A computer implemented method for determining a centerline of a three-dimensional tubular structure is described. The method includes providing an edge-detected data set of voxels that characterize a boundary of the tubular structure according to a three-dimensional voxel data set for the tubular structure. A gradient field of a distance transformation is computed for the edge-detected dataset. A voxel data set corresponding to a centerline of the tubular structure is computed according to derivative of gradient field. A trajectory within the tubular structure is computed based on the centerline.