Geodesic voting methods: overview, extensions and application to blood vessel segmentation

In this article we present new methods to segment thin tree structures, which are, for example, present in microglia extensions and cardiac or neuronal blood vessels. Many authors have used minimal cost paths, or geodesics relative to a local weighting potential P, to find a vessel pathway between two end points. We use a set of such geodesic paths to find a tubular tree structure with minimal interaction. Recently, we have introduced a set of methods called geodesic voting. In this article, we review all these methods and present some extensions. We also adapt these methods to the segmentation of complex tree structures in a noisy medium and apply them to the segmentation of blood vessels in 2D and 3D.