Blood vessel segmentation is one of the most studied topics in computer vision, due to its relevance in daily clinical practice. Despite the evolution the field has been facing, especially after the dawn of deep learning, important challenges are still not solved. One of them concerns the consistency of the topological properties of the vascular trees, given that the best performing methodologies do not directly penalize mistakes such as broken segments and end up producing predictions with disconnected trees. This is particularly relevant in graph-like structures, such as blood vessel trees, given that it puts at risk the characterization steps that follow the segmentation task. In this paper, we propose a similarity index which captures the topological consistency of the predicted segmentations having as reference the ground truth. We also design a novel loss function based on the morphological closing operator and show how it allows to learn deep neural network models which produce more topologically coherent masks. Our experiments target well known retinal benchmarks and a coronary angiogram database.

中文翻译：

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血管分割的拓扑相似指数和损失函数

由于其在日常临床实践中的相关性，血管分割是计算机视觉中研究最多的主题之一。尽管该领域一直面临着演变，特别是在深度学习出现之后，重要的挑战仍未解决。其中之一涉及维管树拓扑特性的一致性，因为性能最好的方法不会直接惩罚错误（例如断段），并最终以断开的树生成预测。这在类似图的结构中尤其重要，例如血管树，因为它会使分割任务之后的表征步骤处于危险之中。在本文中，我们提出了一个相似性指数，它捕获了预测分割的拓扑一致性，并将其作为参考。我们还设计了一种基于形态闭合算子的新型损失函数，并展示了它如何允许学习产生更多拓扑相干掩码的深度神经网络模型。我们的实验针对众所周知的视网膜基准和冠状动脉血管造影数据库。