This paper proposes an original method for extracting the centerline of 3D objects given only partial mesh scans as input data. Its principle relies on the construction of a normal vector accumulation map build by casting digital rays from input vertices. This map is then pruned according to a confidence voting rule: confidence in a point increases if this point has maximal votes along a ray. Points with high confidence accurately delineate the centerline of the object. The resulting centerline is robust enough to allow the reconstruction of the associated graph by a simple morphological processing of the confidence and a geodesic tracking. The overall process is unsupervised and only depends on a user-chosen maximal object radius. Experiments show a good behavior on standard mesh scans. Moreover, the proposed method is not only competitive with state-of-the-art methods on perfect data, but appears to be much more reliable on imperfect or damaged data, like holes, partial scans, noise, and scans from only one direction.