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We deal with image processing applied to three-dimensional (3D) analysis of vascular morphology in magnetic resonance angiography (MRA) images. It is, above all, a state-of-the-art survey. Both filtering and segmentation techniques are discussed. We briefly describe our most recent contribution : an anisotropic non-linear filter which improves visualization of small blood vessels. Enhancement of small vessels is obtained by combining a directional L-filter applied according to the locally estimated orientation of image content and a 2D Laplacian orthogonal to this orientation.
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1
ADVANCES OF BLOOD VESSEL MORPHOLOGY ANALYSIS IN 3D MAGNETIC
RESONANCE IMAGES 1
Maciej Orkisz, Marcela Hernández-Hoyos, Philippe Douek, Isabelle Magnin
CREATIS, CNRS Research Unit (UMR 5515), affiliated to INSERM, Lyon, France
CREATIS INSA 502, 69621 Villeurbanne cedex, France, maciej.orkisz@creatis.insa-lyon.fr
Abstract We deal with image processing applied to three-dimensional (3D) analysis of
vascular morphology in magnetic resonance angiography (MRA) images. It is, above all, a state-of-the-
art survey. Both filtering and segmentation techniques are discussed. We briefly describe our most recent
contribution : an anisotropic non-linear filter which improves visualization of small blood vessels.
Enhancement of small vessels is obtained by combining a directional L-filter applied according to the
locally estimated orientation of image content and a 2D Laplacian orthogonal to this orientation.
Key words: 3D image processing, medical imaging, magnetic resonance angiography, image
enhancement, image segmentation
1. Introduction
Our work is motivated by diagnosis, treatment planning and follow-up of arterial diseases.
Atherosclerosis is the principal acquired affection of the arterial wall. Its consequences depend
on its localization and on the size of the vessel. They are of two natures : arterial lumen
obstruction (stenosis) and arterial wall vulnerability which may lead to excrescence
(aneurysm) and rupture. Diagnosis of these pathologies is greatly aided by imaging
techniques. There are several challenges concerning angiography images. They obviously
should clearly display the pathological artery segment. In the case of severe obstructions, the
physician also needs to assess the collateral vascularization, i.e. to see a network of thin
vessels around the diseased region. Qualitative assessment is usually done in two-dimensional
(2D) projection images. However, the choice and planning of pharmacological, intra-vascular
or surgical treatment depend on precise measurements such as length, different diameters and
section areas of the diseased segment. These quantitative measurements should take full
advantage of 3D information. The latter requirement, as well as the invasive character of the
conventional 2D X-ray digital subtraction angiography (DSA), are the reasons for which 3D
imaging techniques such as MRA and spiral computed tomography (CT) tend to replace DSA.
Like the medical objectives, image processing challenges are twofold : 1) vessel enhancement
and noise removal to improve the qualitative analysis, 2) 3D segmentation and quantification
for the sake of (semi-)automated measurements. Both tasks are difficult, due to the specificity
of the data. Questions how to enhance thin vessels and not to amplify noise, how to remove
1 This work is in the scope of the scientific topics of the PRC-GDR ISIS research group of the French
National Center for Scientific Research (CNRS).
2
noise and not to wipe out thin vessels, are still an issue. Similarly, most segmentation
techniques are designed for large and homogenous regions, while many blood vessels are not
thicker than 3 pixels, their structure is complex, with ramifications, and their intensity is often
relatively heterogeneous, due to partial volume effect, flow artifacts and other effects. In
section 2, an outline of the state of the art of the angiography image processing shall be given.
In section 3, our contribution in vessel enhancement field shall be presented.
2. State of the art
There is a rich literature about 2D DSA image enhancement and segmentation methods. Many
of them could be extended to 3D, but computational cost of these extensions would often be
prohibitive. Although some of these methods shall be cited hereafter, we will focus on the
techniques developed specifically for 3D MRA.
2.1. Filtering
We subdivide the filtering techniques into two categories : 1) techniques which try to
eliminate noise while conserving vessels, 2) techniques which try to enhance vessels while
avoiding noise amplification.
2.1.1. Smoothing
Isotropic low-pass filtering removes noise as well as thin vessels and hence is unsuited for
vascular images. Several authors proposed an anisotropic approach where local orientation of
structures is first estimated and filtering is locally done along this orientation so as to preserve
small vessels and not to blur boundaries of larger structures. This approach implies a two-
stage processing (1. orientation estimation, 2. filtering) and there are many possible
combinations of methods used at each stage. In [9], smoothing was carried out by anisotropic
diffusion in the direction of the least principal curvature. One of the methods proposed in [2]
applied a morphological operation of crest detection, using directional (linear) tools, and
selected the direction giving the strongest response. Another one selected the local orientation
from a set of discrete orientations (sticks), by choosing the stick with the smallest intensity
variance. In [14] a more robust criterion was proposed, which combined homogeneity within
the stick on the one hand and intensity difference between the neighboring sticks on the other
hand. In both cases, the median filter was then applied within the selected stick. In [7], the
local orientation was estimated using six 3D filters in quadrature. A low-pass filter was then
applied in the estimated direction for the purpose of smoothing, while a high-pass filter was
applied orthogonally to this direction for the purpose of enhancement.
2.1.2. Enhancement
Smoothed images are less noisy, than the original ones, but thin vessels often remain hardly
visible, because their initial intensities are low. To enhance them, each point's intensity can be
3
replaced by a parameter reflecting the anisotropy of the point's neighborhood. One feature of
the vessels is their continuity : image intensity and local orientation vary slowly along the
vessel. Starting from each point, a path having this property can be sought, and the parameter
can be set equal to the path length [10]. Designed for 2D DSA images, this algorithm would
however be too time consuming in 3D.
There were several attempts to characterize the anisotropic properties of the vascular images
by non-linear combinations of outputs of directional filters. In [4], a set of directional mean-
filters was used. The difference between the strongest and the weakest response was used as
anisotropy measure. Indeed, the mean intensity along a vessel should be larger than in
perpendicular directions. Directional derivatives can also be exploited. They should be close
to zero when calculated along a vessel, and should have large absolute values in orthogonal
directions. Various combinations of such filters were proposed in [5] [6].
Directional second derivatives can also be brought together in a Hessian matrix, so as to
exploit the matrix's eigenvectors and eigenvalues
1,
2,
3. Indeed, tubular structures should
give rise to
10 (the associated eigenvector is tangential to the vessel axis) and to |
2|>>|
1|,
2
3 (the associated eigenvectors lie within the plane locally orthogonal to the vessel).
Different combinations of these eigenvalues were proposed to enhance points likely to belong
to vessels. Moreover, if appropriately designed and applied at multiple scales, such
combinations should give the strongest response at one particular scale corresponding to the
vessel caliber [16], [13], [19]. Similar geometrical considerations concerning the principal
curvatures led to the use of the Weingarten matrix eigenvalues [11], [15]. However, a common
problem of the methods based on derivatives is their noise-sensitivity.
2.2. Segmentation
In spite of the advances in the image processing field, interactive thresholding is still the
unique segmentation tool used in the commercial medical image processing software
packages! However, several automated algorithms were developed in research laboratories to
improve segmentation reproducibility. Three principal approaches can be cited : automatic
adaptive thresholding, region-growing and vessel-tracking.
2.2.1. Adaptive thresholding
Usually an adaptive threshold is global and is based on image intensity histogram. In [3] the
threshold was calculated iteratively, starting from the image mean value
plus two standard
deviations
. At each iteration,
i and
i were recalculated after eliminating non-isolated
voxels above the current threshold. In [18] and [22], prior knowledge of the actual image
acquisition protocol was used to choose intensity distribution model and to deduce the
threshold from the histogram, by identifying the model's parameters. Uniform distribution of
vessel intensities was assumed. The threshold was set at the intersection between this
distribution and the background tissues distribution. The latter was modeled by Gaussians in
4
time-of-flight (TOF) MRA and by a Rician in phase-contrast (PC) MRA. In [20], the authors
also argued that the threshold should depend on the actual image acquisition protocol. They
suggested setting the threshold at 50% of the maximum vessel signal in the TOF MRA and
contrast-enhanced (CE) MRA, and at 10% in the PC MRA.
2.2.2. Seeded region-growing
Region-growing algorithms require an initial seed selection which usually is manual in
medical applications. New voxels are then agglomerated to the current region as far as they
satisfy a homogeneity criterion. The criterion often is an intensity threshold. The threshold
may vary along the vessel to adapt itself to local intensity statistics. In [1], the threshold was
set equal to max (
b+2
b,

v-2
v), where
v,

v and
b,
b respectively were the intensity
mean values and standard deviations for voxels already classified as belonging to a vessel and
for the remaining ones within a small volume around a current voxel. In [26], the region-
growing of both vessel and background was carried out by competition, using two criteria
based on the histograms of intensity gradient and of maximum principal curvature. A
directional region-growing was proposed in [10]. Local orientations were first estimated for
each pixel, by seeking the discrete orientation maximizing the mean intensity within the
corresponding stick. New pixels were then agglomerated as far as their orientation agreed with
the seed's local orientation. A very interesting method for automated selection of seeds was
recently proposed in [27]. It exploits the depth map constructed during maximum intensity
projection (MIP). This map, considered as an image, is continuous within regions
corresponding to the vessels and presents strong discontinuities elsewhere. A continuity
measure calculated in this image is used to segment the 2D MIP image. Since depth of thus
obtained regions is known, they are used as seeds in 3D.
2.2.3. Vessel-tracking
The vessel-tracking algorithms in 3D images use (often implicitly) a generalized-cylinder
model, i.e. an association of an axis (centerline) and a surface (vessel wall). Two approaches
can be distinguished. The first one begins by the centerline extraction, then the vessel wall is
sought. In [11] [15] the centerline was obtained by chaining local maxima of the principal
curvature and no attempt was done to estimate the vessel wall position. An improved
continuity of the axis and its reduced noise-sensitivity was obtained in [23][24] using a B-
spline curve (snake). An energy function was designed to attract the snake towards local
maxima of an anisotropy measure based on the Hessian matrix eigenvalues. A B-spline
approximation (active surface) was also used for the vessel wall. The corresponding energy
was minimum when the surface was close to isosurface corresponding to an acquisition
protocol dependent threshold. In [25], the axis was extracted using inertia moments. The
actual vessel boundaries were not extracted. Instead, an estimate of the vessel radius along the
axis was deduced from the inertia moments.
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In the second approach, named "virtual catheter", axis and boundaries are interdependent. At
each step, contours are sought in the plane orthogonal to the current axis orientation, the axis
position is re-estimated, the centerline is extended according to the corrected orientation, and
so on. In [8], the boundary points were sought radially starting from the current axis position
and taking into account the neighboring radii. The axis position was then corrected using the
contour's gravity center and the centerline was extended linearly. In [12], linear extension was
replaced by a B-spline approximation and the contour detection took into account the
neighboring slices to improve continuity. In [17], the local axis orientation was updated in a
more complex manner, using intersections between the vessel and eight straight lines equally
spaced around the axis and parallel to its current orientation. For the boundary detection in the
plane orthogonal to the axis, the authors suggested the use of active contours. Active contours
were also used in [13] for the same purpose. In [21], the boundaries were sought more
roughly, using a radial search of gradient maxima, starting from different candidate points.
The lengths of thus obtained radii were used to calculate a confidence coefficient for each
starting point and to select the point which was the likeliest to lie on the centerline. In [28], the
boundary search was improved. To obtain a closed contour in the initial coordinates the
algorithm sought the minimum cost path in polar coordinates, i.e. a line as straight and as
vertical as possible, passing through the points with the most negative gradient values.
3. Our contribution
We have already published our contribution in both fields : anisotropic non-linear smoothing
[14] and vessel-tracking [25]. Here we propose an operator designed to enhance small vessels
while limiting noise amplification. To this purpose we re-use the orientation estimation
technique described in [14] and our new operator replaces the median filter used in the
smoothing context. Let us briefly recall how the local orientation is estimated. It is selected
from a set of discrete orientations represented by "sticks". For the voxels located within
vessels, the "best-oriented" stick should locally be parallel to the vessel axis and it should be
(almost) entirely included either in the vessel or in the background, to ensure a good
homogeneity of the intensity within the stick. Consequently, some of the neighboring sticks
parallel to the central stick should belong to the same region as the central stick while the
other ones should be located outside this region. Hence the intensity within each of these
neighboring sticks should also be homogenous, but there should be a large intensity difference
between the central stick and the neighboring sticks lying outside the region it belongs to. Let
i
S
= {Sij: j = 0,1,…,n} be a set of n+1 parallel neighboring sticks for the i-th orientation,
where Si0 is the central stick. Let
ij be the intensity standard deviation for Sij and let gij be the
directional mean gradient between Sij and Si0. The averages respectively of
ij (j = 0,1,…,n)
and of |gij| (j = 1,…,n), shall be noted
i
and
i
g
. The best orientation is the one which
maximizes the following criterion :
HDi =
i
g
-
i
(1)
6
which simultaneously takes into account the intensity homogeneity along the sticks (weighted
by a coefficient
), and the intensity difference between the central stick and its neighbors.
Because of the mixed use of a homogeneity measure and of a difference measure, we called
this operator HD-filter.
3.1. Vessel enhancement operator
Knowing the local orientation it is possible to implement an enhancement scheme similar to
the one proposed in [7], i.e. to apply a kind of low-pass filter along this orientation and a high-
pass in the orthogonal plane. In fact, true low-pass filters (mean, Gaussian) give poor results
for very thin and tortuous vessels. Instead, we prefer using L-filters. Let us recall that these
filters are based on sorting the voxels in the increasing order of intensity : I1 IL, where L
is the number of voxels (in our case L is the length of the sticks). An L-filter is any linear
combination of thus sorted intensities, with coefficients ak depending on the rank k. When ak =
1/(2W+1) for k = k0 = (L+1)/2, k01,… k0W and ak = 0 for the remaining ranks, one obtains a
truncated mean. Note that W = 0 gives the conventional median filter. Let {moptj: j = 0,1,…,n}
be the truncated mean values for the considered set of sticks Sopt, opt is the orientation selected
by the HD operator. To obtain the enhancement effect we replace the initial intensity of the
central voxel in Sopt0 by :
f = (n+1)mopt0 - (mopt1 + …+m optn) (2)
It can be interpreted as combining mopt0 with a 2D Laplacian applied on the truncated mean
values. This combination can be weighted. Similarly, W can be tuned to choose a compromise
between smoothing and enhancement effect. Figures 1 and 2 were obtained using W = 0.
3.2. Results
This new operator was tested on CE MRA images from 9 patients. Such images are obtained
by acquiring two data volumes, one before and the other one after intravascular injection of a
contrast agent (gadolinium), and by subtracting the latter from the former. Ideally (without
motion artifacts) the subtraction should eliminate non-vascular tissues. In practice it also
amplifies noise. Due to a high computational cost of the 3D orientation estimation the tests
were carried out in 2D for MIP images.
Our method was compared with a conventional isotropic image enhancement technique which
consists in adding to the image its Laplacian. In the sequel the latter shall be referred to as
isotropic, while our operator shall be called anisotropic. The comparison was both qualitative
and quantitative. The qualitative inspection focused on the visibility of small vessels. The
quantitative comparison was based on contrast and noise measurements. An automatic vessel
tracking applied to user-selected vessel segments allowed us to measure the mean signal inside
and outside the vessels, as well as noise standard deviation in the vessels' vicinity. Let us note
7
that noise level is usually measured in an image region outside the patient's body. This choice
is not appropriate in the case of MRA images since the noise level depends on the local signal
level. The measurements were performed for 65 arterial segments of different diameters
ranging from 1 to 8 pixels and representing different vascular regions : from carotid arteries to
lower-limb arteries, including the abdominal aorta and its branchings.
Fig. 1. Images of carotid arteries region : original (left) and enhanced by the anisotropic (middle) and
isotropic (right) operator.
Fig. 2. Images of abdominal aorta, renal and iliac arteries : original (left) and enhanced by the anisotropic
(middle) and isotropic (right) operator.
Visual inspection of figures 1 and 2 clearly shows that the arteries appear sharper after
application of both the isotropic and anisotropic operators. The conventional isotropic operator
however strongly amplifies noise, while our anisotropic operator produces a moderate noise
amplification. This qualitative impression was confirmed by the measurements. Indeed, on
average our anisotropic operator produced a significant improvement of the contrast (50,5 %)
8
and a smaller amplification of the noise standard deviation (41,5 %). This resulted in a
contrast-to-noise ratio improvement (11,7 %). The isotropic operator produced a similar
contrast enhancement (45 %) but noise level was strongly amplified (106,6 %) which led to a
contrast-to-noise ratio degradation (-26,3 %).
4. Conclusions
It is very difficult to enhance thin line-like objects and to avoid noise amplification. Our new
method using an L-filter applied along the vessels and a Laplacian applied in the plane locally
orthogonal to the vessel axis, seems to be a reasonable compromise. It strongly improves the
contrast while noise is moderately amplified. This method was successfully applied to
magnetic resonance angiography images in which it improved the visualization of small blood
vessels. It can therefore be used in practice to aid the assessment of collateral or peripheral
vascularization. However, it should not be used as preprocessing before stenosis diagnosis and
quantification, because vessel diameters are not necessarily preserved, especially near
bifurcations. Future work will focus on the computational cost reduction and on an application
of our operator to automated seed detection for the sake of segmentation.
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... The second approach exploits the geometrical specificity of the vessels, in particular their orien- tation and tubular shape. Techniques that use this approach tend to use vessel-tracking [27][28][29][30][31] and (often implicitly) a generalized-cylinder model, i.e. an association of an axis (centerline) and a surface (vessel wall) [32][33]. Consequently, the segmentation process involves two tasks: centerline extraction and vessel contour detection in the planes perpendicular to the axis. ...
Chapter
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... One of them consists in defining: 1) a set of discrete line segments, often called "sticks", centred on a current voxel (volume element, i.e. 3D image point) and having various orientations and 2) a "vesselness" criterion calculated for each stick and used to deduce a kind of "probability" that the central voxel belongs to a vessel and/or to estimate the local orientation of the vessel. Criteria based on such measures as mean intensity [6,27], intensity variance [51], directional second derivatives of the intensity [10,11] and on their combinations [36,37] have been proposed. An example of such a criterion can be cited from [36]: ...
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Thesis
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