  Vessel segmentation and centerline extraction are two crucial preliminary
tasks for many computer-aided diagnosis tools dealing with vascular diseases.
Recently, deep-learning based methods have been widely applied to these tasks.
However, classic deep-learning approaches struggle to capture the complex
geometry and specific topology of vascular networks, which is of the utmost
importance in most applications. To overcome these limitations, the clDice
loss, a topological loss that focuses on the vessel centerlines, has been
recently proposed. This loss requires computing, with a proposed soft-skeleton
algorithm, the skeletons of both the ground truth and the predicted
segmentation. However, the soft-skeleton algorithm provides suboptimal results
on 3D images, which makes the clDice hardly suitable on 3D images. In this
paper, we propose to replace the soft-skeleton algorithm by a U-Net which
computes the vascular skeleton directly from the segmentation. We show that our
method provides more accurate skeletons than the soft-skeleton algorithm. We
then build upon this network a cascaded U-Net trained with the clDice loss to
embed topological constraints during the segmentation. The resulting model is
able to predict both the vessel segmentation and centerlines with a more
accurate topology.
