SEGMENTATION OF VESSEL GEOMETRIES FROM MEDICAL

IMAGES USING GPF DEFORMABLE MODEL

Si Yong Yeo

, Xianghua Xie

, Igor Sazonov

and Perumal Nithiarasu

College of Engineering, Swansea University, Swansea , U.K.

College of Science, Swansea University, Swansea , U.K.

Keywords:

Vessel segmentation, Geometric potential force, Deformable model, Image segmentation, Level set methods.

Abstract:

We present a method for the reconstruction of vascular geometries from medical images. Image denoising is

performed using vessel enhancing diffusion, which can smooth out image noise and enhance vessel structures.

The Canny edge detection technique which produces object edges with single pixel width is used for accurate

detection of the lumen boundaries. The image gradients are then used to compute the geometric potential ﬁeld

which gives a global representation of the geometric conﬁguration. The deformable model uses a regional

constraint to suppress calciﬁed regions for accurate segmentation of the vessel geometries. The proposed

framework show high accuracy when applied to the segmentation of the carotid arteries from CT images.

1 INTRODUCTION

The human circulatory system consists of vessels that

transport blood throughout the body, providing the

tissues with oxygen and nutrients. It is known that

vascular diseases such as stenosis and aneurysms are

often associated with changes in blood ﬂow patterns

and the distribution of wall shear stress. Modelling

and analysis of the hemodynamics in the human vas-

cular system can improveour understanding of vascu-

lar disease, and provide valuable insights which can

help in the development of efﬁcient treatment meth-

ods. In recent years, computational ﬂuid dynamics

(CFD) has been widely used for patient-speciﬁc mod-

elling of blood ﬂow in vascular structures (Steinman,

2002; Cebral et al., 2003; Taylor and Figueroa, 2009;

Taylor and Steinman, 2010). Despite the involve-

ment of numerous groups working in this ﬁeld, and

rapid advancement in efﬁcient computational meth-

ods, there has been limited applications of compu-

tational hemodynamics in clinical practice. This is

largely due to the challenges involved in the design of

an integrated framework which can efﬁciently and ac-

curately automate the interdisciplinary computational

modelling process, which includes image segmenta-

tion, mesh generation and CFD simulation.

One of the main challenges in the computational

modelling of hemodynamics is the accurate recon-

struction of the vascular geometry. Anatomically ac-

curate geometric models of the vascular structures are

essential for realistic ﬂow simulations and analysis.

The anatomical information used to reconstruct the

geometric models are usually provided in the form of

medical image datasets (scans) from imaging modal-

ities such as computed tomography (CT) and mag-

netic resonance (MR) imaging. Manual reconstruc-

tion of the vasculature geometries can be tedious and

time consuming. There is also the issue of variabil-

ity between the geometries extracted manually by dif-

ferent individuals, and variability of geometries ex-

tracted by the same individual at different occasions.

In order to allow computational ﬂow modelling to be

efﬁciently applied as a diagnostic or predictive tool,

the amount of user intervention required in the pro-

cess should be reasonably small. In particular, a con-

siderable amount of user intervention is often required

in the reconstruction of an accurate geometric model

for the simulation of ﬂow dynamics. Therefore a ro-

bust and efﬁcient method that can be used to accu-

rately segment the geometric structures from medical

image datasets can be very useful and advantageous

in the modelling process. Here, we propose a robust

framework for the segmentation of vessel geometries

using the GPF deformable model. The framework is

then applied to efﬁciently segment the geometries of

carotid arteries from CT images.

Although several techniques exist for the segmen-

tation of vascular structures from medical images, it

remains an intricate process due to factors such as im-

age noise, partial volume effects, image artifacts, in-

323

Yeo S., Xie X., Sazanov I. and Nithiarasu P..

SEGMENTATION OF VESSEL GEOMETRIES FROM MEDICAL IMAGES USING GPF DEFORMABLE MODEL.

DOI: 10.5220/0003849303230332

In Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods (SADM-2012), pages 323-332

ISBN: 978-989-8425-98-0

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

tensity inhomogeneity and changes in topology. In

(Mori and Yamaguchi, 2001), the coordinate points

for the center line of the aortic arch were extracted

from volume rendered MR images. A cubic spline

was then used to represent the aortic centerline, and

cross-sectional grids were generated on normal planes

at equidistant points along the curve. This generated

a curved tube with circular cross section of uniform

radius, which is not representative of the geometry

of the aorta. In (Tokuda et al., 2008), the centerline

and diameter information of the vessels was extracted

from the image dataset, and the vascular model was

reconstructed using non-uniform rational B-splines

(NURBS). Such techniques may often smooth out ge-

ometric information that can be important to the com-

putation of accurate ﬂow dynamics, such as those at

bifurcations.

The 3D models of the vascular structures in (Wang

et al., 1999) were reconstructed by extracting the 2D

contours of the vessels at each of the image slices

of the MR image dataset, and then lofting through

the contours to create the surface models of the ves-

sels. The different vessels were then merged using

boolean operations in solid modelling. The cross

sections of a particular vessel may however intersect

with cross sections of branching vessels, and the ge-

ometry at these positions have to be approximated.

Other authors such as (Xu et al., 1999; Augst et al.,

2003; Younis et al., 2004; Giordana et al., 2005; Peiro

et al., 2008) also reconstructed 3D surface models of

the vessels from 2D contours extracted from image

slices. This sometimes requires positioning and ori-

enting the 2D contours according to the medial axis

of the vessels, and curve and surface interpolation are

used to approximate and reconstruct the surface mod-

els. However, the 2D contour extraction techniques

used do not provide control over 3D smoothness, and

3D geometric properties from the image datasets are

not considered.

A simple thresholding technique was used in

(Nanduri et al., 2009) to extract the binary image of

the vessels, and the vascular model was reconstructed

using an isosurface algorithm. The thresholding tech-

nique however does not consider the spatial charac-

teristics of the image, and is sensitive to image noise

and inhomogeneous intensity. In (Yi and Ra, 2003;

Sekiguchi et al., 2005), region growing algorithms

were applied to segment the vascular structures from

CT and MR angiography data. The region grow-

ing techniques are, in general, sensitive to noise, and

can often lead to non-contiguous regions and over-

segmentation. In addition, thin structures are often

not extracted due to variations in image intensities.

The watershed transform was used in (Abdel-Dayem

and El-Sakka, 2005; Ding et al., 2007) to extract the

geometry of the carotid. In this approach, the im-

age is interpreted as a landscape or topographic sur-

face, with the pixel intensity representing the eleva-

tion of the topographic surface. Consider water on

the landscape ﬂowing towards regions with local min-

ima, the watersheds are the lines that partition these

regions. In this way, the image is partitioned into ho-

mogeneous regions with the watersheds deﬁning the

boundaries of the regions. The watershed transform

tends to be sensitive to noise and often produces over-

segmentation. It is also difﬁcult for the watershed

technique to extract thin structures and weak object

edges.

In (Ladak et al., 2000; Gil et al., 2000), a 3D dy-

namic surface model was used to delineate the bound-

ary of carotid arteries. An initial triangulated model

was placed within the interior of the carotid ves-

sels, and an inﬂation force was applied to deform the

model towards the vessel wall. In particular, the in-

ﬂation force is applied only when the vertices of the

model are within the lumen, i.e., at locations with im-

age intensity below a user-speciﬁed threshold. An

image-based force is further applied to the surface

model to better localize the boundary. It may however

be difﬁcult to select an appropriate threshold value

that delineates the vessel wall closely due to inho-

mogeneous image intensity. This approach is sensi-

tive to noise, and manual editing is often required to

move the vertices towards the vessel wall. In (Stein-

man et al., 2002), a 2D discrete dynamic contour was

ﬁrst used to extract the vessel contours, a dynamic

surface model was then inﬂated to reconstruct the sur-

face model using the binary images of the extracted

contours. This however does not consider the 3D ge-

ometric information from the image dataset. In (Yim

et al., 2001; Cebral et al., 2001; Cebral et al., 2004),

the surface models for each of the vessel branches of

the carotid artery were reconstructed independently

using a tubular deformable model. A surface merg-

ing algorithm is then required to reconstruct the sur-

face model of the carotid bifurcation from the trian-

gulated surfaces of the vessel branches. This particu-

lar approach requires the determination of the axis of

each of the vessels, which can be done manually by

selecting a reasonable amount of points from image

slices to represent the curves of the structure. Due

to the smoothing effect of this technique, regions of

high curvature such as those at bifurcations or steno-

sis may not be modeled accurately. These explicit

deformable models represent contours and surfaces

parametrically, which requires the tracking of points

on the curves and surfaces during deformation. It is

therefore difﬁcult for explicit deformable models to

ICPRAM 2012 - International Conference on Pattern Recognition Applications and Methods

324

deal with topological variation and complex shapes.

Implicit deformable models have been applied in

the segmentation of vascular structures in (Nilsson

and Heyden, 2003; Antiga and Ene-Iordache, 2003;

Deschamps et al., 2004; Svensson et al., 2006; Antiga

et al., 2008). However, many of these techniques use

an attraction force ﬁeld which acts on contours or sur-

faces only when they are close to the object bound-

aries. As such, initial contours have to be placed

close to the object boundaries, which can be tedious in

complex geometries. A constant pressure term such

as the one in (Malladi et al., 1995), is often used to

monotically expand or shrink the deformable model

towards the image object boundaries, which can over-

whelm weak object edges. In addition, the initial con-

tours have to be placed either inside or outside object

boundaries, which can be difﬁcult for compact and

narrow structures. Many of these techniques are also

sensitive to image noise, and have difﬁculties in ex-

tracting deep boundary concavities.

2 PROPOSED METHOD

In this section, a robust framework is proposed for

the reconstruction of vascular geometries from medi-

cal images. The approach consists of image denoising

using vessel enhancing diffusion (Enquobahrie et al.,

2007; Manniesing et al., 2006), optimal edge detec-

tion using the Canny edge ﬁlter (Canny, 1986), and

robust segmentation of the vascular geometries using

GPF deformable model (Yeo et al., 2011).

2.1 Vessel Enhancing Diffusion Filtering

The formulation of the vessel enhancing diffusion ﬁl-

ter (Enquobahrieet al., 2007; Manniesing et al., 2006)

is based on a smoothed version of the vesselness mea-

sure used in (Frangi et al., 1998). In this approach, an

anisotropic diffusion ﬁlter with strength and direction

determined by the vesselness measure is applied to

enhance the geometric structures of the vessel. The

vesselness measure is determined by analyzing the

eigensystem of the Hessian matrix given as:

H =









(1)

which describes the geometric information at each

point of a 3D image I based on the local intensity vari-

ations. Here, the derivatives of the image I are com-

puted as convolution with derivatives of the Gaussian

function, i.e. I

= I(x) ∗

∂

∂x

(x), where G

denotes

the Gaussian function with standard deviation σ. The

principal curvatures and directions are given by the

maximum and minimum eigenvalues and the corre-

sponding eigenvectors. With the eigenvalues given

such that |λ

| ≤ |λ

|, the vesselness measure

is deﬁned as: if λ

≥ 0 or λ

≥ 0, V

(λ) = 0; other-

wise

(λ) =



1− e

−R

2α



·e

−R

2β



1− e

−S

2γ



·e

|λ

(2)

with

|λ

(3)

|λ

(4)

S =

+ λ

(5)

in which R

and R

can be used to differentiate tubu-

lar structures from blob-like and plate-like structures,

while S is used to differentiate between foreground

vessel structures and background noise. The parame-

ters α, β and γ are weighting factors which control the

sensitivity of the vesselness measure, and c is a small

constant.

For a multiscale analysis, the vesselness function

is computed for a range of scales, and the maximum

response is selected using the following equation:

V = max

min

≤σ≤σ

max

(λ) (6)

A diffusion tensor is then deﬁned such that vessel dif-

fusion takes place in the direction of the vessel, while

diffusion perpendicular to the vessel direction is in-

hibited. The diffusion tensor can therefore be used to

preserve vessel structures and is given as:

D = Qλ

′

(7)

where Q is a matrix containing the eigenvectors of the

Hessian matrix H, and λ

′

is a diagonal matrix with

elements given as:

′

= 1+ (w− 1) ·V

(8)

′

= λ

′

= 1+ (ε − 1) ·V

(9)

with w, ε and s as tuning parameters. The anisotropic

diffusion is then deﬁned as:

= ∇· (D∇L) (10)

where L(0) is set as the input image. Figure 1 demon-

strates that the vessel enhancing diffusion ﬁlter can be

applied to enhance the vessel structures and smooth

out noise in the image. The algorithm for the vessel

enhancing diffusion ﬁlter has been implemented us-

ing the Insight Toolkit (Ibanez et al., 2005).

SEGMENTATION OF VESSEL GEOMETRIES FROM MEDICAL IMAGES USING GPF DEFORMABLE MODEL

325

Figure 1: Vessel enhancing diffusion and image object edge representation of CT image dataset 1, from left to right - orig-

inal image, image with vessel enhancing diffusion, image gradient magnitude, Canny edge with image gradient intensities,

geometric potential ﬁeld.

2.2 Edge Representation for Vessel

Geometries

Image object edges are usually represented as regions

with high intensity contrasts. Image gradients can be

determined using the gradient operator or the Sobel

ﬁlter. These techniqueshowever produces object edge

width of a few pixels. This can easily cause nearby

structures to be connected. For complex geometries

such as those in medical images, it is often neces-

sary to determine ﬁne edges using more robust edge

detection techniques (Deriche, 1987; Petrou and Kit-

tler, 1991) for accurate representation of the image

structures. The Canny edge detection (Canny, 1986)

can produce object edges with single pixel width, and

can therefore be used for accurate edge detection of

the vessel structures. In the Canny edge detection

technique, image smoothing is ﬁrst applied to reduce

noise interference. This can be performed using the

Gaussian ﬁlter or other smoothing techniques such as

vessel enhancing diffusion (Manniesing et al., 2006).

The image gradients are then computed to determine

the magnitudes and directions of the edges. Image

pixels with magnitudes which are not local maxima

in the directions of the edges are suppressed. Hyster-

isis thresholding is then applied to ﬁlter out spurious

edges caused by noise. Image pixels with edge mag-

nitude greater than a high threshold, i.e. f

edge

(x) > T

are considered as edges, while pixels with edge mag-

nitude lower than a low threshold, i.e. f

edge

(x) < T

are removed. Image pixels with edge magnitudes in

between the threshold values, i.e. T

≤ f

edge

(x) < T

which are connected to edge pixels are also consid-

ered as edges. The image gradients at the detected

edges are then used to compute the geometric poten-

tial ﬁeld, see (Yeo et al., 2011) for more detail. As

shown in Figure 1, the geometric potential ﬁeld gives

a more coherent representation of the image object

boundaries as it utlizes global edge pixel interactions

across the image.

2.3 Segmentation of Vessel Geometries

using GPF Deformable Model with

Region Constraint

It is shown in (Yeo et al., 2009a; Yeo et al., 2009b;

Yeo et al., 2011) that the GPF deformable model can

be used to efﬁciently segment complex geometries

from biomedical images. By using pixel or voxel

interactions across the whole image domain, the de-

formable model is more robust to image noise and

weak edges. The dynamic vector force ﬁeld changes

according to the relative postition and orientation be-

tween the geometries, which allows the deformable

model to propagate through long tubular structures.

Here, the GPF deformable model is applied to seg-

ment the geometries of human carotid arteries from

CT images. Some of the main challenges in the seg-

mentation of the carotid geometries include intensity

inhomgeneity, weak edges and adjacent veins with

similar intensities to the carotids. In addition, calciﬁ-

cations which are attached to the arterial walls should

not be included in the reconstructed geometries. Al-

though, the calciﬁed plaques often appear as relatively

bright regions compared to soft tissues, plaques with

lower densities may have similar intensities to the lu-

men. As the intensities of the plaques vary with the

ICPRAM 2012 - International Conference on Pattern Recognition Applications and Methods

326

Figure 2: Image slice from CT image dataset 2 showing contours (top row) and corresponding pixels (bottom row) extracted

using: from left to right - GPF deformable model, GPF deformable model with intensity threshold and GPF deformable model

with region constraint.

Figure 3: Image slice from CT image dataset 4 showing contours (top row) and corresponding pixels (bottom row) extracted

using: from left to right - GPF deformable model, GPF deformable model with intensity threshold and GPF deformable model

with region constraint.

densities, it is not easy for techniques such as global

intensity threshold to remove the plaques from the ex-

tracted geometries. In this section, a region constraint

is added to the deformable model such that it does not

propagate across the calciﬁed regions. This is done by

constraining the deformable model from propagating

across regions with image gradient magnitude larger

than a user speciﬁed value, T

max

. As the calciﬁed re-

gions usually have relatively large image gradients,

the threshold value can be easily selected by observ-

ing the histogram of the image gradient magnitude.

The deformable model with region constraint can thus

be expressed as:

∂φ

∂t



0 if |∇I| > T

max

αgκ|∇φ| − (1− α)(F· ∇φ) otherwise

(11)

where α is a weighting parameter, g is the edge stop-

ping function, κ is the curvature and F is the geo-

metric potential force deﬁned in the GPF model (Yeo

et al., 2011).

Figures 2 and 3 depict a z-axis slice of the ex-

tracted geometry. As shownin the ﬁgures, some calci-

ﬁed regions have similar intensity to the lumen, which

caused the deformable model to include them in the

extracted geometries. The intensities of the plaques

vary which makes it difﬁcult for a global intensity

threshold to suppress them. It is shown that by adding

the region constraint, the deformable model can easily

get around the calciﬁed regions to segment the carotid

geometries accurately.

3 RESULTS AND DISCUSSION

In this section, experimental results on the segmen-

tation of the cartoid geometries using the proposed

framework are shown. In particular, 6 datasets from

CT imaging (provided by Wolverhampton NHS trust)

are used in the experiment. The volumes of interest

containing the carotid arteries are extracted from the

image datasets to reduce the size of the input datasets.

The robust framework which consits of vessel diffu-

sion enhancing, computation of optimal object edge

representation and deformable model with regional

constraint is then applied for the reconstruction of

vessel geometries.

Figures 4 to 7 depict the segmentation of the

carotid geometries using the GPF deformable model

with region constraint. As shown in Figures 4 and 6,

the bidirectional and dynamic vector force allows the

ﬂexible cross-boundary intializations of the model to

easily propagate and convergeto the geometries of the

SEGMENTATION OF VESSEL GEOMETRIES FROM MEDICAL IMAGES USING GPF DEFORMABLE MODEL

327

Figure 4: Segmentation of carotid artery from CT image dataset 1 (61x71x125) using GPF deformable model (CPU-time,

276s).

Figure 5: Segmentation of carotid artery from CT image dataset 3 (70x80x120) using GPF deformable model (CPU-time,

206s).

Figure 6: Segmentation of carotid artery from CT image dataset 5 (70x80x120) using GPF deformable model (CPU-time,

1379s).

Figure 7: Segmentation of carotid artery from CT image dataset 6 (70x80x120) using GPF deformable model (CPU-time,

185s).

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328

Figure 8: Comparison of geometry segmented from CT image dataset 1 using image slices taken along z-axis direction: blue

- manual, orange - GPF deformable model.

Figure 9: Comparison of geometry segmented from CT image dataset 3 using image slices taken along z-axis direction: blue

- manual, orange - GPF deformable model.

carotid arteries. The extraction of the vessel geome-

tries from image datasets 1 and 4 took only 276s and

494s, while the extraction from image datasets 2 and 5

took 1216s and 1379s due to factors such as intensity

variation, low constrast, multiple branches and com-

plex topologies. A graphical user interface has been

developed, which can be used to set multiple initial

contours for fast convergence. It can also be used

to remove inconsistency in object boundaries due to

low resolution of the images, artifacts, etc., or small

branches which do not affect the computational ﬂow

analysis. As shown in Figure 5 and Figure 7, one can

easily speed up the segmentation process by placing

multiple initial contoursor surfaces, as the model con-

verges to the vessel geometries in 206s and 185s when

applied to image datasets 3 and 6 respectively. Note

that the deformable model easily propagate through

the stenotic carotid bifurcations and get around the

calciﬁed regions to efﬁciently segment the carotid ge-

ometries from the CT images.

The reconstructed vessel geometries using the

proposed framework are compared against geome-

tries from manual segmentation. Figures 8 to 11 de-

pict the comparison of the extracted geometries us-

ing random cross-section slices taken along the z-

axis direction. The blue and orange contours rep-

resent the cross-section of the geometries extracted

manually and using the GPF deformable model re-

spectively. As shown in the ﬁgures, the image dataset

consist of other tissue structures which may affect the

geometric reconstruction. In particular, vessels adja-

cent to the carotid artery can often cause other mod-

els to leak out due to the similar intensity. The ge-

ometric potential ﬁeld provides a more coherent and

global representation of the object edges, and allows

the deformable model to extract the geometry accu-

SEGMENTATION OF VESSEL GEOMETRIES FROM MEDICAL IMAGES USING GPF DEFORMABLE MODEL

329

Figure 10: Comparison of geometry segmented from CT image dataset 4 using image slices taken along z-axis direction: blue

- manual, orange - GPF deformable model.

Figure 11: Comparison of geometry segmented from CT image dataset 6 using image slices taken along z-axis direction: blue

- manual, orange - GPF deformable model.

rately. By adding a region constraint, the proposed

model can easily get around the calciﬁed regions as

the deformable model propagates through the tubular

structures to segment the vessel geometry as depicted

in Figures 9, 10 and 11. The proposed framework can

therefore be applied to segment the vessel geometries

efﬁciently from the images. As shown in the ﬁgures,

the vessel geometries segmented using the GPF de-

formable model with region constraint exhibit consid-

erably small deviations from the manually extracted

geometries.

Table 1 presents the accuracy of the segmented

geometries using the proposed method. The fore-

ground (FG) and background (BG) accuracy of the

geometries were measured as the percentages of true

foreground and background voxels which were seg-

mented as foreground and background respectively.

The normalized overall accuracy is given as the aver-

age of FG and BG to measure the accuracy of cor-

Table 1: Comparison of the segmented carotid geometries

using the GPF deformable model with manual segmenta-

tion: Foreground (FG), background (BG) and overall accu-

racy measured in %.

CT image dataset GPF

FG (%) 89.9

1 BG (%) 99.9

Overall (%) 94.9

FG (%) 89.8

2 BG (%) 99.9

Overall (%) 94.8

FG (%) 96.0

3 BG (%) 99.9

Overall (%) 97.9

FG (%) 99.1

4 BG (%) 99.8

Overall (%) 99.5

FG (%) 93.8

5 BG (%) 99.5

Overall (%) 96.7

FG (%) 94.4

6 BG (%) 99.6

Overall (%) 97.0

FG Average (%) 93.9

BG Average (%) 99.8

Overall Average (%) 96.8

ICPRAM 2012 - International Conference on Pattern Recognition Applications and Methods

330

rectly extracted voxels to reduce measurement bias

towards the large number of background voxels in

the image. It is shown that the proposed framework

provides signiﬁcantly accurate geometries with over-

all acurracies of 94.9%, 94.8%, 97.9%, 99.5%, 96.7%

and 97.0% for image datasets 1 to 6, and an average

overall accuracy of 96.8%.

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