Segmentation and Visualization of Human Coronary Artery Trees from CTA Datasets

International Journal of Computer Applications Technology and Research
Volume 5–Issue 9, 603-611, 2016, ISSN:-2319–8656
www.ijcat.com 603
Segmentation and Visualization of Human Coronary Artery
Trees from CTA Datasets
Qian Huang
Computer Science Department
Wright State University, United States
______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Abstract: The volume information extracted from computed tomography angiogram is very useful for cardiologists to diagnose various diseases.
An approach is presented to segment human coronary artery trees from the volumetric datasets. The coronary arteries’ surfaces are recovered
by triangle mesh with the boundary points extracted from the coronary artery voxels segmented. The positions where the calcified plaques occur
are identified by mapping the intensities of boundary points of the coronary artery trees on the triangle meshed surfaces. If different values of
the computed maximum principle curvatures of boundary points surrounding the lumen cross section are mapped on the triangle meshed surfaces
of the segmented coronary artery trees, the cross section structure of the coronary artery lumen segment is noncircular cross section structure.
Keywords: Segmentation, visualization, coronary arteries, calcified plaque, maximum principle curvature.
_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
1. INTRODUCTION
Computed tomography angiogram (CTA) [1] plays a significant
role as a clinical tool in the diagnosis of the coronary artery
diseases. It provides three-dimensional information [2], allows
for a better understanding of cardiac three-dimensional anatomy
[4], [5], medical diagnosis [6], and ongoing investigations of
acute and chronic coronary heart diseases [7]. The noninvasive
[9] manner empowered with the visualization of vessels attracts
cardiologists to apply it in clinical environments. Segmenting and
visualizing coronary artery trees and deriving quantitative data
[18] from CTA image datasets for inspecting the coronary lesions
is what many algorithms’ goal to focus on.
Several algorithms have been developed to segment and visualize
vessels in three dimensions [3], for instance, level set method
[10], active contour algorithm [14], vesselness measurement [11],
[12], expectation maximization estimation algorithm [15],
moment-based shape analysis for voxel clusters [16], shape
model based algorithms such as tubular model in three
dimensions [17], the algorithm of combining graph-cuts and
robust kernel regression to segment coronary lumens [18], [19].
The standard marching cube algorithm [21] generates a high
resolution isosurface with an isovalue of image intensity to
represent the object’s surface. The vertices of the set of triangles
build the boundary point cloud of the object. A gradient based
algorithm is used to extract vessel boundaries, the vessel
boundaries are represented as an unstructured point cloud in
three-dimensional image space. The locations of the vessel
boundaries are defined among a set of voxels with the maximum
gradient magnitude along the gradient direction. In this work, this
algorithm will be applied to produce a boundary point cloud
representing the coronary artery boundaries of a human heart.
The existences of the calcified and soft plaques are harmful to the
health of a human body [22-24]. Calcified plaques are with high
intensities [15]. Assuming voxels’ intensities of the segmented
coronary arteries are a Gaussian distribution brings out calcified
plaques’ being identified. The computed mean value plus three
standard deviations of the intensities is the threshold value to
recognize the calcified plaques [25]. Stenoses or soft plaques are
studied to be detected with profiles of artery lumen sectional area
or vessel radiuses along the vessels’ centerlines [15], [27], [30].
The detections of the artery lumen, calcified and soft plaques or
stenoses are clinical useful [31-33]. A coronary artery
segmentation method is presented in this work to segment the
voxels representing the coronary artery trees from CTA datasets.
A triangle mesh method is used to recover the coronary artery
surface from those detected vessels’ boundary points. The
positions of calcified plaques can be identified from the
recovered triangle surfaces. The computed maximum principle
curvatures of the coronary boundary points are mapped on the
triangle surfaces.
2. SEGMENT THE CORONARY
ARTERIES WITH MULTIPLE
ISOVALUES
2.1 Downsample the CTA Datasets
Similarly as [8], the sampling theorem in three dimensions is
applied in this work. The discrete image dataset is obtained by
sampling a continuous function 𝑓𝑐(𝑥, 𝑦, 𝑧) on a lattice with
interval (𝑋, 𝑌, 𝑍). For different sampling rate of a continuous
function, the lattice interval (𝑋, 𝑌, 𝑍) takes different values.
Different lattice interval value represents different voxel size.
Then for the same continuous function, the discrete image dataset,
when sampled at lower sampling rate, has larger lattice interval,
therefore larger voxel size. For the same spatial dimensions, if the
discrete image dataset is sampled at high sampling rate, the voxel
size is smaller, and the number of the resulted voxels is greater
than those sampled at low sampling rate.
According to marching cube algorithm, to compute the vessel
boundary points from the original size of the CTA dataset, each
voxel has to be computed. The extracted boundary point cloud
includes the boundary points of arteries, chambers and other
tissue structures. In a discrete image dataset, the vessels and other
tissue structures are expressed as connected voxels. For the
original image dataset, the number of voxels representing the
vessels and other tissue structures is greater than those of image
dataset with low sampling rate. Then the resulted boundary points
from the original size of CTA dataset are more than those from
the downsampled CTA dataset.
Consequently, the amount of memory space involved for
computing a downsampled CTA dataset is decreased. To
downsample the image dataset, the image dataset is convolved
with a sinc function and the original continuous function is

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reconstructed, so that it can be resampled. The sinc function has
infinite support, therefore, the windowed sinc function has to be
used, which truncates the sinc function by multiplying it with a
window function. After downsampling the volumetric image
dataset, the size of the dataset is changed to 1/3 of the original
image size in both rows and columns, respectively, and 1/1.6 of
the original image dataset size in the number of slices.
2.2 Detect Coronary Artery Regions
Computation of all voxels in each image slice will produce many
boundary points including other tissue structures besides the
boundaries of the vessels, and the involved memory is of large
amount. It is better to segment the regions containing coronary
arteries for the extraction of their boundary points. Mathematical
morphological operators can cluster a set of connected pixels
with a structure element. In this work, such operators are applied
to detect the coronary artery regions.
Dilation morphological operation is to move a structure element
inside the region of interest, and outputs the locus of the pixels
covered by the structure element when its center moves inside the
region of interest. The intensities of the artery regions are higher
compared with those of the heart muscles. For each image slice,
its average intensity is computed. If the pixels’ intensities in each
image slice are higher than the average intensity plus or minus a
small offset defined by the user for segmenting different coronary
artery trees, the center of a 3x3 square structure element is placed
on them. All the pixels covered by this square are defined as the
foreground region. Erode this foreground region with an 8x8
square when the downsampled dataset is being processed and
with a 24x24 square when an original dataset is being operated.
Small regions of foreground voxels can be removed via this
operation. The resulted erosion set is dilated with a 4x4 square
(with a downsampled dataset) or 12x12 square (with an original
dataset) again. The difference of the foreground region and the
resulted set is the region where coronary arteries exist. With this
region, the produced boundaries belong to other tissue structures
and the involved memory can be reduced. An image slice as an
instance of the coronary artery region detected is shown in Figure.
1 (a).
2.3 Analyze Image Histograms of the CTA
Datasets with the Original Size
The image displays an object when its average intensity is
different from its adjacent areas. The histogram provides an
image’s gray-level distribution. Multimodal histograms can
occur when the image contains multiple objects of different
average brightness. The CTA datasets’ intensity histograms are
shown in Figure. 2. There are three peaks in both of the
histograms. The first one represents the background objects and
its intensity is the lowest. The second one indicates the blood’s
intensity and its intensity is between the lowest and the highest.
The third one is recognized as the objects with the highest
intensities, for instance, the bones or calcified plaques, etc.
2.4 Segment with Multiple Isovalues
The standard marching cube algorithm is applied to extract an
object’s boundary point cloud. It is to find a boundary point
linearly interpolated along the edge between two adjacent voxels
in 𝑥 , 𝑦 , or 𝑧 direction. Thus the object’s boundary points
generated by the standard marching cube algorithm vary with the
intensity threshold value defined by the user. Since the varying
contrast agent among the coronary arteries, multiple threshold
values, similarly as in [26], are used in this work to extract
coronary artery boundaries in the marching cube algorithm. The
tested CTA datasets’ intensities are ranged from 0 to 4095. These
multiple threshold values are selected inside an
intensity region around the second peak value in the CTA
dataset’s intensity histogram. The intensity threshold values are
listed in Table I.
TABLE I THE MULTIPLE INTENSITY THRESHOLD VALUES
Dataset Intensity values
1 1022 1102 1145 1187
2 1343 1445 1500 1562.5
Since multiple thresholds are used, multiple boundary layers are
perhaps produced for the vessels. To reduce multiple boundary
layers to one layer, the point with maximum gradient magnitude
is kept among the neighboring boundary points near the gradient
line of each boundary point.
2.5 Determine the Coronary Arteries’
Centerlines
The computed boundary point cloud is tetrahedralized,
centerpoints can be calculated by applying a topological analysis
of the vector field based on the gradient field within every
tetrahedron. The computed centerpoints can be connected via a
line segment when their nearest neighboring centerpoints are
found. The centerpoint can be connected with another
centerpoint that is also closest to it and is in the reverse direction.
Thus this centerpoint’s neighbors are determined.
To differentiate the coronary artery centerpoints from the
computed centerpoint cloud, one experienced medical technician
can pick one seed centerpoint among the centerpoint cloud. This
centerpoint is recognized as a coronary artery centerpoint; the
neighboring centerpoints, which it is connected to, are
recursively marked as coronary artery centerpoints. Several seed
(a)
(b)
Figure. 1 (a) an image slice with the coronary artery
region detected, (b) an original image slice without
detection operation

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centerpoints with a downsampled dataset are selected to find the
other portions of a coronary artery tree’s centerlines. The number
of seed centerpoints with an original dataset is more than a
downsampled dataset.
2.6 Find the Coronary Artery Boundaries
For each coronary artery centerpoint, the boundary points are
recognized as boundary points of the coronary arteries when they
are enclosed in a ball with the radius of current centerpoint. These
boundary points’ normals must point inward of the vessel that
encloses the current centerpoint. The tetrahedra attached by each
of these boundary points are defined as the vessel tetrahedra
except those, of which, there are any vertices’ normals pointing
outward of the vessel. The vertices of vessel tetrahedra are
identified as the boundary points of the coronary arteries.
2.7 Segment the CTA Dataset with the
Original Size
The coronary artery boundary voxels of the original CTA dataset
can be located from those coronary artery boundary points from
the downsampled CTA dataset and are dilated with a 3x3x3 cube
when a right artery tree is segmented and a 5x5x5 cube when a
left artery tree is segmented. If the voxels belong to the detected
coronary artery region, they are again processed with the same
procedures to the downsampled datasets, for instance,
segmenting with multiple isovalues, tetrahedralizing the
boundary points, determining the coronary artery centerlines and
finding the coronary artery boundaries. To extract the coronary
artery centerlines, the centerlines represent small vessel branches
are removed manually. Thus the vessel tetrahera are defined and
the coronary artery boundary points are found.
A scan-conversion algorithm [20] for lines computes the
coordinates of the voxels that line on or near an ideal, infinitely
thin straight line in three dimensions. In principle, the sequence
of voxels is required to lie as close to the ideal line as possible
and to be as straight as possible. The line segment can be drawn
with a sequence of voxels described above with given start point
and end point of this line segment. Scan converting polygons as
area-defining primitives could be done a line segment at a time.
Similarly, scan converting a tetrahedron as a volume-defining
primitive can be completed a triangle at a time. Then the voxels
representing a tetrahedron can be identified. And the coronary
artery voxels can be obtained from all the vessel tetrahedra. The
coronary artery boundary points are triangulated with a surface
mesh. And the coronary artery voxels also include the voxels by
the scan converting each triangle.
3. VISUALIZE THE CORONARY
ARTERY TREES
The intensities of voxels that are not coronary artery voxels are
set to zero. Those voxel sets of coronary arteries are smoothed
with recursive Gaussian filter, and then are processed with the
gradient based extraction algorithm. The triangle mesh is applied
to the resulted boundary points to recover the surfaces of the
segmented coronary artery trees.
3.1 Rendering the Surfaces of the Coronary
Artery Trees
Two main visualization techniques for three-dimensional
medical images are surface rendering and direct volume
rendering (DVR) [13]. Rendering an object’ surface with triangle
mesh belongs to the surface rendering visualization category. In
DVR, a projected two-dimensional image represents the entire
three-dimensional dataset. The projected two-dimensional image
does not allow DVR to capture all the three-dimensional surface
information completely. Figure. 3 (a), (b), (c), (d) display the
surfaces recovered by the triangle mesh on the segmented
coronary artery trees. The number of boundary points, the
triangles and hole triangles are listed in the Table II, 1 represents
dataset 1, 2 indicates dataset 2. A hole triangle means at least one
edge of the triangle connects only one triangle.
TABLE II. THE TRIANGLE MESH WITH THE ARTERY TREES’
BOUNDARY POINTS
Artery
tree
point
number
triangle
number
Hole
triangle
number
Left 1 32481 64961 14
Right 1 33694 67400 0
Left 2 44189 88376 12
Right 2 27008 54008 9
3.2 Identify Calcified Plaques on the Triangle
Meshed Surfaces of the Coronary Artery
Trees
For the varying contrast agent among the coronary arteries,
intensities of the boundary points are assumed as with Gaussian
distribution. The mean (𝜇 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑝𝑜𝑖𝑛𝑡 ) and standard deviation
(a)
(b)
Figure. 2 intensity histograms of CTA datasets (a) dataset 1,
(b) dataset 2
0
10000
20000
30000
40000
50000
60000
70000
185
579
726
873
1020
1167
1314
1461
1608
1755
1902
2049
2196
2343
2490
2637
2784
0
10000
20000
30000
40000
50000
60000
70000
800
940
1080
1220
1359
1499
1639
1779
1918
2058
2198
2338
2477
2617
2757
2897
3039

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( 𝜎 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑝𝑜𝑖𝑛𝑡 ) of intensities of the boundary points are
computed. Figure. 4 shows the intensities of the artery trees’
boundary points mapped on the triangle mesh. The intensity
values are displayed varying from low to high with color ramping
map. The calcified plaques are having higher intensities
compared with their neighboring intensities and are included in
the vessel lumens by the multiple isovalue based algorithm. The
color red represents those boundary points with intensities higher
than 𝜇 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑝𝑜𝑖𝑛𝑡 + 4𝜎 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑝𝑜𝑖𝑛𝑡 . The calcified plaques
can be perceived as a small block with the color red or light red
if that light red’s surrounding areas are colored green. Thus the
calcified plaques with intensities lower than the threshold values
can be identified. These calcified plaques are identified correctly
as those are recognized from each image slice when the
intensities of the boundary points are mapped on the triangle
mesh.
Figure. 5 shows instances of the calcified plaques recognized
from image slices circled with orange color. Figure. 5 (c) also
displays one calcified area circled with blue color, which is not
recognized with the boundary point intensity mapping, a false
negative error. With tested coronary arteries, this calcified plaque
detection method has zero false positive and only one false
negative.
Figure. 6 visualizes the calcified plaques as sets of voxels colored
orange, and they are recognized since they have higher average
intensity than that of the blood of the coronary arteries. The
calcified plaques are inside the vessel lumens by the multiple
isovalue based algorithm and they are included in the segmented
coronary artery voxels. Assume the blood intensities of the
coronary arteries are with Gaussian distribution. The calcified
plaques are recognized as those voxels which intensity values are
greater than 𝜇 𝑣𝑜𝑥𝑒𝑙 + 3𝜎𝑣𝑜𝑥𝑒𝑙, 𝜇 𝑣𝑜𝑥𝑒𝑙 is the mean intensity of the
segmented coronary artery voxels, 𝜎𝑣𝑜𝑥𝑒𝑙 is the standard
deviation. The calcified plaques with intensities less than the
threshold value cannot be determined. In dataset 1 and 2, there
(a)
(b)
(c)
(d)
Figure. 3 triangle mesh on the artery trees (a) left 1, (b)
right 1, (c) left 2, (d) right 2, 1 represents dataset 1, 2
indicates dataset 2.
(a)
(b)
Figure. 4

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(a) (b)
Figure. 5
(c)
Figure. 5 calcified plaques recognized from image
slices (a) left 1, (b) right 2, (c) left 2, 1 represents
dataset 1, 2 indicates dataset 2.
(a)
Figure. 6
(b)
Figure. 6
(c)
Figure. 4
(d)
Figure. 4 intensities of the artery trees’ boundary points mapped
on the triangle meshed surfaces (a) left 1, (b) right 1, (c) left 2,
(d) right 2, 1 represents dataset 1, 2 indicates dataset 2.

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is one false positive calcified area in the left coronary artery tree
of dataset 1, and there are still three false negative areas in the
left coronary artery tree of dataset 2.
3.3 Mapping Maximum Principle Curvatures
of Boundary Points on the Triangle Meshed
Surfaces of the Coronary Artery Trees
The maximum principal curvature of a torus is a constant which
is equal to the reciprocal of the minor radius [29], and the
maximum principal curvature of a circular cylinder is also a
constant with a value of the reciprocal of the radius of circle base
[29]. This work uses the hypotheses that if the real lumen cross
section structure is deviated from the circular cross section
structure, different values of the maximum principle curvatures
of boundary points are surrounding the lumen cross section on
the triangle meshed surfaces of coronary artery trees.
According to the curvature computation in [28], the maximum
principal curvatures can be derived from the local Hessian matrix
at each surface triangle’s vertex. They are mapped on the
recovered triangle meshed surfaces of the coronary artery trees.
The mean value of those maximum principle curvatures of
boundary points is computed. In Figure. 7 (a), (b), (e), (f), (i), (j),
(m), (n), (q), (r), the color blue represents those values of
maximum principle curvature that are greater than the mean value.
Figure. 7 (b), (f), (j), (n) show the large views of the coronary
artery segments located with line segments, different colors are
displayed surrounding the lumen segments. The boundary points
of these artery segments show light blue or green colors for low
maximum principle curvature values and blue colors for high
maximum principle curvature values. The positions of high (low)
maximum principle curvatures are displayed at symmetric
locations around the lumen segment’s axis. These artery
segments are investigated by the maximum intensity projection
(MIP) technique. It is one of recommended image post
processing formats for interpreting the coronary CTA dataset
[34]. In this work, the MIP images are parallel projected. From
the three-dimensional positions where the line segments are
placed, the slab volumes containing the positioned artery
segments can be found. Figure. 7 (c), (d), (g), (h), (k), (l), (o), (p)
are the MIP images of the slab volumes containing the vessel
segments that are located with line segments. Figure. 7 (c), (g),
(k), (o) are the MIP images of one side view to project the slab
volume onto the projection plane where the side of colors with
high values of the maximum principle curvatures can be
perceived. The MIP images of another view are shown in Figure.
7 (d), (h), (l), (p), they are created when the slab volume is
projected onto the projection plane where the side of colors with
low values of the maximum principle curvatures can be observed.
The MIP images of these two side views illustrate different radii
can be obtained from these two sides views at the same cross
sections of the artery segments. The different radii displayed by
these MIP images agree with the different colors mapped by
maximum principle curvatures. (q) is another view of mapping
maximum principle curvatures on the triangle meshed surface of
left coronary artery of dataset 1. The artery segment positioned
by the line segment is surrounding with blue color completely
displayed in (r). The MIP images of the two side views of this
artery segment in (s) and (t) display not obvious difference of
radiuses at the same cross sections of the artery segment
positioned by the line segment, which agree with the same color
mapped by the maximum principle curvatures.
In this work, the computed maximum principle curvatures are
inspected at positions without detected calcified plaques. The
tested coronary artery segments located by the line segments
show that if different values of the computed maximum principle
curvatures of boundary points are surrounding the same lumen
cross section on the triangle meshed surfaces of coronary artery
trees, the lumen displays different radiuses surrounding the same
cross section by MIP images, which further indicates this cross
section structure is not a circular cross section structure.
4. CONCLUSIONS
The method presented to segment coronary artery trees is capable
to obtain the sets of voxels representing coronary arteries. The
positions of the calcified plaques can be identified when the
intensities of boundary points of the coronary artery trees are
mapped on the triangle meshed surfaces. If different values of the
computed maximum principle curvatures of boundary points
surrounding the lumen cross section are mapped on the triangle
meshed surfaces of the segmented coronary artery trees, the cross
section structure of the coronary artery lumen segment is
noncircular cross section structure.
(c)
Figure. 6
(d)
Figure. 6 calcified plaques visualized as orange
voxels inside the coronary artery boundaries (a)
left 1, (b) right 1, (c) left 2, (c) right 2, 1
represents dataset 1, 2 indicates dataset 2.

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(a) (b)
(c) (d)
Figure. 7
(e)
(f) (g) (h)
Figure. 7
(i) (j)
(k) (l)
Figure. 7
(m)
(n) (o) (p)
Figure. 7

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(s) (t)
Figure. 7 maximum principle curvatures mapped on the
triangle meshed surface of (a) left coronary artery of dataset 1,
(e) right coronary artery of dataset 1, (i) left coronary artery of
dataset 2, (m) right coronary artery of dataset 2; (b), (f), (j),
(n) large view of the artery segment located with line segment
in (a), (e), (i), (m), respectively; (c), (g), (k), (o) small radius
from the MIP image in one side view of a slab volume
containing the artery segment in (b), (f), (j), (n), respectively;
(d), (h), (l), (p) large radius from MIP image in another side
view to the same slab volume in (c), (g), (k), (o) respectively.
another view of maximum principle curvatures mapped on the
triangle meshed surface of (q) left coronary artery of dataset 1,
(r) large view of the artery segment located with line segment
in (q), (s) and (t) are MIP images in two sides views of the
slab volume containing the artery segment located with the
line segment in (q).

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