Li Hua, Yezzi Anthony
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA.
IEEE Trans Med Imaging. 2007 Sep;26(9):1213-23. doi: 10.1109/tmi.2007.903696.
In this paper, we propose an innovative approach to the segmentation of tubular structures. This approach combines all of the benefits of minimal path techniques such as global minimizers, fast computation, and powerful incorporation of user input, while also having the capability to represent and detect vessel surfaces directly which so far has been a feature restricted to active contour and surface techniques. The key is to represent the trajectory of a tubular structure not as a 3-D curve but to go up a dimension and represent the entire structure as a 4-D curve. Then we are able to fully exploit minimal path techniques to obtain global minimizing trajectories between two user supplied endpoints in order to reconstruct tubular structures from noisy or low contrast 3-D data without the sensitivity to local minima inherent in most active surface techniques. In contrast to standard purely spatial 3-D minimal path techniques, however, we are able to represent a full tubular surface rather than just a curve which runs through its interior. Our representation also yields a natural notion of a tube's "central curve." We demonstrate and validate the utility of this approach on magnetic resonance (MR) angiography and computed tomography (CT) images of coronary arteries.
在本文中，我们提出了一种用于管状结构分割的创新方法。该方法结合了最小路径技术的所有优点，如全局极小值、快速计算以及对用户输入的有效整合，同时还具备直接表示和检测血管表面的能力，而这一特性迄今为止一直是主动轮廓和表面技术所特有的。关键在于，不是将管状结构的轨迹表示为三维曲线，而是提升一个维度，将整个结构表示为四维曲线。这样我们就能充分利用最小路径技术，在两个用户指定的端点之间获得全局最小化轨迹，以便从噪声或低对比度的三维数据中重建管状结构，而不会像大多数主动表面技术那样对局部极小值敏感。然而，与标准的纯空间三维最小路径技术不同的是，我们能够表示完整的管状表面，而不仅仅是穿过其内部的一条曲线。我们的表示方法还产生了一种关于管子“中心曲线”的自然概念。我们在冠状动脉的磁共振（MR）血管造影和计算机断层扫描（CT）图像上展示并验证了该方法的实用性。
