This paper presents 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 utilize a set of such geodesic paths to find a tubular tree structure by seeking minimal interaction. We introduce a new idea that we call geodesic voting or geodesic density. The approach consists of computing geodesics from a set of end points scattered in the image which flow toward a given source point. The target structure corresponds to image points with a high geodesic density. The “Geodesic density” is defined at each pixel of the image as the number of geodesics that pass over this pixel. The potential P is defined in such way that it takes low values along the tree structure, therefore geodesics will migrate toward this structure thereby yielding a high geodesic density. We further adapt these methods to segment complex tree structures in a noisy medium and apply them to segment microglia extensions from confocal microscope images as well as vessels. 
Geodesic voting for the automatic extraction of tree structures. Methods and applications