  Accurately segmenting thin tubular structures, such as vessels, nerves, roads
or concrete cracks, is a crucial task in computer vision. Standard deep
learning-based segmentation loss functions, such as Dice or Cross-Entropy,
focus on volumetric overlap, often at the expense of preserving structural
connectivity or topology. This can lead to segmentation errors that adversely
affect downstream tasks, including flow calculation, navigation, and structural
inspection. Although current topology-focused losses mark an improvement, they
introduce significant computational and memory overheads. This is particularly
relevant for 3D data, rendering these losses infeasible for larger volumes as
well as increasingly important multi-class segmentation problems. To mitigate
this, we propose a novel Skeleton Recall Loss, which effectively addresses
these challenges by circumventing intensive GPU-based calculations with
inexpensive CPU operations. It demonstrates overall superior performance to
current state-of-the-art approaches on five public datasets for
topology-preserving segmentation, while substantially reducing computational
overheads by more than 90%. In doing so, we introduce the first multi-class
capable loss function for thin structure segmentation, excelling in both
efficiency and efficacy for topology-preservation.
