Confluent Vessel Trees with Accurate Bifurcations
This work addresses the challenge of accurately reconstructing complex vasculature in medical imaging, which is crucial for applications like disease diagnosis and treatment planning, though it is incremental as it builds on existing unsupervised methods by incorporating flow directedness.
The paper tackled the problem of unsupervised reconstruction of complex near-capillary vasculature with thousands of bifurcations, where standard undirected tubular graph methods produce errors at bifurcations due to ignoring flow directedness. They introduced a new concept of confluence for oriented curves and an efficient algorithm using minimum arborescence on directed graphs, resulting in significantly improved reconstruction accuracy at bifurcations in empirical tests on large sub-voxel volumes.
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.