Assessment of Intrathoracic Airway Trees: Methods and In Vivo Validation.

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Assessment of Intrathoracic Airway Trees:
Methods and In Vivo Validation
K´ alm´ an Pal´ agyi1,2, Juerg Tschirren2, Eric A. Hoffman3, and Milan Sonka2
1Dept. of Image Processing and Computer Graphics,
University of Szeged, H-6720 Szeged, Hungary
palagyi@inf.u-szeged.hu
2Dept. of Electrical and Computer Engineering,
The University of Iowa, Iowa City IA 52242, USA
{juerg-tschirren,milan-sonka}@uiowa.edu
3Dept. of Radiology,
The University of Iowa, Iowa City IA 52242, USA
eric-hoffman@uiowa.edu
Abstract. A method for quantitative assessment of tree structures is re-
ported allowing evaluation of airway tree morphology and its associated
function. Our skeletonization and branch–point identification method
provides a basis for tree quantification or tree matching, tree–branch di-
ameter measurement in any orientation, and labeling individual branch
segments. All main components of our method were specifically devel-
oped to deal with imaging artifacts typically present in volumetric med-
ical image data. The proposed method has been tested in a computer
phantom subjected to changes of its orientation as well as in repeatedly
CT-scanned rigid and rubber plastic phantoms. In this paper, validation
is reported in six in vivo scans of the human chest.
1Introduction
Tubular structures are frequently found in living organisms. The tubes – e.g.,
arteries or veins are frequently organized into more complex structures. Trees
consisting of tubular segments form the arterial and venous systems, intratho-
racic airways form bronchial trees, and other examples can be found. Computed
tomography (CT) or magnetic resonance (MR) imaging provides volumetric im-
age data allowing identification of such tree structures. Frequently, the trees
represented as contiguous sets of voxels must be quantitatively analyzed. The
analysis may be substantially simplified if the voxel-level tree is represented in a
formal tree structure consisting of a set of nodes and connecting arcs. To build
such formal trees, the voxel-level tree object must be transformed into a set
of interconnected single-voxel centerlines representing individual tree branches.
Therefore, the aim of our work was to develop a robust method for identification
of centerlines and bifurcation (trifurcation, etc.) points in segmented tubular
tree structures acquired in vivo from humans and animals using volumetric CT
or MR scanning, rotational angiography, or other volumetric imaging means.
M.ˇSonka et al. (Eds.): CVAMIA-MMBIA 2004, LNCS 3117, pp. 341–352, 2004.
c ? Springer-Verlag Berlin Heidelberg 2004

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342K. Pal´ agyi et al.
Many researchers focused on this task in the past [2,3,6,7,8,11,13,14]. De-
spite of the wealth of previous work, no perfect skeletonization technique exists
to date. Our new approach that is presented below is attempting to overcome
most of the existing problems. Since our work is driven by the need for quanti-
tative analysis of intrathoracic airway trees from multidetector CT images, we
concentrated on developing a method serving this purpose. However, the result-
ing approach is widely applicable to a variety of medical image data.
2Methods
The reported method allows to quantitatively analyze tubular tree structures.
Assuming an imperfectly segmented tree was obtained from volumetric data
in the previous stages, the presented technique allows to obtain a single–voxel
skeleton of the tree while overcoming many segmentation imperfections, yields
formal tree representation, and performs quantitative analysis of individual tree
segments on a tree–branch basis. The input of the proposed method is a 3D
binary image representing a segmented voxel–level tree object. All main compo-
nents of our method were specifically developed to deal with imaging artifacts
typically present in volumetric medical image data. As such, the method consists
of the following main steps:
1. Topological correction of the segmented tree: Internal cavities (i.e., connected
“0” voxels surrounded by “1” voxels), holes (i.e., “0” voxels forming tunnels),
and bays (i.e., disturbances without a topological change) are eliminated
by sequential forward and backward scanning (instead of the conventional
object labeling) and morphological closing.
2. Identification of the tree root: In the pulmonary CT images, the center of the
topmost nonzero 2D slice in direction z (detected by 2D shrinking) defines
the root of the formal tree to be generated and belongs to the trachea. The
detected root voxel acts as an anchor point during the centerline extraction
(i.e., it cannot be deleted by the forthcoming iterative peeling process).
3. Extraction of the 3D centerlines – skeletonization: A sequential 3D curve–
thinning algorithm was developed for extracting both geometrically and
topologically correct centerlines.
4. Tree pruning: False segments are removed by using both the length and
depth information.
5. Identification of branch points: In a centerlines, three types of points can
be identified: endpoints (which have only one 26–neighbor [5]), line–points
(which have exactly two 26–neighbors), and branchpoints (which have more
than two 26–neighbors) that form junctions (bifurcations, trifurcations, etc.).
6. Generation of a formal tree structure: The centerlines are converted into a
graph structure (each voxel corresponds to a graph node/vertex and there
is an edge between two nodes if the corresponding voxels are 26–adjacent. A
similar structure is assigned to the branchpoints. In the branch-tree, a path
between two branch– or endpoints is replaced by a single edge.

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Assessment of Intrathoracic Airway Trees: Methods and In Vivo Validation 343
7. Tree partitioning: All voxels of the elongated binary tree (after the topo-
logical correction) are partitioned into branches — each voxel is assigned
a branch–specific label. A gray–level image is created, in which value “0”
corresponds to the background and different non–zero values are assigned to
the voxels belonging to different tree branches/partitions.
8. Calculating associated measures: For each partition/branch of the tree, the
following quantitative indices are calculated: branch length, branch volume,
branch surface area, and branch radius.
The entire process has been described in [9,10], therefore, only the critical
steps are now described in more detail.
2.1
One of the well-known approaches to centerline determination is to construct
a 3D skeleton of the analyzed object. However, some of the properties of 3D
skeletons in discrete grids are undesirable. Specifically, in the case of 3D tubu-
lar objects, we do not need the exact skeleton, since a 3D skeleton generally
contains surface patches. We need a skeletonization method that can suppress
creation of such surface patches. As a solution, a 3D curve–thinning algorithm
was developed that is preserving line–end points and can thus extract both geo-
metrically and topologically correct centerlines. As part of this process, a novel
method for endpoint re–checking was developed based on comparisons between
the centerline configuration at some stage of thinning and the previous object
configuration.
Thinning is a frequently used method for producing an approximation to
the skeleton in a topology–preserving way [5]. Border points of a binary object
that satisfy certain topological and geometric constraints are deleted in the iter-
ation steps. In case of tubular 3D objects, thinning has a major advantage over
other skeletonization methods. Curve–thinning (i.e., iterative object reduction
preserving line-end points) can directly produce one voxel wide centerlines.
We proposed a sequential curve–thinning algorithm [9,10]. One iteration step
of the object reduction process is decomposed into six successive sub–iterations
according to the six main directions in 3D. Each sub–iteration consists of two
phases; at first the border points according to the actual deletion direction that
are simple (i.e., their deletion does not alter the topology of the image [5]) and
not line–end points are marked as potential deletable. Then marked points are
checked: a marked point is deleted if it remains simple and is not a line–end
point after the deletion of some previously visited marked points. In addition, in
some special cases, simple points are also deleted if they have become line-end
points. That endpoint re–checking process statistically decreases the number of
unwanted/false side branches in the created centerlines [10].
It can produce maximally thinned (i.e., 1-voxel wide) centerlines (see Fig.
1, since all simple points are deleted. The produced centerline is topologically
equivalent to the original elongated object, since simple points are deleted se-
quentially. Our algorithm is topology-preserving by definition of simple points,
therefore, the proof is self-evident.
Centerline Extraction

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344K. Pal´ agyi et al.
Additionally, our method allows an easy and efficient implementation. It is
much faster than the thinning algorithms employed, e.g., in [13].
Fig.1. The segmented volume of a human airway tree and its centerlines ex-
tracted by the proposed curve–thinning algorithm
2.2Pruning
Unfortunately, each skeletonization algorithm (including ours) is rather sensitive
to coarse object boundaries or surfaces. As a result, the produced (approxima-
tion to the) skeleton generally includes false segments that must be removed
by a pruning step. Applying a proper pruning method that would yield reli-
able centerlines is critical in all tree-skeletonization applications. An unwanted
branch causes false generation numbering and consequently false measurements
corresponding to the individual segments of the tree (including length, volume,
surface area, etc.).
We have developed a centerline pruning that uses both the branch length
and the distance-from-surface (depth) information for the identification of the
following pruning candidate: all branches are deleted if their lengths are shorter
than a given threshold tland their associated branchpoints are not closer to the
border/surface of the elongated tree (after topological correction) than a given
threshold td:
The pruning process can be repeated for different pairs of thresholds (tl,td).
In our experience, 2 to 4 iterations typically provide satisfactory results for in
vivo airway trees. The result of our pruning is demonstrated in Fig. 2.

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Assessment of Intrathoracic Airway Trees: Methods and In Vivo Validation345
Fig.2. A part of a segmented tree and its centerline before pruning (left) and
after pruning (right). The applied pruning technique can delete unwanted long
branches from thick parts and unwanted shorter ones from thinner parts, while
correct branches are typically preserved throughout the tree
2.3Tree Partitioning
The aim of the partitioning procedure is to partition all voxels of the binary tree
into branches — each voxel is assigned a branch-specific label. There are two
inputs into the process — the binary image after topological corrections, and the
formal tree structure corresponding to the centerlines. The output is a gray–level
image, in which value “0” corresponds to the background and different non-zero
values are assigned to the voxels belonging to different tree branches/partitions
(Fig. 3).
Fig.3. The the partitioned volume of a human airway tree close to total lung
capacity (TLC)
The automated partitioning consists of two steps. First, only the voxels in
the centerlines are partitioned so that each branch/partition of the centerlines
has a unique label. Non-skeletal tree voxels are then partitioned by isotropic

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346K. Pal´ agyi et al.
label propagation — each voxel in the tree gets the label of the closest skeletal
point.
2.4Calculating Associated Measures
For each partition/branch of the tree, the following measures/indices are calcu-
lated:
– branch length — defined as a Euclidean distance between the parent and
child branchpoints (in mm),
– branch volume — defined as a volume of all voxels belonging to the branch
(in mm3),
– branch surface area — defined as a surface area of all boundary voxels be-
longing to the branch (in mm2),
– branch radius — derived from the branch length and the branch volume
assuming “cylindrical” partition (in mm):
?
radius =
volume
π · length.
Determining the first three indices is fairly straightforward, but calculating
a reliable approximation to the branch radius is rather complicated. The two
ends of a partition/branch are “conic”, therefore, they must be suppressed to
get measurements only from the “cylindrical” partitions.
3 Experimental Methods
Performance of the reported method was assessed in 343 computer phantom
instances subjected to changes of its orientation, in a rigid plastic phantom CT-
scanned under 9 orientations, in a rubber plastic phantom CT-scanned under 9
orientations, and in six in vivo scans of human lungs.
3.1Phantoms
The computer phantom [4] is a 3-dimensional structural model of the human
airway tree (Fig. 4a). The model consists of 125 elongated branches and its
centerlines have 62 branchpoints and 64 endpoints (including the root of the tree)
— all positions of the branchpoints are known. The generated object is embedded
in a 300 × 300 × 300 binary array containing unit-cube voxels. Independently,
the phantom was rotated in 5 degree steps between −15 and +15 degrees along
all three axes.
The second phantom is a hollow rigid plastic one (Fig. 4b), derived from
an in vivo scanned human bronchial tree, transformed in a computer graphics
representation, and built by a rapid prototyping machine. The third phantom is
a hollow rubber plastic one (Fig. 4c), casted from a normal human bronchial tree

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Assessment of Intrathoracic Airway Trees: Methods and In Vivo Validation 347
(a)(b)(c)
Fig.4. The computer phantom (a), the rigid phantom (b), and the rubber phan-
tom (c) in their neutral orientations and their centerlines
and consists of about 400 branches and 200 branchpoints. The physical phantom
was embedded in potato flakes (simulating lung tissue). The rigid and the rubber
phantoms were imaged in 9–9 orientations using multi-row detector computed
tomography (4-slice spiral CT, Mx8000, Philips Medical Systems) with voxel size
0.439×0.439×0.5mm and 0.488×0.488×0.5mm, respectively. The volume sizes
were 512 × 512× 300− 400 and 512× 512× 500− 600 voxels, respectively. The
rotation angles defined 9–9 phantom orientations in the scanner, the orientations
were separated by 15◦intervals in the x − z and y − z planes.
From the 9–9 CT phantom images, segmentation was performed to separate
bronchial airways from the lung parenchyma yielding a binary image used as an
input to the reported skeletonization algorithm. For each of the 342+9+9 = 360
phantom trees, skeletonization was performed fully automatically and the result-
ing skeletons were not interactively edited. For each instance of the computer
phantoms, the branchpoint position error was determined. It was defined as a
Euclidean distance between the skeletonization-determined and true coordinates
of the corresponding branchpoints.
For a subset of 9 computer phantoms, the 9 rigid and the 9 rubber phantoms,
the above introduced quantitative indices were determined for the first 5 genera-
tions of the matched trees. Here, the reproducibility was determined by assessing
differences between the reference tree and the tree analyzed in different orienta-
tions, after registering the analyzed tree with the reference tree. The quantitative
measurements described above were compared in different orientations.
3.2In Vivo CT Scans
The method was tested in six in vivo scans of the human chest. For each subject, a
scan close to total lung capacity (TLC) was acquired by multi-detector row spiral
computed tomography with voxel size 0.683×0.683×0.6mm3(4-slice spiral CT,

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348K. Pal´ agyi et al.
Mx8000, Philips Medical Systems). The volume sizes were 512×512×450−550
voxels. The segmented in vivo trees are not isometric (i.e., the voxels are cuboids
instead of cubes) and contain numerous “thin” branches. To facilitate repro-
ducibility assessment, a “more regular” reference tree was constructed for each
segmented subject (see Figs. 5-6). The reproducibility analysis was performed
in the reference trees artificially rotated in 8 different ways.
(a) #br(181) (b) #br(131)(c) #br(149)
(d) #br(54) (e) #br(29)(f) #br(41)
Fig.5. The first three in vivo TLC trees (a-c) and the corresponding reference
trees (d-f) (#br means the number of branches)
The reference tree construction consisted of the following steps:
– Centerlines from the segmented in vivo tree were extracted and the formal
tree structure with the associated measures was created. Let S be the set
of the skeletal voxels and let radius(s) denote the radius of the branch
containing s ∈ S (in voxel).
– A new tree Rt(S) is formed in the following way:
?
where t ≥ 0 is an integer threshold for suppressing “thin” branches and
d(r,s) denotes the Euclidean distance between r and s (in voxel).
Rt(S) =
s∈S, radius(s)>t
{ r | d(r,s) ≤ radius(s) },

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Assessment of Intrathoracic Airway Trees: Methods and In Vivo Validation349
In other words, the reference tree is a collection of spheres in which the center
of each sphere is a skeletal voxel in a “thick” branch of the original tree and
the radius of a sphere is derived from the (cylindrical) radius associated with
the corresponding branch of the original tree. Note, that the dimensions of the
original and the reference volumes are the same and the reference volume is
isometric (unit cube voxels 1 mm3).
The extraction of the centerlines from each segmented tree was driven by the
same pruning parameters. For each of the 6 in vivo trees, skeletonization was
performed fully automatically and the resulting skeletons were not interactively
edited. Each of the 6 reference trees was created by the same thickness parameter
(t = 2). Figs. 5-6 show the original and reference trees and their centerlines. Note,
that the reference trees are “more cylindrical” and contain much smaller number
of branches than the original ones.
(a) #br(147)(b) #br(85)(c) #br(122)
(d) #br(36) (e) #br(24)(f) #br(32)
Fig.6. The last three in vivo TLC trees (a-c) and the corresponding reference
trees (d-f) (#br means the number of branches)
For each reference tree, 8 rotated instances were created, the orientations
were separated by 15◦intervals in the x − z and y − z planes. For each of the
6 trees, a set of 9 trees (i.e., the reference tree in neutral position and its 8 ro-
tated instances), skeletonization and quantitative analysis were performed fully
automatically using the same parameters setting for all 54 trees. Again, the

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350K. Pal´ agyi et al.
quantitative measurements described above were compared in different orienta-
tions.
3.3 Statistical Assessment
The reproducibility results are reported separately for the three phantom studies
and for in vivo data. The average branchpoint positioning errors are only calcu-
lated for the computer phantom for which the true branchpoint positions were
known. These errors are presented as mean ± standard deviation and reported
in voxels. All other reproducibility indices were compared using Bland-Altman
statistic for which the average value of all corresponding measurements was used
as an independent variable. The reproducibility showing 95% confidence intervals
are presented in the form of Bland-Altman agreement plots [1].
4Results
In the computer phantoms, the average branchpoint positioning error showed
subvoxel accuracy of 0.93 ± 0.41 voxel size [10].
The reproducibility of the associated in the tree kinds of phantoms is dis-
cussed in [9,10].
The reproducibility of the quantitative tree morphology indices in in vivo CT
scans are given in Fig. 7. In all cases, the relatively large differences between the
surface and volume indices are to be expected due to a high sensitivity of these
measures to minor partitioning errors, especially in short branches. Compare
with the high reproducibility of the branch diameter and length measures.
5Conclusion
The presented automated method for skeletonization, branchpoint identifica-
tion and quantitative analysis of tubular tree structures is robust, efficient, and
highly reproducible. It facilitates calculation of a number of morphologic indices
described above as well as indices not considered in this work — branch angle,
curvature, and many others.
The developed approach is built on the following novel concepts and skele-
tonization algorithm: fast curve-thinning algorithm to increase computational
speed, endpoint re-checking to avoid generation of spurious side branches, depth-
and-length sensitive pruning, exact tree-branch partitioning allowing branch vol-
ume and surface measurements, identification of non-branching tree segments,
achieving sub-voxel accuracy of branch point positioning, and performing exten-
sive validations on complex phantoms and in vivo scans.
Acknowledgments
This work was supported by the NIH grant HL–064368.

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Assessment of Intrathoracic Airway Trees: Methods and In Vivo Validation 351
(a)(b)
(c)(d)
Fig.7. Reproducibility in the 54 “reference” trees derived from in vivo CT data.
a) Branch length, b) Branch volume, c) Branch surface area, and d) Average
branch radius
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