DIMENSION REDUCTION BASED ON CENTROIDS FOR

MULTIMODAL ANATOMICAL LANDMARK-BASED 3D/2D

REGISTRATION OF CORONARY ANGIOGRAMS

Klaus Drechsler and Cristina Oyarzun Laura

Department of Cognitive Computing & Medical Imaging

Fraunhofer Institute for Computer Graphics Research IGD, Darmstadt, Germany

Keywords:

Cardiology, Catheterization, Dimension Reduction, 3D/2D Registration, Exhaustive Search, Search Space

Reduction.

Abstract:

We present an anatomical landmark-based rigid 3D/2D registration algorithm to register computed tomogra-

phy angiography (CTA) datasets with coronary angiograms (CA) gathered during a cardiac catheterization.

It has to solve for six transformation parameters (three rotation and three translation parameters). An ex-

haustive search in a six dimensional search space is usually computationally very expensive and algorithms

using optimization strategies can get lost in local minima. We propose a method based on centroids to reduce

search space from six to four dimensions. Modern C-Arm devices store a lot of information about the acqui-

sition geometry that are used to further reduce the search space. We use this method to develop an efﬁcient

smart exhaustive search to solve for the six transformation parameters in a competitive time. With our method

registration errors of < 2 mm are feasible. Execution times of < 1 sec. can be reached on a QuadCore CPU.

1 INTRODUCTION

The blockage of the coronary arteries, which bring

oxygen rich blood to the heart muscle, can lead to

damaged/death parts of the muscle. This in turn can

lead to a heart attack, which is the leading cause of

death worldwide. The current gold standard for de-

tecting these blockages (called plaques) is an invasive

coronary angiography. A coronary angiography is the

process of injecting a contrast agent directly into the

coronary arteries through a catheter and monitoring

this process using a C-Arm X-Ray device that is able

to record the injection as a video sequence.

We assume that in the near future the diagnos-

tic of the coronary arteries will be done using non-

invasive computed tomography angiography (CTA)

and that only the intervention, if necessary, will be

done in a catheter laboratory (to insert e.g. stents) or

in an operation room (to do a bypass surgery). This

assumption is not unrealistic: A steadily increasing

number of hospitals are already using CTA for diag-

nostic purposes and papers successfully investigating

CTA for this use case were published (e.g. (Hoffmann

et al., 2005) and (Mieres et al., 2007)). A combina-

tion of preoperatively gathered CTA dataset and oper-

atively gathered CA will further enhance the trust in

CT for the assessment of the coronary arteries. We

use a tool that is able to carry out an automated quan-

titative analysis of the coronary arteries using CTA

datasets (Wesarg et al., 2006), whose output has been

positively evaluated in a clinical study (Khan et al.,

2006), (Wesarg et al., 2008). Our goal is to display the

analysis results of this tool (the found pathologies like

plaques) directly in the CA of the patient. Thus, the

problem can be reduced to a 3D/2D rigid registration

problem. It has to ﬁnd three rotation and three trans-

lation parameters that bring the 3D CTA volume into

a position within a virtual C-Arm device that equals

the position of the patient on the table when the 2D

CA was gathered using the real C-Arm device. A vir-

tual CA gathered by the virtual C-Arm device is then

appromimately the same than the CA gathered by the

real C-Arm device.

In this paper we present a landmark-based 3D/2D

registration algorithm to register CTA datasets with

CAs. Therefore the CTA is used to generate an ar-

tiﬁcial CA, called digitally reconstructed radiographs

(DRR), which is used in an intermediate step and dis-

1

Drechsler K. and Oyarzun Laura C.

DIMENSION REDUCTION BASED ON CENTROIDS FOR MULTIMODAL ANATOMICAL LANDMARK-BASED 3D/2D REGISTRATION OF CORONARY ANGIOGRAMS.

DOI: 10.5220/0002826100490056

In Proceedings of the International Conference on Imaging Theory and Applications and International Conference on Information Visualization Theory and Applications (VISIGRAPP 2010),

page

ISBN: 978-989-674-027-6

played side-by-side with the CA to allow the user to

select anatomical correspondences. Afterwards an ex-

haustive search is executed to solve for the six param-

eters (three rotation and three translation parameters).

We introduce a novel method to reduce the search di-

mension from six degrees of freedom to four, which

to the best of our knowledge has never been applied

to this problem before. Although we used this method

to speed-up an exhaustive search algorithm, it can be

also used with more advanced optimization strategies.

However, compared to other methods an exhaustive

search does not get lost in local minima. We show

in an experiment that RMS registration errors of < 2

mm are feasible and execution times of less than 1

sec. can be reached on a QuadCore CPU.

The remainder of this paper is organized as fol-

lows. The next section presents related work. The

following section 3 describes the workﬂow of the reg-

istration process from an user point of view. In sec-

tion 4 the used methods are described. Especially our

registration and dimension reduction methods are de-

tailed. In section 5 the results of an experiment are

presented and discussed in section 6. And in section

7 we ﬁnally conclude this paper.

2 RELATED WORK

When developing applications that combine and use

information gathered from different modalities, regis-

tration plays an important role. 3D/2D registration al-

gorithms can be classiﬁed as intensity-based, feature-

based or as hybrid approaches between those two.

Feature-based methods can be further classiﬁed ac-

cording to the type of feature used.

A system that uses external features is described

by Filippatos in (Filippatos, 2006). They use a

ﬁducial-based registration to match the 3D CT vol-

ume to the intraoperative x-ray image. Therefore they

calculate the transformation matrix that matches the

3D points (that correspond to ﬁducial markers in the

CT volume) with the corresponding 2D x-ray points

and use it to initialize the 3D volume in an adequate

position.

The work presented in (Lau and Chung, 2006)

uses internal features. They studied how to avoid

the problem of local minima that occurs in high-

dimensional image registration. For their experiments

they used the vessels centerline as feature. The opti-

mization method consist of calculating the result of

the cost function in a low resolution environment, op-

timizing it with Powells method using sum of squared

differences as metric, and doing a ﬁnal optimization

with the best obtained transformation matrix in the

high resolution environment. The authors report an

execution time of 13 min. on one 2.5 GHz processor

with 512 GB RAM using Matlab. They estimate that

they can achive an execution time of approximately

30 sec. using C++ and further optimizations.

In (Langs et al., 2004) the authors describe a reg-

istration method based on internal features. In their

registration approach the user has to mark two corre-

sponding points in the 3D model of the vessels and

the 2D x-ray image. However, if a doctor has to select

a point in 3D and a corresponding point in 2D then

he has either to reconstruct a 3D image from the 2D

x-ray or a 2D image from the 3D model in his head

to decide which points correspond. We avoid this by

generating a DRR from the CT-data and let the user

select the point in two similar 2D images. The au-

thors report execution times of approximately 0.3 sec.

Unfortunately it is not clear how they solved for the

six transformation parameters. It seems that they use

the primary and secondary angle of the C-Arm de-

vice together with two manually selected points to di-

rectly solve an equation to get the remaining param-

eters. But because of patient movement between ac-

quisitions and error-prone points this seems not the

way to go.

In (Groher et al., 2007) the authors propose an au-

tomatic 3D/2D registration algorithm based on bifur-

cations as internal features. They use shape context

descriptors to establish correspondences between bi-

furcations in both modalities. The authors used a rigid

phantom for their experiment and reached an execu-

tion time of 2-6 sec. for the registration.

The work presented in (Turgeon et al., 2005) be-

longs to the class of intensity-based methods. It deals

with similarity-based 3D/2D registration of coronary

angiograms using binary images instead of gray scale

images. The authors obtain a 4D model of the heart

composed of realistic 2D and 3D images to create a

simulation environment for evaluation purposes. The

registration is carried out using entropy correlation

coefﬁcient as metric and the downhill simplex method

as optimization strategy. The execution time of their

algorithm is between 17 and 32 sec. on two 3 GHz

Xeon processors with 1 GB of RAM.

3 APPLICATION WORKFLOW

In this section the workﬂow from a user point of view

is described. We assume that the C-Arm is calibrated

and that the intrinsic parameters are known. Basically

the workﬂow consists of six consecutive steps as fol-

lows.

IMAGAPP 2010 - International Conference on Imaging Theory and Applications

1

Figure 1: The coronary angiogram and a DRR calculated from CT data is displayed. The user user has to select corresponding

landmarks in both images.

Step 1 - Image Selection. As described in the in-

troduction section, during the catheterization a video

sequence of the process is recorded. In the ﬁrst step

an appropriate image from this sequence has to be se-

lected. An image is considered as appropriate if the

displayed heart cycle corresponds to the heart cycle in

which the CTA data was gathered and if the injected

contrast agent is still in the arteries. Using available

ECG information, this is not difﬁcult to do.

Step 2 - DRR Creation. The task of the next step is

to create a DRR from the CTA dataset that shows the

heart approximately in the same position as the heart

in the CA that was selected in step 1. State-of-the-

art angiographic C-Arm devices store lots of infor-

mation, including the rotational angles of the C-Arm

during the recording of the video sequence. This in-

formation is used to create the DRR. However, older

C-Arm devices do not store all rotational angles, so

that user intervention would be necessary to approxi-

mately ﬁnd the missing angles.

Step 3 - Display DRR and CA. In this step the cre-

ated DRR and CA are displayed side-by-side on two

monitors (see ﬁg. 1) or overlapped on one monitor. In

the latter case the user can crossfade the two images

using a slider.

Step 4 - Select Corresponding Point Pairs. In this

step the user has to select n corresponding anatomical

landmarks in both images as depicted in ﬁg. 1. Typi-

cally n = 4 is sufﬁcient, but more points can improve

the quality of the ﬁnal result.

Step 5 - Align Points. After the user has selected

n corresponding landmarks, the points in the DRR

image will be automatically aligned to the closest

vessel centerline. This enables the backprojection

of the selected 2D DRR points to 3D space of the

CTA volume, which is required to carry out a 3D/2D

landmark-based registration. Therefore we developed

a concept that we call ’alignment map’. The 3D

centerline voxels are projected into 2D space with

the same parameters used for creating the DRR. The

alignment map contains the projected 2D points and

the corresponding 3D points of the centerline. The

effect of aligning the points is shown in ﬁg. 2. After

aligning the points, they can be backprojected to 3D

space by querying the alignment map.

Step 6 - Carry out Registration. At this point the

following parameters are given.

• n corresponding 2D points (a

, d

), i : 0...n − 1

• 3D points D

= map(d

) (using the alignment

map)

• Matrix K with intrinsic parameters of the C-Arm

device, which includes the focal length which

can be found as source-to-detector distance dist

std

which can be found in the DICOM header

• Primary (γ) and secondary (α) angles found in the

DICOM header

• The source-to-object distance dist

sto

found in the

DICOM header

Given these parameters the problem can be formu-

lated as follows. Find euler angles α, β, γ and t =

) such that

= K · (R

α,β,γ

· D

+t) (1)

Because the selected corresponding landmarks are

error-prone and not exact the problem turns out to be

a minimization problem.

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13

Figure 2: The selected point in the left image is aligned to the closest vessel centerline as shown in the right image. This

enables the backprojection of this 2D point into 3D space using our alignment map. The images show an extreme example to

illustrate the idea. Usually points are selected that are somewhere on a vessel or at least very close to it and not that far away.

4 METHODS

The following subsection gives an overview of used

algorithms to extract the heart, segment arteries and

generate DRRs. Afterwards our registration method

is described.

4.1 Image Processing

Cardiac CT data normally contains non-cardiac struc-

tures such as ribs, lungs or the sternum. These struc-

tures obscure the view to the heart, but an isolated

heart is necessary to make a visualization of the coro-

nary arteries on the surface of the heart possible. We

use the approach presented in (Jaehne et al., 2008)

which is desribed as follows. A partition (labels) of

the anatomical structures by automatically selecting

thresholds using Otsus method (Otsu, 1979) is ob-

tained. The two brightest gray levels are used to cal-

culate the center of gravity for every axial slice, which

lies in the middle of the heart. From this point ra-

dial search rays are send out in order to ﬁnd the outer

boundary of the heart. These rays will be too long at

places where overlapping structures like the aorta or

the sternum are present, thus preventing this method

to function properly. These parts are handled as fol-

lows. On each side of the aorta and the sternum the

last rays which hit lung tissue and therefore have the

correct length are automatically detected. Interpola-

tion is then used to correct the rays between them.

The found end points are connected and a binary mask

is generated which is used as a mask on the original

CT data to extract the heart.

The result of the previous algorithm is used to seg-

ment the coronary arteries using a tracking based seg-

mentation algorithm, which is described in (Wesarg

and Firle, 2004). The data is preprocessed with an

adaptive threshold ﬁlter that takes the gray values of

three user provided seed points (start, direction and

end point) and the CT data as inputs. It takes into ac-

count that the contrast agent is not equally distributed

in the vessel. It follows an opening operation to re-

move connections to neighboring tissues and to the

vessel wall behind hard plaques. The actual algorithm

gets the results of the opening operation, the original

image and the output of the adaptive threshold ﬁlter

to calculate a path (centerline and border) between a

start and end point that lies within the vessel. After-

wards a 3D model is generated using the marching

cubes algorithm (Lorensen and Cline, 1987).

We use the approach presented in (Lacalli et al.,

2008) to calculate a DRR of the heart. First a pre-

processing of the original CT data is carried out to

avoid insufﬁcient results due to non-cardiac structures

and large cardiac cavities (e.g. ventricles and atria)

that are ﬁlled with contrast agent. The latter would

occlude the coronary arteries in the DRR and must

therefore be removed. To remove the cavities from

the extracted heart a thresholding operation on the la-

beled CT data (that was generated in the heart extrac-

tion step described above) is ﬁrst applied to remove

everything but the highest label that correlates with

both the cavities and the arteries. The coronary arter-

ies are then removed by an erosion operation followed

by a neighborhood ﬁlter along all the three orthogonal

axes. Finally a dilation operation is applied to restore

the original size of the cavities. The result is used as a

mask to remove the cavities from the extracted heart.

A perspective projection is then carried out to gener-

ate the DRR to simulate a coronary angiogram.

IMAGAPP 2010 - International Conference on Imaging Theory and Applications

1

4.2 Registration Method

As written in the previous section, we are dealing with

a minimization problem. We use the root mean square

(RMS) error as metric that we are minimizing using

our algorithm. The RMS error is deﬁned as

RMS

error

− d

)

(2)

where a

is the selected point in the CA and d

the

transformed and projected point D

calculated accord-

ing to equation 1 as

= K · (R

α,β,γ

· D

+t) (3)

Source

(0,0,0)

Detector

(0,0,dist

std)

Table

(0,0,dist

sto

)

Patient surface

(0,0,dist

sto

-dim

)

search space

}

Figure 3: The image shows the most important ideas to re-

duce the dimensions and search space. The blue points in

the cube are the points D

. The red line is the centroid line

from source to the centroid of the points a

. The search

space is limited by the table and the patient surface.

We developed an algorithm that we call ’smart ex-

haustive search’ that guarantees to ﬁnd the minimum

RMS

error

(because it does an exhaustive search) and is

very well parallelizable. A normal exhaustive search

has to take six degrees of freedom into account and

thus would be very inefﬁcient for our application. The

key idea behind our algorithm is to reduce the dimen-

sions to four degrees of freedom (three rotation and

one translation parameter) and then further reduce the

remaining search space by taking all the given param-

eters into account.

We explain now how we reduced the degrees of

freedom from six to four. Therefore we deﬁne that

the source of the C-Arm device is always at the origin

of the world coordinate system and the detector plane

is dist

std

away in the z-dimension, thus src = (0, 0, 0)

and det = (0, 0, dist

std

). We further deﬁne the centroid

of the n 2D points a

centroid



c2d



n−1

∑

(4)

The result of equation 4 is enhanced by a z-

component, which is set to the source-to-detector dis-

tance dist

std

, thus centroid

is guaranteed to lie on

the detector plane:

centroid

2DZ





c2d

dist

std





(5)

Next we construct a line, called centroid line

or cline, from the source of the C-Arm device to

centroid

2DZ

(see red dotted line in ﬁg. 3), which is

given by

cline(p) =









= src + p · (centroid

2DZ

−src) (6)

Parameter p has to be between 0 and 1 and indi-

cates the distance from src in direction of det. Fur-

ther, we deﬁne the rotated and translated points D

= (R

α,β,γ

· D

+t) (7)

and equally to equation 4 the centroid of the n 3D

points D

centroid





c3d





n−1

∑

(8)

Now it can be observed that, after a successful reg-

istration,in the theoretical case where the given land-

marks are accurately known, the centroid of D

must

lie on cline(p) and K · centroid

= centroid

2DZ

(see

ﬁg. 3). We can then calculate the resulting transla-

tion vector t from parameter p using equation 6. This

knowledge can be used to reduce the degrees of free-

dom from six to four by moving centroid

during the

exhaustive search along cline(p), thus we only have

to solve for four parameters, namely α, β, γ and p to

minimize equation 2. In practice the landmarks are

not accurately known, but error-prone. The effect of

moving centroid

along cline(p) in this case is that

the error between corresponding landmarks is aver-

aged.

We further reduce the search space by taking the

source-to-object distance dist

sto

and the physical di-

mension in z-direction dim

of the CT volume into ac-

count. The name ’source-to-object’ is a little bit mis-

leading. It is really the distance between the source

of the C-Arm device and the table where the object

(the patient) is laying on. Thus, equation 2 is minimal

when centroid

lies on cline(p) somewhere between

the table at coordinates (0, 0, dist

sto

) and the patient

surface at coordinates (0, 0, dist

sto

−dim

) (see ﬁg. 3).

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1

Table 1: Summary of the used parameters.

Parameter α β γ dim

dist

sto

Value 0.1 n/a -30.9 300 700

The search space can be reduced even more by

taking the given angles α and γ into account. Even

if the values are accurately known, the patient is not

lying in the same position as he was during the CTA

acquisition. Thus, these values can only be used as

rough estimations. In (Byrne et al., 2004) the au-

thors searched ±8 degrees around the given values.

We found that for our dataset searching ±20 degrees

around the stored values is necessary to ﬁnd the mini-

mal RMS

error

. Thus, this value varies between differ-

ent C-Arm devices and different CTA/CA pairs.

4.3 Parallelization

The described method can be parallelized using n pro-

cessors by dividing parameter p into n equal sized

parts and let each processor execute independently the

described method for one part. Then, the processor

that calculated the smallest RMS

error

has found the

solution.

5 RESULTS

We evaluated our algorithm with one CTA/CA dataset

pair. The analysis tool mentioned in the introduc-

tion that we use to analyze the coronary arteries is

able to segment single branches of the coronary artery

tree and to calculate the vessel centerline. To qual-

itatively verify the registration results, we overlaped

these centerlines with the CA. We searched ±20 de-

grees around all given angles and around 0 for β. We

repeated the experiment two times. The ﬁrst time

with a step width of 1 (experiment A), the second

time with a step width of 2 (experiment B). There-

fore we modiﬁed equation 6 by normalizing the vec-

tor centroid

2DZ

− src. With this modiﬁcation pa-

rameter p has to be between 0 and the length of

centroid

2DZ

− src before normalization. All experi-

ments were executed on a PC equipped with an Intel

2.5 GHz DualCore CPU, 4 GB RAM and Windows

7 x64 as operating system. Table 1 summarizes the

parameters we used for the registration.

The registration was done using the workﬂow de-

scribed in section 3 and repeated four times using four

to seven corresponding point pairs. The results are

presented in table 2 and 3. For qualitative evalua-

tion we overlapped the centerlines of two segmented

branches of the coronary arteries in the CTA dataset

Table 2: Quantitative results of experiment A using a step

width of 1 mm.

Landmarks pairs 4 5 6 7

RMS error [mm] 0.81 0.76 1.16 1.5

SingleCore [s] 23.1 24.9 28.0 32.8

QuadCore [s] 5.8 6.2 7.0 8.2

Table 3: Quantitative results of experiment B using a step

width of 2 mm.

Landmarks pairs 4 5 6 7

RMS error [mm] 0.83 0.78 1.2 1.54

SingleCore [s] 1.8 1.9 2.0 2.4

QuadCore [s] 0.45 0.48 0.5 0.6

with the CA. The results are shown in ﬁg. 4. There

were no visible differences between experiment A and

B. The estimated values for a QuadCore CPU were

calculated by dividing the execution time on a Sin-

gleCore CPU by four.

6 DISCUSSION

A general problem for methods based on the vessel

centerline as feature is that they rely on good ves-

sel segmentation algorithms which in turn depend on

good datasets where the contrast agent is spread op-

timally. This is also the case with our method. We

had three CTA/CA dateset pairs and were only able to

apply our method to one pair. The reason was mainly

that the contrast agent was not very well visible in the

CT datasets.

There is no visible and measurable difference be-

tween the top two images of ﬁg. 4, but a short part of

the overlapped vessel centerlines is cleary not over-

lapped correctly near the root of the coronary artery

tree. In the bottom two images this problem is re-

duced by selecting more point correspondences at the

cost of slightly misalignments at other places of the

vessel tree. Although the RMS error was greater for

the bottom images, they generally look better than the

images in the top row. This is due to the fact that the

calculated centroids average landmark errors during

the registration process.

Because we manually selected a frame from the

recorded angiography, it could be that we selected

one that was not the best choice, hence the misalign-

ments. But using ECG information this should not be

a problem in general. Another reason could be that

the manually selected points were not corresponding

very well and thus introducing an error in the regis-

tration process.

The manual selection of corresponding points is

IMAGAPP 2010 - International Conference on Imaging Theory and Applications

1

Figure 4: Qualitative results with four (top left), ﬁve (top right), six (bottom left) and seven (bottom right) manually selected

corresponding point pairs.

currently the biggest disadvantage of our method. An

interesting approach to solve for this can be found

in (Groher et al., 2007). The authors developed a

method to automatically ﬁnd corresponding bifurca-

tions in 2D and 3D images based on shape context

descriptors.

There were no signiﬁcant visible differences be-

tween experiment A and B, but using a step width of

2 in experiment A is signiﬁcant faster.

In other experiments we found that it is important

which landmarks are chosen. If only landmarks from

one vessel branch are chosen, then it is likely that the

other branches will be fairly misaligned. This can

be acceptable if only one branch is of interest. But

in general it can be said, as a rule of thumb, that as

much landmarks as possible should be spread over the

whole vessel tree. Fortunately, the process of select-

ing corresponding landmark pairs is quite easy and

fast.

As can be seen from table 2 and 3 the process-

ing time needed to solve for the six transformation

parameters is, thanks to the presented strategies to re-

duce the dimensions and search space, quite compet-

itive when taking the estimated times into account.

If faster processing times are needed, the exhaustive

search can be replaced by more advanced optimiza-

tion strategies at the cost of risking to get lost in local

minima. Another option would be to use more pro-

cessors for the calculation and/or specialised architec-

tures like CUDA.

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1

7 CONCLUSIONS

We presented a novel dimension reduction method

based on centroids that we successfully applied to a

multimodal anatomical landmark-based 3D/2D reg-

istration problem. We used this method to speed-up

an exhaustive search to solve for the six transforma-

tion parameters. In an experiment we have shown that

this method produced good results with competitive

processing times. The presented dimension reduc-

tion technique is not limited to exhaustive search, but

can also be used in combination with optimizers to

speed-up feature-based 3D/2D registration problems,

where features represents anatomical landmarks like

e.g. branch points.

Future work includes the automated detection

of corresponding point-pairs as inspired by (Groher

et al., 2007) and the use of more advanced optimiza-

tion strategies together with the presented dimension

reduction method to further speed-up the registration

for real-time usage. Furthermore, we are thinking

about ways to take the complete vessel centerlines

into account to improve the registration results.

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