Vascular Tree Structure: Fast Curvature Regularization and Validation

This work addresses the challenging problem of accurate vessel structure analysis in high resolution 3D biomedical images. Typical segmentation methods fail on recent micro-CT data sets resolving near-capillary vessels due to limitations of standard first-order regularization models. While regularization is needed to address noise and partial volume issues in the data, we argue that extraction of thin tubular structures requires higher-order curvature-based regularization. There are no standard segmentation methods regularizing surface curvature in 3D that could be applied to large 3D volumes. However, we observe that standard measures for vessels structure are more concerned with topology, bifurcation angles, and other parameters that can be directly addressed without segmentation. We propose a novel methodology reconstructing tree structure of the vessels using a new centerline curvature regularization technique. Our high-order regularization model is based on a recent curvature estimation method. We developed a Levenberg-Marquardt optimization scheme and an efficient GPU-based implementation of our algorithm. We also propose a validation mechanism based on synthetic vessel images. Our preliminary results on real ultra-resolution micro CT volumes are promising