Suri Jasjit S, Liu Kecheng, Singh Sameer, Laxminarayan Swamy N, Zeng Xiaolan, Reden Laura
MR Clinical Science Division, Philips Medical Systems, Inc., Cleveland, OH 44143, USA.
IEEE Trans Inf Technol Biomed. 2002 Mar;6(1):8-28. doi: 10.1109/4233.992158.
The class of geometric deformable models, also known as level sets, has brought tremendous impact to medical imagery due to its capability of topology preservation and fast shape recovery. In an effort to facilitate a clear and full understanding of these powerful state-of-the-art applied mathematical tools, this paper is an attempt to explore these geometric methods, their implementations and integration of regularizers to improve the robustness of these topologically independent propagating curves/surfaces. This paper first presents the origination of level sets, followed by the taxonomy of level sets. We then derive the fundamental equation of curve/surface evolution and zero-level curves/surfaces. The paper then focuses on the first core class of level sets, known as "level sets without regularizers." This class presents five prototypes: gradient, edge, area-minimization, curvature-dependent and application driven. The next section is devoted to second core class of level sets, known as "level sets with regularizers." In this class, we present four kinds: clustering-based, Bayesian bidirectional classifier-based, shape-based and coupled constrained-based. An entire section is dedicated to optimization and quantification techniques for shape recovery when used in the level set framework. Finally, the paper concludes with 22 general merits and four demerits on level sets and the future of level sets in medical image segmentation. We present applications of level sets to complex shapes like the human cortex acquired via MRI for neurological image analysis.
几何可变形模型（也称为水平集）由于其拓扑保持能力和快速形状恢复能力，给医学图像带来了巨大影响。为了便于清晰、全面地理解这些强大的前沿应用数学工具，本文试图探索这些几何方法、它们的实现方式以及正则化器的集成，以提高这些拓扑独立的传播曲线/曲面的鲁棒性。本文首先介绍了水平集的起源，接着是水平集的分类。然后我们推导了曲线/曲面演化和零水平曲线/曲面的基本方程。本文接着聚焦于水平集的第一类核心类别，即“无正则化器的水平集”。这类展示了五个原型：梯度、边缘、面积最小化、曲率相关和应用驱动。下一部分致力于水平集的第二类核心类别，即“有正则化器的水平集”。在这类中，我们展示了四种：基于聚类的、基于贝叶斯双向分类器的、基于形状的和基于耦合约束的。专门有一整节介绍在水平集框架中用于形状恢复的优化和量化技术。最后，本文总结了水平集的22个一般优点和四个缺点以及水平集在医学图像分割中的未来发展。我们展示了水平集在通过MRI获取的复杂形状（如人类皮质）用于神经图像分析中的应用。
