A differential geometric approach to automated segmentation of human airway tree

Abstract

Airway diseases are frequently associated with morphological changes that may affect the physiology of the lungs. Accurate characterization of airways may be useful for quantitatively assessing prognosis and for monitoring therapeutic efficacy. The information gained may also provide insight into the underlying mechanisms of various lung diseases. We developed a computerized scheme to automatically segment the 3-D human airway tree depicted on computed tomography (CT) images. The method takes advantage of both principal curvatures and principal directions in differentiating airways from other tissues in geometric space. A "puzzle game" procedure is used to identify false negative regions and reduce false positive regions that do not meet the shape analysis criteria. The negative impact of partial volume effects on small airway detection is partially alleviated by repeating the developed differential geometric analysis on lung anatomical structures modeled at multiple iso-values (thresholds). In addition to having advantages, such as full automation, easy implementation and relative insensitivity to image noise and/or artifacts, this scheme has virtually no leakage issues and can be easily extended to the extraction or the segmentation of other tubular type structures (e.g., vascular tree). The performance of this scheme was assessed quantitatively using 75 chest CT examinations acquired on 45 subjects with different slice thicknesses and using 20 publicly available test cases that were originally designed for evaluating the performance of different airway tree segmentation algorithms.

Fig. 17

Screenshots of the segmentation results on the 20 publicly available test cases from EXACT’09.

Fig. 1

Schematic flowchart of the airway segmentation algorithm

Fig. 2

An example of the lung volume segmentation using the adaptive thresholding operation and its three-dimensional surface model: (a) shows the segmented lung volume in overlay (red), (b) shows the three-dimensional model of (a) at an iso-value of −650 HU, (c) is a “cut-out” version of (b), and (d) shows an local enlarged region indicated by the box in (c). The arrow in (b) indicates a juxtapleural nodule.

Fig. 3

An example demonstrating the impact of the iso-value (threshold) on the lung anatomical structure modeling: (a) shows a CT examination, (b) shows the enlarged version of the region indicated by a box in (a), and (c)–(h) show the anatomical structures within the indicated region in (b) as modeled at different iso-values, i.e., −950 HU, −850HU, −750 HU, −650 HU, −550 HU, and −450 HU, respectively. The tubular regions in (c) indicate the inner airway wall regions depicted on the image in (b).

Fig. 4

An illustration of the Rusinkiewicz curvature estimation (a) and the Laplacian smoothing (b) using a 1-ring mesh. In (a), (u, v) is the local coordinate system of the triangle in bold; in (b), the vertex $v_i^{\prime }$ is the centroid for the 1-ring triangles around v_i. The smoothing and shrinking effects after applying the Laplacian operation to the structure in (c) 5 and 20 times are shown in (d) and (e), respectively.

Fig. 5

An example demonstrating the performance of the Rusinkiewicz’s method in estimating the principal curvatures and the principal directions: (a) shows local lung anatomical structures with three basic shapes, namely planar, spherical, and cylindrical, (b) and (c) show color-coded visualizations of the maximum and the minimum curvatures respectively, (d) and (e) depict the maximum and the minimum curvature directions respectively for local regions with typical shapes.

Fig. 6

The lung surface model (a) at an iso-value of −850 HU is subdivided into an “airway” component (b) and a non-airway component (c), following the application of the set of curvature filtering criteria.

Fig. 7

Illustration of the small planar region filtering procedure: (a) shows a cylindrical shape, (b) shows a plane like surface patch, (c) and (d) show the normal vector distributions of a cylindrical shape and the plane like patch in (a) after aligning their averaged minimum curvature directions with the z-axis, (e) shows tubular regions and surface patch regions using the locally enlarged region in Fig. 6(b), (f) shows the local region identified by the arrow in Fig. 6(b), (g) shows the airway after the application of the filtering operation, and (h) shows the “cleaned up” result for the region shown in (f).

Fig. 8

(a) and (b) show local enlargements of trachea regions after applying the normal vector distribution based filtering to regions shown in Fig. 6(b) and Fig. 6(c); (c) and (d) show the airway set (A) and non-airway set (B) after applying the “puzzle game” operation to the regions in Fig. 6(b) and Fig. 6(c). The arrows indicate the “holes” or missing airway regions.

Fig. 9

Illustration of the ring-collapse operation: (a) shows a 2-ring triangle mesh, (b) shows the collapsed triangle mesh of (a) where the dashed edges in (b) are removed from the triangle mesh, and (c) and (d) show the local region indicated by the box in Fig. 4(c) before and after the ring-collapse operation.

Fig. 10

An example of the mapping of the identified airway tree from the geometric space onto the CT image space: (a) and (b) shows a coronal view and a sagittal view of the mapped results and the superimposed geometric airway tree, respectively.

Fig. 11

Airway trees are shown (bottom row) after performing the segmentation algorithm on the three-dimensional lung anatomical structures modeled at different iso-values: (a) −750HU, (b) −800 HU, (c) −880 HU, and (d) −900 HU. The airway tree identified at an iso-value of −850 HU is shown in Fig. 10. For better visualization, only a fraction of the lung anatomical structures are displayed.

Fig. 12

Airway centerline extraction and labeling: (a) shows the segmented airways; (b) shows the centerline and branch points of (a); and, (c) shows a mixed rendering of (a) and (b) at different locations and from different perspectives. The regions in light green in (c) indicate centerlines and regions in green represent inner airway walls.

Fig. 13

Examples of airway tree segmentations selected from the first group (i.e., Case #1 - Case #30) with the better performance (the left column: Cases #23 and #27), mid-level performance (the middle column: Cases #5 and #18), and worst performance (the right column: Cases #12 and #20). All examinations have a slice thickness of 0.625 mm and were reconstructed with a “standard” kernel.

Fig. 14

Examples of airway tree segmentations selected from the second group (i.e., Case #31 - Case #45) with the better (“high”) performance (the left column: Cases #45), mid-level (“average”) performance (the middle column: Case #40), and “poor” performance (the right column: Case #39). These examinations were reconstructed with “bone” kernel and have three different slice thickness of 0.625 mm (the top row), 1.25 mm (the mid row), and 2.5 mm (the bottom row), respectively.

Fig. 15

An example of the use of the developed scheme to segment vascular tree depicted on CT images: (a) shows the segmented three-dimensional vascular tree, and (b) shows a mixed rendering of (a) superimposed on the corresponding CT images.

Fig. 16

Two examples of the airways segmentations results is severely diseased cases: (a) shows an examination (Case #25) with bronchiectasis, (b) shows the segmented airway tree of the examination in (a); (c) shows an examination (Case #2) with severe COPD displayed at a threshold of −950 HU, and (d) shows the airway tree as segmented from the examination in (c).