CLGeoDice: Bridging Topology and Geometry with Continuous Distance Maps for Vessel Segmentation

Accurate segmentation of coronary arteries from Computed Tomography Angiography (CTA) is critical for cardiovascular disease diagnosis and intervention planning. However, existing loss functions face fundamental limitations. The Dice metric prioritizes larger structures over thin vessels and treats all error types equally. Topology-aware losses, such as Centerline Dice (clDice) and Centerline Boundary Dice (cbDice), address topological errors but remain sensitive to deformations, which is particularly problematic for datasets with thin structures and noisy annotations. To address these limitations, we propose CLGeoDice, a geometry-aware topological framework comprising both a loss function for training and a unified evaluation metric for clinical assessment. CLGeoDice transforms discrete skeleton matching into a continuous, linear distance metric by constructing a distance-based heatmap. This heatmap establishes a smooth relationship between predicted and ground truth vessel geometry. The continuous formulation eliminates gradient truncation inherent in binary losses and provides geometrically aware gradients that are robust to annotation noise. The proposed CLGeoDice score serves as a clinically meaningful evaluation metric that simultaneously captures topological connectivity and geometric precision, offering superior assessment capabilities compared to existing metrics. Experimental validation on a multi-center coronary CTA dataset (160 scans) demonstrates that CLGeoDice achieves state-of-the-art performance.