A geodesic voting method for the segmentation of tubular tree and centerlines

This paper presents a geodesic voting method to segment tree structures, such as cardiac or cerebral blood vessels. Many authors have used minimal cost paths, or similarly geodesics relative to a weight potential P, to find a vessel between two end points. Our goal focuses on the use of a set of such geodesic paths for finding a tubular tree structure, using minimal interaction. This work adapts the geodesic voting method that we have introduced for the segmentation of thin tree structures to the segmentation of centerlines and tubular trees. The original approach of geodesic voting consists in computing geodesics from a set of end points scattered in the image to a given source point. The target structure corresponds to image points with a high geodesic density. Since the potential takes low values on the tree structure, geodesics will locate preferably on this structure and thus the geodesic density should be high. Geodesic voting method gives a good approximation of the localization of the tree branches, but it does not allow to extract the tubular aspect of the tree. Furthermore, geodesic voting does not guarantee that the extracted tree corresponds to the centerline of the tree. Here, we introduce an explicit constraint that moves the high geodesic density to the centerline of the tree and simultaneously approximates the localization of the boundary of the tubular structure. We show results of the segmentation with this approach on 2D angiogram images. This approach can be extended to 3D images in a straight forward manner.