水平集方法在医学图像分割中的一个应用

Application of Level Set Method in Medical Image Segmentation

摘要: 图像分割是目标识别，资源分类等研究的基础。在医学临床诊断，视频监控计算机视觉等多个林谷都有重要的应用。水平集方法以一种紧凑的方式来表达集合主动轮廓曲线的演化，并且为之提供稳定的数值计算。Chan和Vese提出的基于简化的Mumford-Shan模型的主动轮廓模型(C-V方法)，能够很的检查出带有空洞的目标的内部区域，但只能处理两相图片的分割。基于C-V模型，Vese Chan推广到实用多个水平集函数来分割多相图像，即Vese-Chan变分多水平模型。该方法有以下优点：可以自动的避免水平集函数覆盖区域的“重叠”和“真空”问题。本文中，我们基于C-V模型以及Vese-Chan变分水平集模型，实现了如何利用单个水平集函数以及两个水平集函数来进行医学图像分割；讨论了这两种方法的优缺点。我们的图像分割数值实验结果验证了理论结果。

Abstract: Image segmentation is the basic of object detection and resource classification, and it has an im-portant application in the field of medical diagnosis, video monitoring and computer vision. Level set method describes the evolution of geometric active contour in a compact way and provides a stable numerical algorithm. Chan and Vese first introduced the active contour model based sim-plified Mumford-Shah model, which could well detect the vacuum of object, but could represent only two phases or segments in the image. Vese-Chan variational level set model was proposed by Vese-Chan as the generalization of C-V model, which needed multiple level set functions for n phases image segmentation; it can represent boundaries with complex topologies. In this paper, based on the C-V model and Vese-Chan variational level set model, we show how to do medical image segmentation through one level set function and two-level set functions respectively. We discuss the advantages and disadvantages of both methods. Our numerical results validate our theoretical predication.