对水平集方法鲁棒初始化的双向快速步进法

Robust Initialization of Level Set Methods Using Two-Way Fast Marching

水平集方法解决应用于图像或运动分割的曲线或曲面演化问题,是一种稳定有效的数值计算工具。本文解决在初始化水平集方法时的两个问题:如何确定任意形状闭合曲线或曲面的内外部,如何高效地重新初始化水平集函数。论文首先对Sethian[4]所提出的快速步进法进行了推广,得到双向快速步进法;据此,改进了生成符号距离函数的方法,以提高水平集方法中重新建立符号距离函数的效率;随后,基于快速步进法,提出一种确定任意形状闭合曲线或曲面内外部的简单快速的方法,用于构造水平集的符号距离函数;最后,对任意形状闭合曲线内外部区分、基于两种初始化算法的水平集方法对任意形状闭合曲线演化和图像分割的实验,证明了本文方法的简单、高效。

Level Set methods are efficient and robust numerical tools for resolving curve evolution. The paper focuses on two problems while implementing Level Set methods, i.e., how to differentiate between the inward and outward of a shape-arbitrary closed 2D curve, and how to efficiently re-initialize the Level Set Function. For this purpose, the paper firstly extend the Fast Marching methods proposed by Sethian to Two-Way Fast Marching, and based on which an effective approach to construction of the Signed Distance Function is then proposed. As an auxiliary tool for SDF construction, a simple labeling approach based on Fast Marching is developed to effectively tell between the inward and outward region of the closed 2D curve or 3D surface. At last, Region Labeling and SDF construction experiments prove that the two proposed methods are correct and simple, and two experiments of image segmentation using Level Set initialized with the proposed robust initialization methods give satisfying results and show efficiency of the proposed approaches.