BIOMEDICAL PAPER

“Gold standard” data for evaluation and comparison of 3D/2Dregistration methods

DEJAN TOMAZEVIC, BOSTJAN LIKAR, & FRANJO PERNUS

Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia

(Received 15 January 2003; revised version received 26 February 2004; accepted 15 May 2004)

AbstractEvaluation and comparison of registration techniques for image-guided surgery is an important problem that has receivedlittle attention in the literature. In this paper we address the challenging problem of generating reliable “gold standard”data for use in evaluating the accuracy of 3D/2D registrations. We have devised a cadaveric lumbar spine phantom with fidu-cial markers and established highly accurate correspondences between 3D CTand MR images and 18 2D X-ray images. Theexpected target registration errors for target points on the pedicles are less than 0.26 mm for CT-to-X-ray registration and lessthan 0.42 mm for MR-to-X-ray registration. As such, the “gold standard” data, which has been made publicly available onthe Internet (http://lit.fe.uni-lj.si/Downloads/downloads.asp), is useful for evaluation and comparison of 3D/2D image regis-tration methods.

Keywords: 3D/2D image registration, computed tomography, “gold standard”, image-guided therapy, magnetic resonance,spine phantom, X-ray projections

Key link: http://lit.fe.uni-lj.si/Downloads/downloads.asp

Introduction

In image-guided surgery, 3D preoperative medical

data, such as computed tomography (CT) and mag-

netic resonance (MR) images, are commonly used to

plan, simulate, guide, or otherwise assist a surgeon in

performing a medical procedure. The plan, specify-

ing how tasks are to be performed during surgery, is

developed in the coordinate system of a preoperative

image. To monitor and guide a surgical procedure,

the preoperative image and plan must be transformed

into physical space, i.e., a patient-related coordinate

system. This spatial transformation is obtained by

acquiring intraoperative data and registering them

to data extracted from preoperative images [1].

More recent and promising approaches to obtaining

the spatial transformation rely on intraoperative

X-ray projections acquired with a calibrated X-ray

device. The location and orientation of a structure

in a 3D CT or MR image with respect to the geo-

metry of the X-ray device is determined by 3D/2D

registration [2–5]. A necessary step before wide-

spread clinical use of any novel registration technique

is the evaluation and validation of the method [6].

One difficulty in evaluating a registration technique

is the need for a highly accurate “gold standard”.

Motivated by the continuing need for data sets and

“gold standards” to test, validate, and measure the

accuracy of different 3D/2D registration techniques,

we have devised a cadaveric lumbar spine phantom,

because it is very hard to establish a “gold standard”

using real patient data. In this paper we describe the

construction of the phantom to which fiducial

markers were attached. Three-dimensional CT, MR

and 2D X-ray images were acquired, and accurate

“gold standard” rigid registration between 3D and

Correspondence: Prof. Franjo Pernus, Ph.D., University of Ljubljana, Department of Electrical Engineering, Trzaska 25, 1000 Ljubljana,Slovenia. Tel: þ386 1 4768 312. Fax: þ386 1 4768 279. E-mail: franjo.pernus@fe.uni-lj.si

Computer Aided Surgery, 2004; 9(4): 137–144

ISSN 1092-9088 print=ISSN 1097-0150 online #2004 Taylor & FrancisDOI: 10.1080=10929080500097687

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2D images was established by means of fiducial

markers. The accuracy of “gold standard” regis-

tration was assessed by determining the target regis-

tration error (TRE) [7].

Methods and results

Phantom creation

The cadaveric lumbar spine, comprising vertebrae

L1-L5 of an 80-year-old female complete with inter-

vertebral disks and several millimeters of soft tissue,

was placed in a plastic tube and tied with thin nylon

strings (Figure 1, left). The tube was filled with

water to simulate soft tissue and thus enable more

realistic MR, CT and X-ray images to be obtained.

Six fiducial markers (Stryker Leibinger, Freiburg,

Germany) were rigidly attached to the outside of

the plastic tube. Each fiducial marker had two com-

ponents: a base that could be screwed to a rigid

body and a replaceable marker. Different markers

were used for the different imaging modalities:

Markers containing a metal ball (1.5 mm in dia-

meter) were used for CT and X-ray imaging, while

markers with a spherical cavity (2 mm in diameter)

filled with a water solution of Dotarem contrast

agent (Gothia, Sweden) were used for MR.

Image acquisition

The CT image (Figure 1, top center) was obtained

using a General Electric HiSpeed CT/i scanner.

Axial slices were taken with intra-slice resolution of

0.27 � 0.27 mm and inter-slice distance of 1 mm.

For MR imaging, a Philips Gyroscan NT Intera 1.5

T scanner and T1 protocol (flip angle 908,

TR ¼ 3220 ms, TE ¼ 11 ms) was used (Figure 1,

top right). Axial slices were obtained with intra-slice

resolution of 0.39 � 0.39 mm and inter-slice dis-

tance of 1.9 mm. The acquired MR image was retro-

spectively corrected for intensity inhomogeneity

using the information minimization method [8]. X-

ray images (Figure 1) were captured by a Pixium

4600 digital X-ray detector (Trixell, Moirans,

France). The detector had a 429 � 429 mm active

surface, with pixel size of 0.143 � 0.143 mm and

14-bit dynamic range. To simulate C-arm acqui-

sition, the X-ray source and sensor plane were fixed

while the spine phantom was rotated on a turntable

(Figure 2). In this way, mechanical distortion due

to gravitational force and other mechanical imperfec-

tions of the C-arms was avoided. By rotating the

spine phantom around its long axis in 208 steps, 18

X-ray images were acquired. These images were

filtered by a 3 � 3 median filter and then sub-

sampled by a factor of two to remove dead pixel

artifacts.

Finding the centers of fiducial markers

Figure 3 shows close-up views of fiducial markers in

CT, MR and X-ray images. In all 3D and 2D

images, a rough position pm of each fiducial marker

was first defined manually. Next, an intensity

threshold IT that separated the marker from the

surrounding tissues was selected for each marker.

Finally, the center pc of each marker was defined as

pc ¼

Pp[V (I(p)� IT )pPp[V (I(p)� IT )

(1)

Figure 1. The spine fastened in a plastic tube (top left); the final phantom with fiducial markers attached to the outside of the tube (bottom

left); CT image (top center); MR image (top right); and AP (bottom center) and lateral (bottom right) X-ray images of the phantom.

138 D. Tomazevic et al.

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where I(p) is the intensity at point p and V is a small

neighborhood around point pm. By this method,

centers of markers may be found with sub-pixel or

sub-voxel accuracy [9,10].

Let XCT and XMR be 3 � 6 matrices, each contain-

ing six 3D vectors representing the centers of fiducial

markers found in CT and MR, respectively:

XCT ¼ ½rCT1 , rCT

2 , . . . , rCT6 �

XMR ¼ ½rMR1 , rMR

2 , . . . , rMR6 �

(2)

where r ¼ (x, y, z)T. Similarly, let Xw be a 2 � 6

matrix containing six 2D vectors representing the

centers of markers found in X-ray images obtained

after rotating the phantom through w degrees

(w ¼ 08, 208, . . . , 3408):

Xw ¼ ½pw1, p

w2, . . . , p

w6 � (3)

where p ¼ (x, y)T.

Retrospective calibration of the X-ray setup

To be able to reconstruct the 3D positions of fiducial

markers from their positions in 2D X-ray images, the

acquisition setup (Figure 2) was retrospectively

calibrated. Calibration required the determination

Figure 3. Close-up views of fiducial markers in CT (left), MR (center) and X-ray (right) images.

Figure 2. X-ray image acquisition.

“Gold standard” data for 3D/2D registration 139

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of 12 geometrical parameters – 3 intrinsic wI and 9

extrinsic wE – denoted by calibration parameter

vector w, w ¼ (wI, wE). The intrinsic parameters

wI ¼ (xs, ys, zs) define the position of the X-ray

source rs in the coordinate systems Ss of the sensor

plane, and therefore define the projection PS(wI) of

any 3D point described in the sensor coordinate

system Ss to the 2D sensor plane. The extrinsic para-

meters wE describe the geometric relation between

the rotating phantom and the X-ray system. Four

parameters define the axis of rotation in the coordi-

nate system Sv of the phantom. We have chosen the

coordinate system of the CT volume for Sv. The

axis of rotation is defined by the point (txv, tyv),

which is the intersection of the axis with the x-y coor-

dinate plane of Sv, and by rotation (vxv, vyv) of the

axis around the x and y of Sv. Similarly, four para-

meters (txs, tys) and (vxs, vys) define the same axis

of rotation in the coordinate system Ss of the X-ray

sensor plane. The last parameter, necessary to deter-

mine the relation between Ss and Sv on the rotation

axis, is distance dvs between the two points of inter-

section (txv, tyv) and (txs, tys). The extrinsic para-

meters wE ¼ (txv, tyv, vxv, vyv, dvs, txs, tys, vxs,

vys)T thus define the transformation TVS(w, wE):

TVS(w, wE) ¼ TRS(txs, tys, vxs, vys)

�T(dvs) �R(w)

�TVR(txv, tyv, vxv, vyv) (4)

This transformation maps, for a given rotation w of

the phantom, any 3D point in coordinate system Sv

to a 3D point in coordinate system Ss (Figure 2).

TVR is the transformation from coordinate system

Sv to the axis of rotation; R(w) is the rotation

around the rotation axis; T(dvs) is the translation

along the rotation axis; and TRS is the final transform-

ation to the coordinate system Ss. For any rotation w,

the projection PVS(w, w) of a 3D point defined in the

coordinate system Sv to the 2D point lying in the

sensor plane defined by Ss is obtained by applying

the projection PS(wI) and the transformation

TVS(w, wE)

PVS(w, w) ¼ PS(wI)TVS(w, wE) (5)

To retrospectively calibrate the X-ray acquisition

system, we thus need to define 12 geometrical

parameters w of the projection PVS(w, w). For this

purpose we have used centers Xw of fiducial

markers found in the X-ray images and the corre-

sponding centers XCT of markers found in the CT

volume. The optimal calibration parameters w are

the ones that bring the fiducial markers XCT in the

CT volume to the best correspondence with the cor-

responding fiducial markers Xw in the X-ray images.

To find the optimal parameters, we projected the

centers of the fiducial markers XCT in the CT

volume to the sensor plane and computed the root

mean squared (RMS) distance Ecalib to the corre-

sponding centers of fiducial markers Xw in the

X-ray images:

Ecalib(w) ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

M

Xw[F

1

N

XNi¼1

(pwi � PVS(w, w)rCT

i )2

vuut(6)

where N and M stand for the number of fiducial

markers and X-ray images, respectively, and F ¼

fw1, w2, . . . , wMg defines the X-ray images taken at

different phantom rotations. To find the optimal

calibration parameters w, we used nine X-ray

images F ¼ f08, 408, . . . , 3208g and iterative optimiz-

ation, which resulted in a minimum RMS distance

(Ecalib) of 0.31 mm. The small RMS indicates that

calibration was performed well and reflects the

uncertainty of fiducial marker localization in CT

and X-ray images.

Reconstruction of 3D markers

Once the X-ray acquisition system had been cali-

brated, the 3D positions of X-ray fiducial markers

could be reconstructed from their positions in 2D

X-ray images. The least-squares solution is used to

obtain the 3D marker position [11], as described

below. Each point piw, representing the center of the

ith fiducial marker in an X-ray image taken at

rotation w of the phantom, was back-projected to

the X-ray source rs, which yielded the imaginary

line Liw (Figure 4). Line Li

w, which defines the per-

spective projection of a 3D marker to the 2D X-ray

plane, can be expressed in the coordinate system Sv

of the phantom by mapping the X-ray source rs to

point cw:

cw ¼ T�1VS(w, wE)rs (7)

and by expressing the line direction in Sv coordinates

as

vwi ¼

T�1VS(w, wE)(p

wi � rs)

T�1VS(w, wE)(p

wi � rs)

�� �� (8)

where rs and piw are points defined in the sensor coor-

dinate system Ss. A marker’s 3D position riR in the

coordinate system Sv was reconstructed by

140 D. Tomazevic et al.

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minimizing the RMS distance Erec from point riR to all

lines Liw:

Erec(rRi ) ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

M

Xw[F

(rRi � cw)� v

wi

�� ��2s(9)

Reconstruction of the 3D positions of six fiducial

markers from the nine X-ray images F ¼ f208,608, . . . , 3408) which were not used for calibration

yielded RMS values of less than 0.06 mm for each

of the six markers. The positions of reconstructed

fiducial markers were incorporated in the 3 � 6

matrix XR ¼ [r1R, r2

R, . . . , r6R].

By using different sets of X-ray images for recon-

struction and calibration, we were able to validate

the calibration procedure. Small RMS values of

0.06 mm indicated that the uncertainty of fiducial

marker localization in X-ray images was less than

that in CT images and that calibration had been

performed well. Therefore, the major source of cali-

bration uncertainty is the uncertainty of fiducial

marker localization in CT images, though its effect

on calibration precision is obviously very small.

“Gold standard” registration and validation

After calibrating the X-ray acquisition system and

reconstructing 3D markers XR from X-ray images,

we were able to establish “gold standard” registration

between X-ray and CT images and between X-ray

and MR images in the coordinate system Sv of the

phantom. This was achieved by a rigid 3D/3D trans-

formation T that minimized the RMS distance Ereg

between the reconstructed fiducial markers XR from

X-ray images and the marker points XCT or XMR

from CT and MR images, respectively:

Ereg(T) ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

N

XNi¼1

rRi � Tri

� �2vuut (10)

where ri stands for either riCT or ri

MR. The closed-

form solution of this minimal RMS problem is

known [12,13]. Rigid transformation T can be

decomposed to the rotation component R, rep-

resented by a 3 � 3 matrix, and translation vector t:

Tr ¼ Rrþ t (11)

The optimal solution for the translation com-

ponent is given as:

t ¼ �rR �R�r (12)

where �rR and �r stand for the mean positions of point

sets XR and X, respectively, where set X is either XCT

or XMR. The optimal solution for the rotation com-

ponent is given as

R ¼ BAT (13)

A and B are two orthogonal matrices obtained by

singular value decomposition (SVD) of the matrix

�XR�X

T¼ ADBT (14)

where D is a diagonal matrix and �XR and �X are the

point sets XR and X, centered at corresponding

mean positions �rR and �r, respectively.

Rigid registration of point sets (XCT, XR) and

(XMR, XR) resulted in a minimum RMS distance

Ereg of 0.27 mm for CT and 0.44 mm for MR-to-

X-ray registration. The higher RMS for MR than

for CT can be attributed to three reasons: First,

CT was used in calibration; second, intra- and

inter-slice resolutions of the MR image were lower

than those of the CT image, resulting in higher

fiducial localization uncertainty; and the third, MR

image suffered from non-rigid spatial distortion.

The minimum RMS distance Ereg is also known as

the fiducial registration error (FRE) and can be used

to evaluate the accuracy of point-based rigid regis-

tration [7]. By knowing the FRE, we can determine

the target registration error (TRE), which is the

distance between the true, but unknown, position

of the target and the target position obtained by

registration. The expected TRE of a target point r

Figure 4. Reconstruction of 3D marker position. Due to the

uncertainty of X-ray marker localization and X-ray setup cali-

bration, the projection lines do not cross at the same point.

“Gold standard” data for 3D/2D registration 141

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can be estimated from FRE [7]:

kTRE2(r)l ¼kFLE2l

N1þ

X3

k¼1

dk

fk

!(15)

where fk is the RMS of the projections of the fiducial

markers to the kth principal axis of marker configur-

ation; dk is the projection of target point r to principle

axis k; N is the number of fiducial markers; and FLE

is the fiducial localization error obtained from the

FRE:

FLE2 ¼N

N � 2FRE2 (16)

Using the above formulation, we validated the

“gold standard” registration by manually defining

eight target points (four per pedicle) on each of the

five vertebrae and computing the mean TRE for

each vertebra. The results of “gold standard” vali-

dation for CT-to-X-ray and MR-to-X-ray regis-

trations are given in Table I. Expected TREs for the

pedicles are less than 0.26 mm for CT-to-X-ray regis-

tration and less than 0.42 mm for MR-to-X-ray

registration.

Publicly available “gold standard” data

The “gold standard” data and detailed information

on how to use it are publicly available from the

Department of Electrical Engineering, University of

Ljubljana, Laboratory of Imaging Technologies web

site (http://lit.fe.uni-lj.si/Downloads/downloads.asp).

The image database consists of 18 X-ray images and

5 CT and 5 MR sub-volumes (Figure 5). In the CT

and MR images, cubic sub-volumes were manually

defined, each containing a single vertebra, approxi-

mately one third of the neighboring vertebrae, and

no fiducial markers. In each sub-volume the areas

occupied by air and the plastic tube were manually

masked and their intensities were replaced by the

average intensity corresponding to water. The edges

between water, the plastic tube, and air were thus

almost eliminated. In this way, any rigid 3D/2D regis-

tration method evaluated using our “gold standard”

data cannot take advantage of markers or edges that

would not be present in actual clinical data. The

markers in X-ray images, which were not excluded

or “airbrushed”, may be considered as outliers,

similar to the way that surgical tools would be in a

clinical setting.

For each CT or MR sub-volume, the “gold stan-

dard” registration position, the coordinates of eight

target points on the pedicles, and 450 randomly

chosen starting positions around the “gold standard”

registration position are also provided in the data-

base. Details of the generation of starting positions

have been previously published in reference 14. Fur-

thermore, the data on our website contain the Matlab

(MathWorks, Natick, MA) source code for analyzing

registration results. The code allows calculation of

TREs and estimation of capturing ranges from the

results of 450 registrations per modality and vertebra.

Figure 5. Transverse and sagittal views of CT (left) and MR (center) sub-volumes, and a lateral X-ray image (right).

Table I. Expected RMS TREs for “gold standard” registration

(in mm).

Vertebrae

L1 L2 L3 L4 L5

CT 0.2 0.15 0.15 0.19 0.26

MR 0.33 0.24 0.24 0.31 0.42

142 D. Tomazevic et al.

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If different registration methods are to be objectively

compared, it is not only important that the same

image data sets be used, but equally important that the

evaluation protocol, criteria for successful registra-

tion, and error metrics be the same. Otherwise, it will

be difficult to place the results of a novel registration

method in the context of previously published work.

Discussion and conclusion

Before an image-guided therapy (IGT) system is put

into clinical use, its individual components must

undergo rigorous validation. Prerequisites for vali-

dation of 3D/2D image registration, which is the

crucial component of an IGT system, are standardi-

zation of validation methodology (including design of

validation data sets), definition of the corresponding

“gold standard” and its accuracy, a validation proto-

col, and design of validation metrics [14]. A fair com-

parison of different registration techniques is possible

only to a limited degree if standard validation metho-

dology is not publicly available. Motivated by the lack

of publicly available “gold standard” data for evalu-

ation and comparison of different 3D/2D rigid regis-

tration methods, we have devised a lumbar spine

phantom, obtained X-ray-to-CT and X-ray-to-MR

“gold standard” registrations, and established the

accuracy of these registrations. We are aware that

there are surgical interventions and radiosurgical

treatments of the spine for which markers are routi-

nely inserted into the spine of the patient. Marker-

based registered CT, MR and X-ray images of the

spine can serve as a truly clinical “gold standard”,

but are very difficult to obtain. Russakoff et al. [15]

reported on the evaluation of intensity-based 3D/

2D spine image registration using clinical “gold stan-

dard data”. Unfortunately, to the best of our know-

ledge, their data are not publicly available. One

problem with such a “gold standard” is the huge

effort required to remove all traces of the implanted

markers from images to avoid bias, i.e., to ensure

that the evaluated registration method could not

take advantage of markers that would not usually be

present in images acquired for image-guided therapy.

Another approach to obtaining more realistic “gold

standard” data is to overlay features segmented from

clinical images on phantom images [5]. Soft tissue,

surgical instruments and other structures can be

overlaid. Although our “gold standard” is not

equivalent to the clinical “gold standard”, and no

structures have been overlaid on our phantom

images, we believe it is sufficiently realistic to allow

fair evaluation and comparison of registration

methods for image-guided therapy. Our database

also contains MR images, and we believe this to be

very valuable.

The X-ray acquisition system was calibrated retro-

spectively by matching the projections of CT markers

with corresponding markers in X-ray images. Cali-

bration with CT markers is generally superior to cali-

bration with MR markers because CT offers better

resolution and spatial stability. This observation

was confirmed experimentally: CT-based calibration

yielded a smaller calibration error Ecalib of 0.31 mm,

compared with 0.47 mm when calibrating the X-ray

system with MR data. CT-based calibration of the

X-ray image acquisition setup already provides regis-

tration of CT to X-ray images, but does not provide

any indices of registration accuracy. Therefore, we

have reconstructed the 3D positions of markers

from calibrated 2D X-ray images, allowing us to

implement 3D/3D registration between the recon-

structed markers and those found in CT and MR

volumes. The result of such a registration reflected

a) the uncertainty of marker localization in 2D X-ray

images; b) the uncertainty of marker localization in

3D CT or MR images; c) the uncertainty of the

X-ray acquisition calibration; and d) the uncertainty

of marker reconstruction. The FRE of 3D/3D

registration, which reflected all these uncertainties,

was used to evaluate the TRE of the “gold standard”

CT-to-X-ray and MR-to-X-ray registrations accord-

ing to the theory developed in reference 7.

The results presented in Table I indicate that the

“gold standard” registration is highly accurate and

therefore useful for testing 3D/2D registration

methods. However, it should be stressed that the

expected TREs for CT-to-X-ray “gold standard”

registration may possibly be a little larger than

those in Table I. This is because the same CT

markers were used for both X-ray system calibration

and CT-to-X-ray registration, which could have

involved the same bias in calibration and registration.

By acquiring a second CT scan at the time of image

acquisition and using one for calibration and the

other for validation bias could be eliminated. Never-

theless, if we assume that localization errors for CT

markers are much smaller than those for MR

markers, the expected TREs for CT-to-X-ray “gold

standard” registration should be close to those

shown in Table I and certainly not larger than the

TRE values for MR-to-X-ray registration.

We believe that, due to the lack of publicly available

“gold standards” for 3D/2D rigid registration, the

presented “gold standard” data will prove useful for

the evaluation of newly developed methods and the

comparison of existing registration methods.

Acknowledgments

The authors would like to thank L. Desbat,

M. Fleute, R. Martin, F. Esteve and U. Vovk for their

“Gold standard” data for 3D/2D registration 143

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generous help and support in the image acquisitions.

This work was supported by the IST-1999-12338

project, funded by the European Commission and

by the Ministry of Education, Science and Sport,

Republic of Slovenia, under grant P2-028.

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