There are many unsolved problems in vascular image segmentation, including vascular structural connectivity, scarce branches and missing small vessels. Obtaining vessels that preserve their correct topological structures is currently a crucial research issue, as it provides an overall view of one vascular system. In order to preserve the topology and accuracy of vessel segmentation, we proposed a novel Morphology Edge Attention Network (MEA-Net) for the segmentation of vessel-like structures, and an Optimal Geometric Matching Connection (OGMC) model to connect the broken vessel segments. The MEA-Net has an edge attention module that improves the segmentation of edges and small objects by morphology operation extracting boundary voxels on multi-scale. The OGMC model uses the concept of curve touching from differential geometry to filter out fragmented vessel endpoints, and then employs minimal surfaces to determine the optimal connection order between blood vessels. Finally, we calculate the geodesic to repair missing vessels under a given Riemannian metric. Our method achieves superior or competitive results compared to state-of-the-art methods on four datasets of 3D vascular segmentation tasks, both effectively reducing vessel broken and increasing vessel branch richness, yielding blood vessels with a more precise topological structure.

翻译：血管图像分割中存在诸多未解决难题，包括血管结构连通性、稀疏分支及小血管缺失。获取保持正确拓扑结构的血管是当前关键研究问题，因其能提供血管系统的全局视图。为保持血管分割的拓扑完整性与准确性，我们提出了一种新型形态学边缘注意力网络（MEA-Net）用于血管样结构分割，以及一种最优几何匹配连接（OGMC）模型来修复断裂的血管段。MEA-Net通过形态学操作提取多尺度边界体素，构建边缘注意力模块以提升边缘与微小目标的分割效果。OGMC模型利用微分几何中的曲线接触概念筛选碎片化血管端点，进而采用最小曲面确定血管间的最优连接顺序。最后，我们通过给定黎曼度量下的测地线计算修复缺失血管。在四个三维血管分割任务数据集上的实验表明，我们的方法相比现有最优方法取得了更优或相当的结果，既能有效减少血管断裂、增加血管分支丰富度，又能生成拓扑结构更精确的血管。