A central axis algorithm for 3D bronchial tree structures

Accurate measurements of the physiological parameters like branching angles, branch lengths and diameters of bronchial tree structures help in addressing the diagnostic questions related to obstructive lung disease. To facilitate these measurements, 3D bronchial trees are reduced to a straight line central axis tree. We designed a two pass algorithm to compute the central axis tree of bronchial tree structures. In the first pass, the topological branching tree structure T is obtained by using a top-down region growing algorithm on the tree volume. In the second pass, T is used to region grow bottom-up from the leaves, in order to obtain accurate centroid points that lie along the axes of the branches. Using these centroid points at each bifurcation, the branch point and the three direction vectors along the branches are computed, by solving a non-linear optimization problem. By connecting the computed branch points at each bifurcation with straight lines, we obtain the central axis tree on which we make the measurements. We also ran our algorithm on 3D tree model (cylindrical branches) that simulate bronchial trees and the computed central axis compared favorably with the ground truth central axis in terms of the measured physiological parameters.