Simultaneous image segmentation and medial structure estimation: application to 2D and 3D vessel tree extraction

We propose a variational approach which combines automatic segmentation and medial structure extraction in a single computationally efficient algorithm. In this paper, we apply our approach to the analysis of vessels in 2D X-ray angiography and 3D X-ray rotational angiography of the brain. Other variational methods proposed in the literature encode the medial structure of vessel trees as a skeleton with associated vessel radii. In contrast, our method provides a dense smooth level set map which sign provides the segmentation. The ridges of this map define the segmented regions skeleton. The differential structure of the smooth map (in particular the Hessian) allows the discrimination between tubular and other structures. In 3D, both circular and non-circular tubular cross-sections and tubular branching can be handled conveniently. This algorithm allows accurate segmentation of complex vessel structures. It also provides key tools for extracting anatomically labeled vessel tree graphs and for dealing with challenging issues like kissing vessel discrimination and separation of entangled 3D vessel trees.