Divergence Prior and Vessel-tree Reconstruction
This work addresses vessel tree reconstruction for medical imaging, offering an incremental improvement by incorporating previously ignored divergence constraints.
The paper tackled the problem of reconstructing vessel trees from 3D volumes by introducing a divergence prior to regularize vector fields, which improved reconstruction quality, especially around bifurcations, and resolved sign ambiguity in flow orientations.
We propose a new geometric regularization principle for reconstructing vector fields based on prior knowledge about their divergence. As one important example of this general idea, we focus on vector fields modelling blood flow pattern that should be divergent in arteries and convergent in veins. We show that this previously ignored regularization constraint can significantly improve the quality of vessel tree reconstruction particularly around bifurcations where non-zero divergence is concentrated. Our divergence prior is critical for resolving (binary) sign ambiguity in flow orientations produced by standard vessel filters, e.g. Frangi. Our vessel tree centerline reconstruction combines divergence constraints with robust curvature regularization. Our unsupervised method can reconstruct complete vessel trees with near-capillary details on synthetic and real 3D volumes.