量和Bregman迭代参数设计的Split Bregman方法,将每个子优化问题转化为简单的Poisson方程求解和解析的软阈值公式.数值算例结果表明,文中方法在计算效率方面要优于传统的方法.

A variational level set model of multiphase image segmentation on implicit surfaces using level set method,intrinsic gradient and binary label functions is proposed in the paper along with its Split Bregman method.First,Chan-Vese model for two-phase image segmentation of planar piecewise constantsmooth images is extended to implicit surfaces.According to binary value labeling functions and the concept of convex relaxation,two-phase image segmentation model is transformed into a global convex optimization problem.Then the two-phase image segmentation model is extended to a multiphase variational image segmentation model on implicit surface using n-1 level set functions for n regions.The convex relaxation method is applied to the proposed variational problem of multiphase image segmentation and transforms the original problem into a sequence of convex sub-problems.To improve efficiency,every sub-optimization problem can be transformed to a problem of solving Poisson equations.Soft thresholding formulas can be employed with Split Bregman method,which introduces auxiliary variables and Bregman iterative parameters.Our experiments show that the proposed method is superior to the traditional ones in computational efficiency.