IEEE Trans Med Imaging. 2015 Sep;34(9):1940-64. doi: 10.1109/TMI.2015.2417112. Epub 2015 Apr 14.
Digital topology and geometry refers to the use of topologic and geometric properties and features for images defined in digital grids. Such methods have been widely used in many medical imaging applications, including image segmentation, visualization, manipulation, interpolation, registration, surface-tracking, object representation, correction, quantitative morphometry etc. Digital topology and geometry play important roles in medical imaging research by enriching the scope of target outcomes and by adding strong theoretical foundations with enhanced stability, fidelity, and efficiency. This paper presents a comprehensive yet compact survey on results, principles, and insights of methods related to digital topology and geometry with strong emphasis on understanding their roles in various medical imaging applications. Specifically, this paper reviews methods related to distance analysis and path propagation, connectivity, surface-tracking, image segmentation, boundary and centerline detection, topology preservation and local topological properties, skeletonization, and object representation, correction, and quantitative morphometry. A common thread among the topics reviewed in this paper is that their theory and algorithms use the principle of digital path connectivity, path propagation, and neighborhood analysis.
数字拓扑和几何是指在数字网格中定义的图像中使用拓扑和几何属性和特征。这些方法已广泛应用于许多医学成像应用中，包括图像分割、可视化、操作、插值、配准、曲面跟踪、对象表示、校正、定量形态测量等。数字拓扑和几何通过丰富目标结果的范围，并通过添加具有增强的稳定性、保真度和效率的强大理论基础，在医学成像研究中发挥着重要作用。本文对与数字拓扑和几何相关的方法的结果、原理和见解进行了全面而简洁的综述，重点是了解它们在各种医学成像应用中的作用。具体来说，本文综述了与距离分析和路径传播、连通性、曲面跟踪、图像分割、边界和中心线检测、拓扑保持和局部拓扑属性、骨架化以及对象表示、校正和定量形态测量相关的方法。本文回顾的主题的一个共同点是，它们的理论和算法使用数字路径连通性、路径传播和邻域分析的原理。
