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.

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