Liver-vessel segmentation is an essential task in the pre-operative planning of liver resection. State-of-the-art 2D or 3D convolution-based methods focusing on liver vessel segmentation on 2D CT cross-sectional views, which do not take into account the global liver-vessel topology. To maintain this global vessel topology, we rely on the underlying physics used in the CT reconstruction process, and apply this to liver-vessel segmentation. Concretely, we introduce the concept of top-k maximum intensity projections, which mimics the CT reconstruction by replacing the integral along each projection direction, with keeping the top-k maxima along each projection direction. We use these top-k maximum projections to condition a diffusion model and generate 3D liver-vessel trees. We evaluate our 3D liver-vessel segmentation on the 3D-ircadb-01 dataset, and achieve the highest Dice coefficient, intersection-over-union (IoU), and Sensitivity scores compared to prior work.

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