# Confluent Vessel Trees with Accurate Bifurcations

arXiv: https://arxiv.org/abs/2103.14268 · HTML: https://mlsanity.com/paper/2103.14268/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 34 references that are in the map.
- First posted on arXiv 26 Mar 2021.

## Builds on (most cited first, 3 of 3)

- [Global Minimum for a Finsler Elastica Minimal Path Approach](https://mlsanity.com/paper/1612.00343/) (2016)
- [Divergence Prior and Vessel-tree Reconstruction](https://mlsanity.com/paper/1811.09745/) (2018)
- [Thin Structure Estimation with Curvature Regularization](https://mlsanity.com/paper/1506.04654/) (2015)

## Built on by (most cited first, 3 of 3)

- [Multi-site, Multi-domain Airway Tree Modeling (ATM'22): A Public Benchmark for Pulmonary Airway Segmentation](https://mlsanity.com/paper/2303.05745/) (2023)
- [Modeling and hexahedral meshing of cerebral arterial networks from centerlines](https://mlsanity.com/paper/2201.08279/) (2022)
- [Morphology Edge Attention Network and Optimal Geometric Matching Connection model for vascular segmentation](https://mlsanity.com/paper/2306.01808/) (2023)

## Abstract (arXiv)

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.