This paper introduces a graph construction method for multi-dimensional and multi-surface segmentation problems. Such problems can be solved by searching for the optimal separating surfaces given the space of graph columns defined by an initial coarse surface. Conventional straight graph columns are not well suited for surfaces with high curvature, we therefore propose to derive columns from properly generated, non-intersecting flow lines. This guarantees solutions that do not self-intersect. The method is applied to segment human airway walls in computed tomography images in three-dimensions. Phantom measurements show that the inner and outer radii are estimated with sub-voxel accuracy. Two-dimensional manually annotated cross-sectional images were used to compare the results with those of another recently published graph based method. The proposed approach had an average overlap of 89.3±5.8%, and was on average within 0.096±0.097mm of the manually annotated surfaces, which is significantly better than what the previously published approach achieved. A medical expert visually evaluated 499 randomly extracted cross-sectional images from 499 scans and preferred the proposed approach in 68.5%, the alternative approach in 11.2%, and in 20.3% no method was favoured. Airway abnormality measurements obtained with the method on 490 scan pairs from a lung cancer screening trial correlate significantly with lung function and are reproducible; repeat scan R(2) of measures of the airway lumen diameter and wall area percentage in the airways from generation 0 (trachea) to 5 range from 0.96 to 0.73.