We present a mathematical airway tree-shape framework
where airway trees are compared using geodesic distances. The framework
consists of a rigorously dened shape space for treelike shapes,
endowed with a metric such that the shape space is a geodesic metric
space. This means that the distance between two tree-shapes can be realized
as the length of the geodesic, or shortest deformation, connecting
the two shapes. By computing geodesics between airway trees, as well as
the corresponding airway deformation, we generate airway branch correspondences.
Correspondences between an unlabeled airway tree and a set
of labeled airway trees are combined with a voting scheme to perform
automatic branch labeling of segmented airways from the challenging
EXACT'09 test set. In spite of the varying quality of the data, we obtain
robust labeling results.