  Extracting complex structures from grid-based data is a common key step in
automated medical image analysis. The conventional solution to recovering
tree-structured geometries typically involves computing the minimal cost path
through intermediate representations derived from segmentation masks. However,
this methodology has significant limitations in the context of projective
imaging of tree-structured 3D anatomical data such as coronary arteries, since
there are often overlapping branches in the 2D projection. In this work, we
propose a novel approach to predicting tree connectivity structure which
reformulates the task as an optimization problem over individual steps of a
recursive process. We design and train a two-stage model which leverages the
UNet and Transformer architectures and introduces an image-based prompting
technique. Our proposed method achieves compelling results on a pair of
synthetic datasets, and outperforms a shortest-path baseline.
