clDice -- a Topology-Preserving Loss Function for Tubular Structure Segmentation

Accurate segmentation of tubular, network-like structures, such as vessels, neurons, or roads, is relevant to many fields of research. For such structures, the topology is their most important characteristic, e.g. preserving connectedness: in case of vascular networks, missing a connected vessel entirely alters the blood-flow dynamics. We introduce a novel similarity measure termed clDice, which is calculated on the intersection of the segmentation masks and their (morphological) skeletons. Crucially, we theoretically prove that clDice guarantees topological correctness for binary 2D and 3D segmentation. Extending this, we propose a computationally efficient, differentiable soft-clDice as a loss function for training arbitrary neural segmentation networks. We benchmark the soft-clDice loss for segmentation on four public datasets (2D and 3D). Training on soft-clDice leads to segmentation with more accurate connectivity information, higher graph similarity, and better volumetric scores.