Promoting the connectivity of curvilinear structures, such as neuronal processes in biomedical scans and blood vessels in CT images, remains a key challenge in semantic segmentation. Traditional pixel-wise loss functions, including cross-entropy and Dice losses, often fail to capture high-level topological connectivity, resulting in topological mistakes in graphs obtained from prediction maps. In this paper, we propose CAPE (Connectivity-Aware Path Enforcement), a novel loss function designed to enforce connectivity in graphs obtained from segmentation maps by optimizing a graph connectivity metric. CAPE uses the graph representation of the ground truth to select node pairs and determine their corresponding paths within the predicted segmentation through a shortest-path algorithm. Using this, we penalize both disconnections and false positive connections, effectively promoting the model to preserve topological correctness. Experiments on 2D and 3D datasets, including neuron and blood vessel tracing demonstrate that CAPE significantly improves topology-aware metrics and outperforms state-of-the-art methods.

翻译：在语义分割中，提升曲线结构（如生物医学扫描中的神经元突起和CT图像中的血管）的连通性仍然是一个关键挑战。传统的逐像素损失函数，包括交叉熵损失和Dice损失，通常无法捕捉高层次的拓扑连通性，导致从预测图中获得的图结构存在拓扑错误。本文提出CAPE（连通性感知路径强制），这是一种新颖的损失函数，旨在通过优化图连通性度量，强制提升从分割图中获得的图的连通性。CAPE利用真实标注的图表示来选择节点对，并通过最短路径算法在预测分割中确定其对应路径。基于此，我们对断连和误报连接均施加惩罚，从而有效促使模型保持拓扑正确性。在包括神经元和血管追踪在内的2D和3D数据集上的实验表明，CAPE显著提升了拓扑感知度量，并优于现有最先进方法。