| 摘要: |
| 将平面图像变分分割的Mumford-Shah模型推广于隐式曲面上图像分割问题.封闭曲面用符号距离函数的零水平集来表达,开式曲面用符号距离函数的零水平集与二值标记函数的交集来表达,借助内蕴梯度、内蕴散度等概念首先建立了隐式曲面上图像分割的Mumford-Shah模型.为了提高通用性,所提出的Mumford-Shah模型的光滑项采用通用形式,可适用于总变差等多种形式的光滑项模型.此外,还通过引进辅助变量和Bregman迭代参数设计所提出模型的Split Bregman算法.多个数值实验对所提出的模型和算法的可行性进行了验证. |
| 关键词: 图像分割 变分方法 隐式曲面 Mumford-Shah模型 Split Bregman算法 |
| DOI： |
| 分类号: |
| 基金项目:国家自然科学基金(61170106) |
|
| Mumford-Shah Model on Implicit Surfaces |
|
DUAN Jin-Ming, PAN Zhen-Kuan, HE Xiao-Chuan, WEI Wei-Bo, LIU Cun-Liang
|
|
College of Information Engineering, Qingdao University, Qingdao 266071, China
|
| Abstract: |
| The Mumford-Shah model for planar image segmentation chas been extended to variational models for image segmentation on implicit surfaces in this paper. The closed surfaces are denoted as zero-level set of signed distance functions, and the open surfaces are expressed as interaction sets of zero-level set and binary functions. With the use of intrinsic gradients and intrinsic divergences, the Mumford-Shah model for image segmentation on implicit surfaces is formulated. In order to improve their generality, the paper uses a generalized smoothness term which can be exemplified for different types. In order to improve computation efficiency, the study designs the Split Bregman algorithms via introducing auxiliary variables and Bregman iterative parameters for the proposed models. Numerical examples validate the models and algorithms finally. |
| Key words: image segmentation variational methods Mumford-Shah model Split Bregman algorithm |
