  Curvilinear structure segmentation is important in medical imaging,
quantifying structures such as vessels, airways, neurons, or organ boundaries
in 2D slices. Segmentation via pixel-wise classification often fails to capture
the small and low-contrast curvilinear structures. Prior topological
information is typically used to address this problem, often at an expensive
computational cost, and sometimes requiring prior knowledge of the expected
topology.
  We present DTU-Net, a data-driven approach to topology-preserving curvilinear
structure segmentation. DTU-Net consists of two sequential, lightweight U-Nets,
dedicated to texture and topology, respectively. While the texture net makes a
coarse prediction using image texture information, the topology net learns
topological information from the coarse prediction by employing a triplet loss
trained to recognize false and missed splits in the structure. We conduct
experiments on a challenging multi-class ultrasound scan segmentation dataset
as well as a well-known retinal imaging dataset. Results show that our model
outperforms existing approaches in both pixel-wise segmentation accuracy and
topological continuity, with no need for prior topological knowledge.
