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We are interested in unsupervised reconstruction of complex near-capillaryvasculature with thousands of bifurcations where supervision and learning areinfeasible. Unsupervised methods can use many structural constraints, e.g.topology, geometry, physics. Common techniques use variants of MST on geodesictubular graphs minimizing symmetric pairwise costs, i.e. distances. We showlimitations of such standard undirected tubular graphs producing typical errorsat bifurcations where flow "directedness" is critical. We introduce a newgeneral concept of confluence for continuous oriented curves forming vesseltrees and show how to enforce it on discrete tubular graphs. While confluenceis a high-order property, we present an efficient practical algorithm forreconstructing confluent vessel trees using minimum arborescence on a directedgraph enforcing confluence via simple flow-extrapolating arc construction.Empirical tests on large near-capillary sub-voxel vasculature volumesdemonstrate significantly improved reconstruction accuracy at bifurcations. Ourcode has also been made publicly available.

Confluent Vessel Trees with Accurate Bifurcations