Knowledge based system for the three dim

1 Introduction
Tim MAINgoal of this paper is the development of a computational vision system for the automatic interpretation
of blood vessels on single and multiple angiographic projections. Although this blood vessel framework can be used
for the interpretation of blood vessels of all kinds, such as
the renal blood vessels, the coronary arteries, the carotid,
cerebral and peripheral vessels, we present solutions for
two practical problems:

(i) the automatic localisation and assessment of the coronary atherosclerotic disease. This system is the first
attempt to build a fully automatic, complete coronary
artery reporting score
(ii) the automatic three-dimensional reconstruction of
blood vessels from two projections. We present results
of the three-dimensional reconstruction of the coronary arteries from two wide-angle angiographic projections and the three-dimensional reconstruction of the
* Correspondence should be addressed to Professor Suetens.
Received 8th Apri/1991

9 IFMBE: 1991
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cerebral blood vessels from a stereoscopic pair of
angiograms.
There are three main reasons why cardiologists and radiologists are interested in automatic blood vessel interpretation systems:
(a) Owing to the high number of standard clinical investigations, there is a need to relieve the burden of tedious
daily routine work in diagnosis.
(b) Departments of radiology and cardiac catheterisation,
which are traditionally diagnostic, have taken on a
therapeutic dimension. The therapeutic procedures,
which require quantitative follow-up studies, can only
be evaluated objectively with accurate delineation
algorithms.
(c) The large amount of complex image data has to be
exploited to the fullest extent. For example, angiography presents only projection information. However,
from a three-dimensional reconstruction of blood
vessels, an additional number of clinically important
parameters becomes available such as the general
outline of the arteries, the haemodynamic resistance of

an obstruction and the blood flow through an artery.
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2 Digital angiography
As the X-ray attenuation coefficient of blood is not very
different from that of the surrounding tissue, straightforward X-ray imaging is not very well suited for the visualisation of blood vessels. However, the image contrast can
be raised significantly by injecting an iodinated contrast
agent into the blood vessels using a catheter. As a consequence, most X-ray photons will be absorbed, resulting in
a high quality image; an angiogram. The quality of a
digital angiographic image can be improved using subtraction techniques (DSA). Prerequisite for a quantitative
analysis and a three-dimensional reconstruction of the
vascular structure from angiographic projections, is the
exact determination of the geometrical characteristics of
each projection, called the 'camera model'. In practice, we
assume the global co-ordinate system (X, Y, Z), fixed in
the isocentre of the angiographic system. Usually, for
example for coronary arteriography, the X-axis is the long
axis of the patient, the Y-axis is oriented from left to right
and the Z-axis has a dorso-ventral direction. In Fig. 1 we
exemplify the characteristics of movement for the standard

BI-Angioskop Siemens angiographic equipment which we
used in our system.* The globe represents the locus of the
centre points of all possible image intensifier planes (x, y).
The radius of the globe is the distance between the iso•

Fig. !

In this case, these projections must be recorded at the
same moment in the heart cycle.
Simultaneous recording can be accomplished using
biplane projection systems and also by using electrocardiogram or ECG triggering. Although the cardiac rate is
usually constant it can be changed by using an external
pace maker. In this paper we present three-dimensional
reconstruction results of the coronary and cerebral blood
vessels. Figs. 2 and 3 represent two angiographic projections (512 x 512 pixels) of the left coronary artery. The
images are recorded with a Siemens' Polytron 1000 (6 in
FOV) using ECG triggering. Fig. 2 is a - 4 4 ~ LAO projection with a cranial inclination of 19~ Fig. 3 is a 28 ~ RAO
projection with a caudal inclination of 19~ For both projections, the X-ray source to image intensifier distance is 89
cm and the isocentre to image intensifier distance is 25 cm.
Figs. 4 and 5 show a stereoscopic pair of projections of a

cerebral blood vessel phantom. The images were also
recorded with a Siemens' Polytron 1000 (6 in FOV). The
X-ray source to image intensifier distance is 85 cm and the
isocentre to image intensifier distance is 17 cm.

z

Characteristics of movement of Siemens' angiographic
equipment

Fig. 2 Original angiogram of LCA in LAO projection

centre and the image intensifier. Two rotations are necessary to reach a projection: first, a rotation ~ in the
transverse plane (around the X-axis), which corresponds to
a C-arm rotation; secondly, a rotation fl in the sagittal
plane (around the Y-axis), which corresponds to an L-arm
rotation.
Although the rotation of the arms allows almost all projection angles, standard projections are r = 30 ~ right
anterior oblique (RAO) projection, and ~ = - 6 0 ~ left
anterior oblique (LAO) projection. Here, right and left are

defined from the standpoint of the patient. A caudal
(towards the feet) or cranial (towards the head) inclination
of 10~ ~ is frequently used to optimally visualise all
branches of the coronary vessels, which could otherwise be
superimposed on each other. A major problem of quantitative coronary arteriography is the simultaneous recording of both standard projections. This is especially
important when two (or more) projections are used for a
three-dimensional reconstruction of the artery trajectory.
* The characteristics of movement for other biplane angiographic
equipment, for example Poly DIAGNOST C and LARC from Philips"
Gloeifampenfabrieken, can be found in the paper by WOLLSCHLAGERet
al. (1986)

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Fig. 3 Original angiogram of LCA in RAO projection
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heuristic models are usually applied for blood vessel labelling:
(a)
(b)
(e)
(d)

angiographic blood vessel models
intersection models
anatomical models
multiple view models

These heuristic models account for most of the knowledge
used for the interpretation of angiograms.

Fi~ 4

Original angiogram of the cerebral blood vessel phantom

3.2 A hierarchical search computational strategy

We use a hierarchical search computational strategy for
the interpretation of angiograms. In the paper by SUETENS
et al. (1991) it is stated that a hierarchical search is a
strategy for computational vision where the solution is
systematically elaborated while reducing the search space
by finding partial solutions using a hierarchy of intermediate models. These models are usually of a heuristic
nature.
3.3 Data representation structures
An essential feature of the computational strategy is the
computation of missing or incomplete attributes in the
image. However, although the contact with the image is
never broken, image operations are usually computationally expensive. Recomputation of some attributes like
curvature or direction has to be avoided. Therefore, at
each interpretation stage we construct a data representation structure which has the following features:

Fig. 5 Original angiogram of the cerebral blood vessel phantom,
the projection angle differs 9~
that of Fig. 4
3 General f r a m e w o r k for i n t e r p r e t a t i o n of
angiograms

In the quest for a paradigm that is able to cope with the
shortcomings of existing approaches, we present a new
framework for the interpretation of angiograms which can
be distinguished from existing approaches by the following
characteristics:

(i) various problem-specific models to interpret angiograms
(ii) new data representation structures
(iii) a hierarchical search strategy
(iv) a rule-based implementation approach
These characteristics will now be described in further
detail.
3.1 Heuristic blood vessel models
When complex problems have to be solved for which no
exact solutions exist or for which the known exact solutions are computationally too expensive, the use of heuristic models to solve the problem is attractive. For example,
no practical exact algorithm exists for the interpretation of
angiograms that guarantees a 'correct' interpretation. The
search space of possible interpretations is incredibly large.
Fortunately, for this problem an approximate solution can
be produced with a reasonable computational effort by

applying some heuristic knowledge. The following four
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(i) fast and easy access of some global characteristics of
blood vessel segments, such as mean length, mean
width and mean intensity.
(ii) on the other hand, geometrical and topological characteristics such as curvature or direction have to be
stored in an image-like data format, where the relative
position of the segments is preserved.
3.4 A rule-based implementation approach
The development of this general framework for the
interpretation of blood vessels on angiograms is closely
related to the implementation paradigm. In the paper by
HAY~S-Ro~ (1987) it was stated that the best means available today for codifying the problem-solving know how of
a human expert are rule-based systems. It seems that
experts can express most of their problem-solving knowledge as a set of 'situation-action' or 'if-then' rules.

4 Blood vessel s e g m e n t e x t r a c t i o n
According to BROWN et al. (1984), the majority of coronary arteries have a circular or elliptical shape. Blood
vessels can be approximated as high intensity regions, with
a high intensity centre line, bordered by two parallel lines
not too far apart.
The ridge points are obtained using an improved maximum intensity detector originally developed by FISCHLER
and WOLF (1983). Straightforward methods described in a
paper by NEVATIA and BABU (1980) were used for thresholding, thinning and linking.
In the next stage, segment-like primitives are constructed. To find the accurate trajectory of a blood vessel
segment, we used a dynamic programming technique. We
implemented the approach described by GERBRANDS et al.
(1986), which has been frequently used in clinical practice.
The result of the interpretation process at this stage is a
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set of mostly disconnected ribbon-like blood vessel segments. However, owing to the nature of DSA, all blood
vessels should be connected. Usually, only one blood
vessel tree network exists. Moreover, blood vessels do not
usually stop abruptly, but fade. Therefore, the semantic

context gives additional information for the detection of
blood vessel segments which have been missed in the previous segmentation phases. This method can also be used
to detect gaps and combine blood vessel segments in a
connected tree network.
5 Blood vessel intersection labelling
Except for stenoses or other malformations blood
vessels are usually continuous connected structures with
slowly changing thickness and intensity. To merge blood
vessel segments we have developed three intersection
models:
(a) A connection consists of two intersecting segments
lying in the same direction, with approximately the
same intensity and the same width, No other blood
vessel segment is present.
(b) A T-branch is an intersection of three vessel segments.
If two segments lie in the same direction, have the same
intensity and the same width, it is very likely that they
belong to the same vessel, in which case these segments
can be merged.
(c) A crossing is an intersection of four vessel segments.
Segments can be merged pair-wise if they have the
same intensity, the same width and if the intensity on
the intersection is increased.
More elaborate models are possible, but we believe that
with these three models most of the intersections can be
determined. Fig. 6 shows the delineated blood vessel segments after applying the intersection model to the original
cerebral angiogram of Fig. 5.

Fig. 6 Blood vessel segments after applying the intersection model
6 A n a t o m i c a l labelling of t h e left coronary
artery
6.1 An anatomical model of the left coronary arteries
The delineated coronary blood vessel segments can be
assigned their anatomical nomenclature by applying an
anatomical model of the left coronary artery (LCA) in
standard RAO and LAO projections. This model, which
incorporates normal variations of the coronary artery
structure, has been developed in a rule-based form using
standard textbooks, such as those by GENSINI (1975) or
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NETTER (1978). After the implementation of the anatomical
model, the system was updated through direct interaction
with cardiologists, the experts in this field. A pictorial representation of the left coronary circulation in standard
RAO projection is given in Fig. 7. Here the following
nomenclature has been proposed:
MLCA
LAD
D
S
CX
OM
PL
PD
ACX
AVN
SN

=
=
=
=
=
=
=
=
=
=
=

main left coronary artery
left anterior descending branch
diagonal branch
septal branch
circumflex artery
obtuse marginal branch
postero lateral branch
posterior descending artery
atrial circumflex artery
atrio ventricular node branch
sinus node branch

For each branch of the left coronary artery, we can
describe the characteristics as they appear during a cardiographic procedure on standard RAO and LAO projecMLCA

AVN

LAD

PD

Fig. 7 Left coronary circulation in RAO projection
tions. In the three-dimensional reconstruction process of
the cerebral blood vessels we have to skip this labelling
phase because no anatomical model is available.
6.2 A discrete relaxation labelling strategy
Once the blood vessel segments have been delineated,
the LCA anatomical model, described above, can be used
to assign the segments to their anatomical labels. For the
interpretation of blood vessels on angiograms, we adopted
the discrete relaxation labelling approach which can be
formulated as follows: A set V of n variables {vl, v2, ...,
v,} is given, which represent blood vessel segments. Associated with each variable vi is a domain D of possible interpretations. On some specified subsets of these variables,
constraint relationships are given that are subsets of the
Cartesian product of the domains of the variables
involved. The set of solutions is the largest subset of the
Cartesian product of all the given variable domains, such
that each n-tuple in that set satisfies all the given constraint relationships. The set of solutions is never empty;
however, a possible solution does not need to be unique, as
there might be a considerable overlap between different
interpretations. For example, depending on the cardiologist, a posterolateral branch can sometimes be identified correctly as a posterior descending branch. The main
reason for multiple solutions is that the set of possible
interpretations is not defined unambiguously. A set {xl,
x2 . . . . , xm}, where xi is the interpretation of the ith
segment, is a possible solution if the outcome of the following formula is 'true':

Q = Pi(x,) A P2(x2) A ... A Pm(xm)
A P1,2(xl, x2) A "'" A Pm-l,m(Xm-~, X,,)
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Here, A corresponds to a conjunction, Pi(xl) is the
Boolean truth value for the unary constraints on the ith
segment with an interpretation of xi. In a similar way, we
can consider Pi, j{xl, x~) as the Boolean truth value of the
binary constraints on the ith and jth segments with the
interpretations i and j, respectively. Although, in general,

Blood vessel segments are very likely to have the same
interpretation if they are in the same direction, have
almost the same intensity and the same width. In this way,
inconsistent interpretations may be skipped according to
topological and geometrical constraints. However, topological knowledge may sometimes be overruled by the

i

Cx

i
LAO

Fig. 8

RAO

Modet for the relationship "above" in RAO and LAO projection

n-ary relationships may be used in the above equation,
most constraints can be formulated as unary and binary
predicates.
Unary labelling constraints are related to specific blood
vessel attributes such as position, direction, grey value and
thickness in a particular projection geometry. For
example, according to our anatomical model, a septal
branch can be identified in RAO projection as a vertical,
mainly thin branch in the top part of the image, while the
main left coronary artery is a horizontal, thick blood vessel
in the top left part of the image. These interpretations will
be skipped for segments not obeying at least one of these
criteria.
After the unary constraints have been applied, the most
likely candidate for the circumflex artery and for the left
anterior descending branch are selected from the possible
set of candidates. Taking this decision allows a reduction
of the search space by applying additional and very
specific unary constraints. These unambiguously labelled
segments can then be used to eliminate unlikely interpretations of other segments by using relational constraints.
These binary or relational constraints are related to
blood vessel interrelationships such as 'above', 'left of',
'thicker than', 'left connected to' and 'same direction'. A
relational model for the relationship 'above' can be identified for each possible interpretation. Fig. 8 provides a pictorial description. Here, an arrow pointing from A to B
means that interpretation A 'is above' interpretation B.
Powerful labelling constraints are the connectivity
relationships, which are stored in a separate knowledge
source. Here, we take advantage of the fact that the left
coronary artery consists of two main branches, namely the
circumflex artery and the left anterior descending branch,
each with its own side branches. Unlikely interpretations
can then be eliminated according to the tree model
depicted in Fig. 7. For example, once a candidate for the
LAD is proposed in RAO projection, all segments on the
right of this segment may only have the interpretation
LAD, septal or diagonal branch. A special example of such
a connectivity relationship is the constraint 'in same direction' which takes into account both topological and anatomical knowledge to label blood vessel intersections.
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existing anatomical model. For example, as can be noted
from Fig. 7, the main left coronary artery and the left
anterior descending branch are clearly distinguished
arteries with a different anatomical label. Consequently,
although these vessels are in the same direction in RAO
projection and have almost the same intensity and the
same width the interpretations LAD and MLCA may not
be eliminated. The result of this stage is a list of blood
vessel segments with their corresponding anatomical
labels. In general, only one or two interpretations remain,
which is a very acceptable result if one takes into account
that, for example, in the RAO projection there is a considerable overlap between the diagonal and the left
anterior descending branch.
Fig. 9 shows all segments in RAO projection with only
one or two remaining interpretations. Dynamic sequences
or more views will be necessary to label the complete cor-

Fig. 9 Labelled L C A blood vessels with one or two interpretations in R A O

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onary blood vessel tree unambiguously. These results can
subsequently be used for a three-dimensional reconstruction of the coronary artery tree from two angiographic
projections, as will be explained in Section 7. Finally, these
labelling results can also be used to assist in an objective
determination of coronary atherosclerosis severity.

a projection point. The epipolar constraint will limit the
search for corresponding points to a one-dimensional
neighbourhood, with an enormous reduction in computational complexity. The epipolar lines have to be computed
according to the projection geometry. To establish a
match relationship, the epipolar constraint has to be valid
for all points on corresponding segments.

7 Three-dimensional reconstruction

7.1.2 Disparity boundaries. The search space can be constrained even more if the size of the anatomical objects can
be estimated. In that case, disparity boundaries or the
maximum (or minimum) differences in position between
two corresponding projections can be computed. For
example, the width of a normal head usually does not
exceed 20cm. Moreover, only one of the hemispheres is
usually visualised with cerebral angiography, which limits
the size of the reconstruction area to about i0cm. If the
camera model is accurately known, we are able to calculate the matching search area in the corresponding image
using the camera model. Only segments meeting this criterion point by point are possible candidates for match
relationships. Moreover, the disparity range will in general
increase with increasing angle between both projections.
As a consequence, matching efficiency will decrease. Therefore the disparity constraint is of limited use for a threedimensional reconstruction of the coronary blood vessels
from two standard RAO and LAO projections.

7.1 Multiple view models
The key problem in three-dimensional reconstruction
from two projections is to find corresponding points in
both images. This is called the 'matching process'. In practice, this implies constructing all segment match relationships (u, v) or combinations of a segment u in the first
image and a segment v in the second image. Let there be N
blood vessel segments in the left image and M segments in
the right image. We define the matching space D as the set
of all match relationships

D = (ui, vj)

i = 1... N
j=I...M

Although, in general, every point in the first image may
correspond to every point in the second image, the camera
model, defined above, and the available anatomical models
can be used to constrain the matching space D. In this
way, the matching process will become more efficient. We
usually apply four matching models, namely
(i) the epipolar constraint restricts the position of corresponding points on corresponding epipolar lines
(ii) in practice, the size of the anatomical object can be
estimated. This estimate can be used to calculate the
minimum (or maximum) disparity between two corresponding projections. Therefore, the disparity constraint limits the search area in the corresponding
image
(iii) in general, blood vessels have a well-defined geometrical structure. As a consequence, a blood vessel projection in one image constrains the appearance of the
same blood vessel in the corresponding projection
(iv) blood vessels must have the same anatomical interpretation in both projections.
7.1.1 Epipolar geometry. The line defined by the two
X-ray sources is called the stereo baseline. Any point in
three-dimensional space, together with the stereo baseline,
defines an epipolar plane. The shaded area in Fig. 10 represents the epipolar plane for this camera geometry. PR
and PR, are the X-ray sources and O is the origin of the
global reference system. Every projection point in the first
image must then correspond to a point on the corresponding epipolar line, defined as the intersection of the epipolar
plane and the second image plane. From the camera model
we are able to compute the corresponding epipolar line of

7.1.3 General blood vessel model. An additional model,
which can be used to constrain the search for match
relationships, is a model of the general appearance of
blood vessels on angiograms. For the three-dimensional
reconstruction of the coronary and cerebral blood vessels,
this is usually related to the following features:
(a) Similar vessel diameter. Except for malformations, e.g.
eccentric lesions, blood vessels usually have a cylindrical structure. As a consequence, vessel diameter does
not depend on projection direction. Therefore, blood
vessels must have a similar width in both projections.
(b) Orientation correspondence. For stereoscopic cerebral
angiography, we assume that the major vessel trajectory is in the lateral plane parallel to the image plane.
The distance from the X-ray source to the film plane is
much larger than the vessel trajectory in the coronal
plane, therefore the projected blood vessel structures
have a similar orientation in both images. On the contrary, this feature is not valid for wide-angle angiography. Therefore, no orientation correspondence can
be taken into account for the three-dimensional reconstruction of the coronary arteries from standard RAO
and LAO projections.
(c) Grey value correspondence. Blood vessels have a
similar intensity in both projections. This is a possible
reliable measurement in case of biplane angiography.
Each measurement Mi (e.g. vessel width, orientation or
intensity correspondence) can be expressed as the inverse
of a variance measure. The measurement Mi is high if the
variance is low:
1

Mi = 1 Q

-Qj~=lIMLij-- MRIjl2

Fig. 10 Epipolar geometry
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(1)

Here, MLI~ and MR~j are the left (or right) values, e.g.
position or diameter, of point j in the match relationship.
The sum is over all points Q of the specified match
relationship. With these measurements, a global confidence
factor H(u, v) for the specified match relationship can be
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computed. This factor can be expressed as a weighted sum
over the various correspondence measures
N

H(u, v) = ~, O, Mi(u, v)

(2)

i=1

where g, is the weight of the matching feature M,, and N
represents the number of matching features. (For this
example N = 3.)

7.1.4 Anatomical models. Blood vessel segments must
have the same anatomical interpretation in both projections. The anatomical model of the coronary arteries can
be used to eliminate conflicting match relationships. Corresponding match relationships must have at least one corresponding interpretation. This constraint is of no use for
the matching of the cerebral blood vessels, as an anatomical model of the cerebral vessels has not yet been implemented.
7.2 A high-level feature matchin9 strategy
The first-step in the reconstruction process involves constructing the set of possible match relationships. For this,
we use the 'epipolarity' constraint, the 'disparity' constraint
and finally the 'same anatomical interpretation' constraint.
This is depicted in Fig. I 1, in which the centre lines of a
few segments and their corresponding match relationships
are shown. The shaded area represents a disparity window
in the right image, in which corresponding segments must

(if) of which H(u, v) exceeds a predefined threshold
(iii) which has no valuable alternatives.
Here, match relationship (u, v) is a valuable alternative for
(u, w) if

H(u, v) - C < H(u, w) < H(u, v) + C

(3)

where C is a predefined variation.
7.2.1 Delineation by resegmentation. The three-dimensional reconstruction process and the delineation process
are not considered to be independent processes. Evidence
in the left image can be used to improve the delineation in
the right image and vice versa. Relational constraints
between patterns may indicate the presence of other patterns which were not found previously due to imperfect
segmentation or simply poor data.
An example is depicted in Fig. 12. Let (L1, R 0 and (L 1,
R2) be two unique match relationships. As the blood vessel
on the left image is one physical entity, a dynamic tracking
algorithm can be used to combine segments R 1 and R 2 in
the right image into one vessel. In a similar way, by using

4

2
left

right

Fig. 12 Delineation by resegmentation

left

right

the interpretation results in the first image, we may look
for evidence to extend blood vessel segments in the corresponding projection. This is demonstrated in Fig. 12 for
segment R 1 .

Fig. 11 Building segment match relationships
lie. Valid match relationships, based on a maximum disparity jump, are (L1, R1), (L1, Ra) and (L 1, R4). The disparity jump for (L 1, R2) is too large for the match
relationship to be valid. Although the match relationship
(L1, Rs) is in the disparity limits, it is eliminated because of
conflicting anatomical interpretations. A similar figure for
segments in the left image can be drawn. Even by applying
the epipolarity, disparity and similar interpretation constraints, a given segment may in general match with
several other segments. Therefore, a confidence factor is
computed for each match relationship which expresses the
likelihood of a specified match relationship occurring,
according to some constraints as orientation correspondence, width correspondence and intensity correspondence.
Solving the reconstruction problem can now be considered as selecting the unique match relationships in the
set D. This is an iterative procedure, as each unique vessel
match relationship will automatically influence the likelihood of other match relationships. Therefore, we will first
select the most likely match relationship as the relationship
(i) which maximises the goodness-of-fit function H(u, v)
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7.2.2 Final three-dimensional result. At this stage we
have obtained combinations of corresponding segments.
Now we have to find the corresponding segment points.
We therefore again use a dynamic programming technique.
We construct the following cost image: the rows depict the
segment points in the first projection; the columns depict
those in the second projection. The intensity value of pixel
(i,j) is defined as the distance between the projection lines
of points i and j in the respective projections. In this cost
image a minimum cost path is searched which gives the
point-to-point correspondence. If one part of a segment is
lying on an epipolar line, this minimum cost path will
result in three-dimensional trajectory with serious oscillations in depth. To overcome this epipolarity problem, an
extra cost is added to the cost image, namely the threedimensional distance between successive points. The final
step is then computation of the three-dimensional reconstructed blood vessel centre line from these corresponding
points. Assuming a cylindrical blood vessel structure, we
computed the diameter perpendicular to each skeleton
point as the minimum of the reconstructed diameters for
each projection. Reconstruction accuracy is heavily influenced by the angle between both projections. The reconstruction of two almost orthogonal coronary projections is
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more accurate than the reconstruction of a stereoscopic
pair of cerebral angiograms.
The blood vessels have been visualised as wire-frame
phantoms on an Iris 2400T workstation. This has been
explained in detail in the paper by VANDERMEULEN et al.
(1986). Figs. 13 and 14 show the original angiograms
together with calculated projections, obtained by projecting the three-dimensional result along t h e same angle in

8 C o r o n a r y atherosclerosis severity
The primary reason to visualise the coronary arteries is
for the localisation and assessment of the atherosclerotic
lesions. Although the exact causes of the disease are not
yet fully understood, it can be described (see the paper by
W H O (1958)) as follows:
'Atherosclerosis is a variable combination of changes of
the intima, consisting of the focal accumulation of lipids,
complex carbohydrates, blood and blood products,
fibrous tissue and calcium deposits, and associated with
medial changes'.
With coronary arteriography, the disease can be recognised as obstructive artery lesions usually accompanied by
a decrease in artery lumen. To be able to quantify these
obstructive lesions, various groups have developed contour
detection methods to estimate the severity of a coronary
lesion. These methods usually make use of a few manually
defined points on the centre line of the artery. The artery
trajectory is then extracted and a diameter or area function is calculated.
Percentage diameter stenosis is defined as

Fig. 13 Original LAO projection and calculated projection

%D - Dres -- Oml, 100%

(4)

DreS

where, D,es is the reference diameter of a normal arterial
segment and Dml. is the minimum diameter at the stenotic
lesion. Assuming a circular cross-sectional lesion, the percentage area stenosis can be calculated from the diameter
function as
% A - D~2f -- D2" 100%

(5)

D~Zf

Fig. 14 Original RAO projection and calculated projection

Fig. 15 Calculated projection of cerebral blood vessel phantom
the transverse plane as for the acquisition of the original
angiogram. However, no inclination was considered. Fig.
15 shows a calculated projection for the cerebral vessel
phantom. This projection was calculated for an angle differing by about 20 ~ from the projection angle of the angiogram of Fig. 4.
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Densitometric analysis is based on the relationship
between the grey value of the image and the path lengths
of the X-rays through the artery. By subtracting the background profile and taking into account the transfer functions of the angiographic equipment, the cross-sectional
area corresponds to the area of the absorption profile.
However, stenosis severity also depends on the anatomical interpretation of the coronary segment. For example, a
50 per cent stenotic lesion proximal on the left anterior
descending branch is much more important than a similar
lesion in one of its distal side branches! Therefore, an
objective severity score has to take into account the relative position and anatomical significance of the specific
artery. For this purpose, we implemented parts of the
coronary artery reporting score which is used in daily
routine at the University Hospital Gasthuisberg. A
detailed description of the reporting score can be found in
the paper by WILLEMS and PIESSENS (1977). According to
this system, we can calculate an overall severity score of
coronary obstructive lesions, using the diameter and area
function and a weighting factor of the relative importance
of the different artery segments. The main left coronary
artery was given a weighting factor 100, the circumflex
artery 30, proximal and midparts of the left anterior
descending artery 40, the distal part 10, the atrial circumflex artery 10, the obtuse marginal branch 30 and the
postero lateral branches 15. According to the reporting
system, we present the following information automatically
for each arterial segment:
(a) Anatomical labels
(b) Percentage diameter stenosis, percentage area stenosis,
calculated reference diameter, obstruction diameter
and extent of the obstruction.
(c) Additional qualitative codes such as: isolated stenosis
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(only one stenosis on the arterial segment); elongated
stenosis (length longer than three times its width); subtotal occlusion (diameter function higher than 90 per
cent but the lumen on both sides of the stenosis can be
discerned); total occlusion (thick blood vessel stops
abruptly).
(d) Stenosis severity score defined as the product of the
diameter function and the anatomical weighting factor.
The final stenosis severity score can be found by summing

The three-dimensional reconstruction of an image from
two projections is a highly underdetermined problem and
it is very unlikely that a complete reconstructed image for
use in clinical practice can be obtained using only these
two projections. However, particularly for the coronary
arteries where the three-dimensional structure is not that
complex, we have demonstrated that useful results can be
obtained by taking advantage of the available anatomical
knowledge.
9.1 Future developments
Although the current implementation of a blood vessel
interpretation system is already useful, additional developments are necessary for use in routine clinical practice:

Fig. 16 RAO projection of stenotic arterial segment and contours
on resampled window

up the individual stenosis severity scores for all the artery
segments.'~ Fig. 16 shows the RAO projection of a stenotic
arterial segment and the contours on the resampled detail
window.

9 Conclusions
The blood vessel interpretation system we have
described, as implemented on a VAX 3200 workstation.
Image processing tasks were implemented in Pascal, while
the high level anatomical knowledge was formalised with
the rule-based language OPS5. It was not possible to give
an exhaustive evaluation of the interpretation system.
However, some conclusions can be drawn.
The most important blood vessels can be delineated and
labelled successfully. The anatomical framework is fairly
robust and takes into account the normal variations of
coronary anatomy and the normal variations in image
acquisition parameters. Moreover, the delineation and
labelling results can be used for quantification purposes to
estimate the severity of coronary atherosclerosis. Nevertheless, a frequent and flexible use of this system in clinical
practice today is impeded by some major problems, among
which are:
(i) a flexible acquisition of the images (especially the
simultaneous recording of images and the geometrical
configuration)
(ii) a correct delineation of superimposed vessels, which is
a main problem for the delineation of the cerebral
arteries
(iii) the lack of dynamic information
(iv) the low processing speed (the whole sequence can take
up to 3 0 C P U min)
(v) the lack of a flexible user interface.
t Willems used also a modifying factor, taking into account the length
and number of the different stenoses and the presence of collateral
circulation

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(a) An important issue is the clinical validation of the
interpretation system.
(b) The current labelling system is based on the interpretation of static images. However, a complete description
of the coronary artery tree can only be obtained using
dynamic sequences. Dynamic sequences will also
provide significant additional diagnostic information
and can be used to determine blood flow.
(c) The most important application of the blood vessel
labelling system is the automatic quantification of stenotic lesions. The cross-section of a blood vessel lesion
can probably be quantified more accurately using the
three-dimensional trajectory of a blood vessel than
with quantification methods making use of only a
single projection like diameter measurements or densitometric analysis.
(at) An interesting research direction is the extension of a
tomographic reconstruction approach with the highlevel feature matching technique described in this
paper. In this way, ambiguous matching can be resolved using high-level semantics. Hopefully, threedimensional positional reconstruction accuracy will
then be sufficient for use in stereotactic neurosurgery.

Acknowledgments--This work is sponsored by the National
Fund for Scientific Research (NFWO) and by the Belgian
National incentive program for fundamental research in artificial
intelligence, initiated by the Belgian State, Prime Minister's
Office, Science Policy Programming. The scientific responsibility
is assumed by its authors.
The authors are very grateful to Philips GmbH Forschungslaboratorium, Hamburg, for the use of their cerebral
blood vessel phantom.

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automatic interpretation of blood vessels on angiograms. He is
currently a Senior Project Scientist with HCS Vision Technology.
His major research interest is the design of flexible image processing tools for the easy development of industrial inspection
tasks.

Paul Suetens was born in Mechelen, Belgium,
in 1954. He received an M.Sc. in Engineering
(Computer Science) front K. U. Leuven (1977)
and obtained his Ph.D. in Computer Science
from the same university in 1983. He is currently a Professor and Staff Member at the
ESAT/M12
(Machine
Intelligence
and
Imaging) Laboratory of the K. U. Leuven and
a Senior Research Associate of the National
Fund for Scientific Research, Belgium. Together with Prof. G.
Marchal he is codirector of the Interdisciplinary Research Unit
for Radiological Imaging. His research focuses on Artificial Intelligence and Computer Vision and their applications in expert
systems, knowledge-based image understanding and medical
imaging.

Authors" biographies
Dominique Delaere was born in Izegem,
Belgium, in 1965. He received a M.Sc. degree
in Electrical Engineering and a M.Sc. degree
in Biomedical Engineering Techniques (1989)
at the Katholieke Universiteit Leuven,
Belgium. He is currently a research assistant at
the ESAT/M12 (Machine Intelligence and
Imaging) of the same university and belongs to
the Interdisciplinary Research Unit for Radiological Imaging. His research interest focuses on applications in
medical imaging.

Guy Marchal was born in Ukkel, Belgium, in
1946. He received his degree of M D at the
University of Leuven in 1970 and his specialisation in Radiology in 1974. He is presently
professor in Radiology at the University Hospitals in Leuven. His main research interests
are new imaging techniques, contrast agents
and noninvasive tissue characterisation. He is
also codirector of the Interdisciplinary
Research Unit for Radiological Imaging.

Carl Smets was born in Turnhout, Belgium, in
1960. He received his MS degree in Physics
and his MS degree in Biomedical Techniques
from the Katholieke Universiteit, Leuven,
Belgium. From 1985-1990 he was a Research
Associate at the Machine Intelligence and
Imaging department of the same university. In
1990 he received his Ph.D. degree for his dissertation on a knowledge-based system for the

Frans Van de Werf was born in Mechelen,
Belgium, in 1947. He obtained an M D degree
at the University of Leuven in 1972 and
specialised in Internal Medicine and Cardiology from 1972 to 1978. He obtained his
Ph.D. in 1982. His present affiliation is the
Division of Cardiology of the University of
Leuven where he is head of Clinic and
Professor of Medicine.

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