Maximal curvature-based segmentation of 3D vessel contours

The segmentation of three-dimensional vascular trees is an important topic in medical image processing. Although it may seem to be an easy task, many different techniques have been proposed in the literature during the last decade and many difficulties remain. One can wonder why the human eye is usually able to understand the connectivity and the topology of the different structures while most algorithms fail to do so. In this paper, we propose an original approach that classifies the different contours by applying a geodesic distance transform on the contours of the vessels, where the evolution speed depends directly on the maximal curvature of the contours. This proposition comes from the observation that the maximal curvature on a standard vessel is usually positive and almost constant while it approaches zero or becomes negative on the contour at the contact with other structures. We describe our method in details and present promising results on synthetic and real images, where the method has been able to detect complex vascular structures without leaking into bones or mixing different vascular networks.