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