Automated anatomical vessel labeling of the abdominal arterial system is a crucial topic in medical image processing. One reason for this is the importance of the abdominal arterial system in the human body, and another is that such labeling is necessary for the related disease diagnoses, treatments and epidemiological population analyses. We define a hypergraph representation of the abdominal arterial system as a family tree model with a probabilistic hypergraph matching framework for automated vessel labeling. Then we treat the labelling problem as the convex optimization problem and solve it with the maximum a posteriori(MAP) combined the likelihood obtained by geometric labelling with the family tree topology-based knowledge. Geometrically, we utilize XGBoost ensemble learning with an intrinsic geometric feature importance analysis for branch-level labeling. In topology, the defined family tree model of the abdominal arterial system is transferred as a Markov chain model using a constrained traversal order method and further the Markov chain model is optimized by a hidden Markov model (HMM). The probability distribution of the target branches for each candidate anatomical name is predicted and effectively embedded in the HMM model. This approach is evaluated with the leave-one-out method on 37 clinical patients’ abdominal arteries, and the average accuracy is 91.94%. The obtained results are better than those of the state-of-art method with an F1 score of 93.00% and a recall of 93.00%, as the proposed method simultaneously handles the anatomical structural variability and discriminates between the symmetric branches. It is demonstrated to be suitable for labelling branches of the abdominal arterial system and can also be extended to similar tubular organ networks, such as arterial or airway networks.

腹部动脉系统的自动解剖血管标记是医学图像处理中的一个重要课题。一个原因是腹部动脉系统在人体中的重要性，另一个原因是这种标签对于相关的疾病诊断、治疗和流行病学人群分析是必要的。我们将腹部动脉系统的超图表示定义为具有用于自动血管标记的概率超图匹配框架的家谱模型。然后我们将标注问题视为凸优化问题，结合几何标注得到的似然性和基于族树拓扑的知识，利用最大后验（MAP）求解。几何上，我们利用 XGBoost 集成学习和内部几何特征重要性分析进行分支级标签。在拓扑学中，定义的腹部动脉系统家族树模型使用约束遍历顺序方法作为马尔可夫链模型进行转移，并进一步通过隐马尔可夫模型（HMM）优化马尔可夫链模型。每个候选解剖名称的目标分支的概率分布被预测并有效地嵌入到 HMM 模型中。该方法采用留一法对37例临床患者的腹部动脉进行评估，平均准确率为91.94%。获得的结果优于 state-of-art 方法，F1 得分为 93.00%，召回率为 93.00%，因为所提出的方法同时处理解剖结构变异性并区分对称分支。它被证明适用于标记腹部动脉系统的分支，也可以扩展到类似的管状器官网络，例如动脉或气道网络。