Divergence Prior and Vessel-Tree Reconstruction

Zhongwen Zhang, Dmitrii Marin, Egor Chesakov, Marc Moreno Maza, Maria Drangova, Yuri Boykov; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2019, pp. 10216-10224


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.

Related Material

author = {Zhang, Zhongwen and Marin, Dmitrii and Chesakov, Egor and Maza, Marc Moreno and Drangova, Maria and Boykov, Yuri},
title = {Divergence Prior and Vessel-Tree Reconstruction},
booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2019}