Segmentation of curvilinear structures such as vasculature and road networks is challenging due to relatively weak signals and complex geometry/topology. To facilitate and accelerate large scale annotation, one has to adopt semi-automatic approaches such as proofreading by experts. In this work, we focus on uncertainty estimation for such tasks, so that highly uncertain, and thus error-prone structures can be identified for human annotators to verify. Unlike most existing works, which provide pixel-wise uncertainty maps, we stipulate it is crucial to estimate uncertainty in the units of topological structures, e.g., small pieces of connections and branches. To achieve this, we leverage tools from topological data analysis, specifically discrete Morse theory (DMT), to first capture the structures, and then reason about their uncertainties. To model the uncertainty, we (1) propose a joint prediction model that estimates the uncertainty of a structure while taking the neighboring structures into consideration (inter-structural uncertainty); (2) propose a novel Probabilistic DMT to model the inherent uncertainty within each structure (intra-structural uncertainty) by sampling its representations via a perturb-and-walk scheme. On various 2D and 3D datasets, our method produces better structure-wise uncertainty maps compared to existing works.

翻译：对血管、道路网络等曲线状结构的分割具有挑战性，原因在于信号相对微弱以及几何/拓扑结构复杂。为促进并加速大规模标注，需要采用半自动方法，例如专家校对。本文针对此类任务聚焦不确定性估计，以便识别高度不确定（即易出错）的结构，供人工标注者核查。与多数现有方法提供逐像素不确定性图不同，我们强调必须基于拓扑结构单元（如连接段与分支片段）估计不确定性。为此，我们借助拓扑数据分析工具，特别是离散莫尔斯理论（DMT），先捕获结构特征，再推理其不确定性。为建模不确定性，我们：（1）提出联合预测模型，在评估某结构不确定性时兼顾相邻结构（结构间不确定性）；（2）提出新型概率化DMT方法，通过“扰动-游走”方案对结构表示进行采样，以建模每个结构内部固有不确定性（结构内不确定性）。在多个2D和3D数据集上的实验表明，与现有方法相比，本文方法可生成更优的结构级不确定性图。