A method for quantitative assessment of tree structures is reported allowing evaluation of airway or vascular tree morphology and its associated function. Our skeletonization and branch-point identification method provides a basis for tree quantification or tree matching, tree-branch diameter measurement in any orientation, and labeling individual branch segments. All main components of our method were specifically developed to deal with imaging artifacts typically present in volumetric medical image data. The proposed method has been tested in 343 computer phantom instances subjected to changes of its orientation as well as in a repeatedly CT-scanned rubber plastic phantom width sub-voxel accuracy and high reproducibility. Application to 35 human in vivo trees yielded reliable and well-positioned centerlines and branch-points.