Minimal path method has been widely recognized as an efficient tool for extracting vascular structures in medical imaging. In a previous paper, a method termed minimal path propagation with backtracking (MPP-BT) was derived to deal with curve-like structures such as vessel centerlines. A robust approach termed CMPP (constrained minimal path propagation) is here proposed to extend this work. The proposed method utilizes another minimal path propagation procedure to extract the complete vessel lumen after the centerlines have been found. Moreover, a process named local MPP-BT is applied to handle structure missing caused by the so-called close loop problems. This approach is fast and unsupervised with only one roughly set start point required in the whole process to get the entire vascular structure. A variety of datasets, including 2D cardiac angiography, 2D retinal images and 3D kidney CT angiography, are used for validation. A quantitative evaluation, together with a comparison to recently reported methods, is performed on retinal images for which a ground truth is available. The proposed method leads to specificity (Sp) and sensitivity (Se) values equal to 0.9750 and 0.6591. This evaluation is also extended to 3D synthetic vascular datasets and shows that the specificity (Sp) and sensitivity (Se) values are higher than 0.99. Parameter setting and computation cost are analyzed in this paper.

最小路径法已被广泛认为是医学成像中提取血管结构的有效工具。在之前的一篇论文中，推导出了一种称为带回溯的最小路径传播 (MPP-BT) 的方法来处理类似曲线的结构，例如血管中心线。这里提出了一种称为 CMPP（受约束的最小路径传播）的稳健方法来扩展这项工作。在找到中心线之后，所提出的方法利用另一个最小路径传播程序来提取完整​​的血管腔。此外，一个名为local MPP-BT的过程被应用于处理由所谓的闭环问题引起的结构缺失。这种方法快速且无监督，在整个过程中只需要一个粗略设置的起点即可获得整个血管结构。各种数据集，包括 2D 心脏血管造影、2D 视网膜图像和 3D 肾脏 CT 血管造影，用于验证。定量评估以及与最近报道的方法的比较，是在有基本事实可用的视网膜图像上进行的。所提出的方法导致特异性 (Sp) 和灵敏度 (Se) 值等于 0.9750 和 0.6591。该评估还扩展到 3D 合成血管数据集，并显示特异性 (Sp) 和灵敏度 (Se) 值高于 0.99。本文分析了参数设置和计算成本。所提出的方法导致特异性 (Sp) 和灵敏度 (Se) 值等于 0.9750 和 0.6591。该评估还扩展到 3D 合成血管数据集，并显示特异性 (Sp) 和灵敏度 (Se) 值高于 0.99。本文分析了参数设置和计算成本。所提出的方法导致特异性 (Sp) 和灵敏度 (Se) 值等于 0.9750 和 0.6591。该评估还扩展到 3D 合成血管数据集，并显示特异性 (Sp) 和灵敏度 (Se) 值高于 0.99。本文分析了参数设置和计算成本。