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Journal of Neuroscience Methods 142 (2005) 67–76

Quantitative comparison of algorithms for inter-subject registration

of 3D volumetric brain MRI scans

Babak A. Ardekania,c,∗, Stephen Guckemusa, Alvin Bachmana, Matthew J. Hoptmanb,c,

Michelle Wojtaszeka, Jay Nierenberga,c

aCenter for Advanced Brain Imaging, Nathan Kline Institute for Psychiatric Research, 140 Old Orangeburg Road, Orangeburg, NY 10962, USA

bClinical Research Division, Nathan Kline Institute for Psychiatric Research, 140 Old Orangeburg Road, Orangeburg, NY 10962, USA

cDepartment of Psychiatry, New York University School of Medicine, USA

Received 13 April 2004; received in revised form 20 July 2004; accepted 22 July 2004

Abstract

The objective of inter-subject registration of three-dimensional volumetric brain scans is to reduce the anatomical variability between the

imagesscannedfromdifferentindividuals.Thisisanecessarystepinmanydifferentapplicationssuchasvoxelwisegroupanalysisofimaging

data obtained from different individuals. In this paper, the ability of three different image registration algorithms in reducing inter-subject

anatomical variability is quantitatively compared using a set of common high-resolution volumetric magnetic resonance imaging scans from

17 subjects. The algorithms are from the automatic image registration (AIR; version 5), the statistical parametric mapping (SPM99), and the

automatic registration toolbox (ART) packages. The latter includes the implementation of a non-linear image registration algorithm, details

of which are presented in this paper. The accuracy of registration is quantified in terms of two independent measures: (1) post-registration

spatial dispersion of sets of homologous landmarks manually identified on images before or after registration; and (2) voxelwise image

standard deviation maps computed within the set of images registered by each algorithm. Both measures showed that the ART algorithm is

clearly superior to both AIR and SPM99 in reducing inter-subject anatomical variability. The spatial dispersion measure was found to be

more sensitive when the landmarks were placed after image registration. The standard deviation measure was found sensitive to intensity

normalization or the method of image interpolation.

© 2004 Elsevier B.V. All rights reserved.

Keywords: MRI; Brain; Image registration; Spatial normalization

1. Introduction

An important methodological consideration for analysis

of human brain imaging data is inter-subject registration or

spatialnormalizationofimagesacquiredfromdifferentindi-

viduals. The aim of inter-subject registration is to reduce the

anatomical variability in three-dimensional (3D) volumet-

ric brain scans obtained from different subjects. For exam-

ple, inter-subject registration allows voxelwise group anal-

ysis of functional magnetic resonance imaging (fMRI) data

(Svensenetal.,2002;Zeffiroetal.,1997),andstudiesofbrain

∗Corresponding author. Tel.: +1 845 398 5471; fax: +1 845 398 5472.

E-mail address: ardekani@nki.rfmh.org (B.A. Ardekani).

white matter using diffusion tensor imaging (Ardekani et al.,

2003; Jones et al., 2002). Another class of applications of

inter-subjectregistrationcanbecategorizedasautomatic‘im-

age understanding’, where higher order information (tissue

type, locations of anatomical landmarks, structural bound-

aries, specific sulci/gyri, etc.) that are known about a tem-

plate image are obtained about a subject or test image after

the subject image is registered to the template by non-linear

spatial transformation or deformation (Collins et al., 1995;

Marroquin et al., 2002; Webb et al., 1999). An additional im-

portant application is the quantification of small changes in

volume observed in anatomical structures over time (Holden

et al., 2002; Rey et al., 2002) that can be used in diagnosis

and evaluation of disease progression and treatment.

0165-0270/$ – see front matter © 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.jneumeth.2004.07.014

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B.A. Ardekani et al. / Journal of Neuroscience Methods 142 (2005) 67–76

Spatial registration is specified in terms of a 3D transfor-

mation or displacement field w: ?3→ ?3which is applied

to the subject image, Is(r), to obtain the spatially normalized

or warped image Iw(r) = Is(r + w(r)). The main objective of

most inter-subject image registration algorithms is to find a

displacement field w such that the warped image Iw(r) is as

‘similar’aspossibletoatemplateimage,It(r).Foragivenpair

of subject and template images Isand It, algorithms mainly

differ in their approach to modeling and estimation of w.

In the SPM99 software package (Friston et al., 1995), the

displacement field w is modeled by a finite orthogonal series

withtrigonometricbasisfunctions.Thealgorithmcomputesa

displacement field by estimating the coefficients of the series

usinganiterativelinearizedleast-squaresapproach.Intheau-

tomated image registration (AIR) software package (Woods

et al., 1998), the displacement field is modeled as a poly-

nomial, and the algorithm computes the displacement field

by estimating the polynomial coefficients using non-linear

least-squares optimization. Other methods of inter-subject

registrationmodelthedisplacementfieldasthedisplacement

field in an elastic object (Bajcsy and Kovaˇ ciˇ c, 1989) or a vis-

cousfluid(Christensenetal.,1997;ChristensenandJohnson,

2001) reacting to internal forces proportional to ‘image mis-

match’ between template and subject volumes. These meth-

ods are governed by partial differential equations that model

the physical phenomenon. In several other methods, the dis-

placementfieldsareestimatedasnon-parametricvectorfields

subject to regularity constraints (Collins et al., 1995; Kjems

et al., 1999; Kosugi et al., 1993).

Although many methods have been proposed for spa-

tial normalization, there are few studies comparing the per-

formance of various algorithms on a common set of real

MRI data. At least two important questions can be raised:

(1) how do the algorithms compare in terms of their abil-

ity to reduce anatomic differences between subjects? And

(2) how does image registration accuracy impact the final

analysis results (e.g., activation maps in fMRI)? The present

paper is concerned with the first question. The latter ques-

tion has been previously addressed primarily in the context

of positron emission tomography (PET) functional imaging

studies (Crivello et al., 2002; Kjems et al., 1999; Senda et

al., 1998). Overall, little difference has been found between

the functional activation maps obtained by processing PET

activationdatausingdifferentinter-subjectregistrationmeth-

ods.Crivelloetal.(2002)attributedthisfindingtothelimited

spatial resolution of PET and the inherent functional vari-

ability across subjects. However, this conclusion may not be

automatically extended to higher resolution fMRI studies or

group analysis of diffusion tensor imaging data. Recently,

Ardekanietal.(2004)studiedtheimpactofinter-subjectreg-

istration on group analysis of fMRI data. They showed that

increased accuracy of inter-subject registration in removing

anatomic variability between subjects results in significant

increases in the sensitivity of activation detection and the

reproducibility of activation maps. Thus, at least in fMRI

studies, it is important for researchers to understand the rel-

ative accuracy of inter-subject registration tools available to

them.

The first objective of the present paper was to present

details of our implementation of an inter-subject registra-

tionalgorithmincludedinourautomaticregistrationtoolbox

(ART). This algorithm is a non-parametric method similar to

those proposed by Collins et al. (1995), Kjems et al. (1999),

and Kosugi et al. (1993) with some new components. The

second objective was to quantitatively compare the perfor-

mance of three different inter-subject registration programs:

(1) SPM99; (2) AIR; and (3) ART. The third aim was to eval-

uate different independent criteria for assessment of regis-

tration accuracy. One measure is the post-registration spatial

dispersion of sets of homologous landmarks located manu-

ally on the images. Another criterion compares the sample

standard deviation (S.D.) of voxel intensity maps computed

from registered image sets. The precise mathematical defini-

tionsofthesemeasuresarepresentedinthefollowingsection.

2. Materials and methods

2.1. Implementation of ART inter-subject registration

Without loss of generality, we assume that the template

image It(r) and the subject image Is(r) are of the same matrix

andvoxeldimensions.Ifnot,thesubjectimageisresizedand

interpolated so that its voxel and matrix dimensions match

those of the template image. The objective of ART is to find

adisplacementvectorw(r)=(ux(r),uy(r),uz(r))ateachvoxel

r.Toachievethis,eachvoxelisvisitedinarasterscanfashion.

Let Ωrbe a neighborhood around and including voxel r. The

template feature vector at voxel r, denoted by ft

to be comprised of elements {It(v): v ∈ Ωr} of the template

image.Similarly,thesubjectfeaturevectoratvoxelr,denoted

by fs

r, is constructed from the voxel values {Is(v): v ∈ Ωr}

of the subject image. We define the similarity between two

arbitrary vectors w1and w2of the same dimension to be:

r, is defined

S(w1,w2) =

wT

?

1Hw2

wT

2Hw2

(1)

where H is an idempotent (H2= H) symmetric centering ma-

trix defined so that it removes the mean of the vector it pre-

multiplies. Note that Eq. (1) is asymmetric in the sense that

S(w1,w2) ?= S(w2,w1). This is of no practical significance

but will save some computation, as will become clear below.

Nextconsiderasearchneighborhood,ψr,aroundandinclud-

ingvoxelr.Letvoxelq∈ψrbethevoxelinthisneighborhood

at which the similarity measure S(ft

is:

r,fs

q) is maximum, that

S(ft

r,fs

q) = max

v∈ΨrS(ft

r,fs

v)(2)

Our initial estimate of the displacement field at voxel r is

w(r) = q − r. Note that Eq. (1) can be made symmetric by

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69

dividing the right-hand side by

however, change the voxel q at which S attains its maximum

and will only increase the computational burden.

Described above is the essence of the registration algo-

rithm implemented in ART. However, there still remain a

number of very important details that need to be addressed.

First, the registration algorithm can benefit from an initial

linear registration, either a six-parameter rigid-body, or a 12-

parameteraffinetransformation.InART,thereisanoptionfor

performinganinitialrigid-bodyregistrationusingthemethod

described by Ardekani et al. (1995).

Next is the issue of speed. The speed of the algorithm

depends on several factors including the number of image

voxels, size of the feature neighborhood Ωr, and size of the

search neighborhood ψr. In ART, the neighborhoods Ωrand

ψrare cubic and centered on voxel r. Initially, the search

neighborhood ψrmust be large enough to enable the algo-

rithm to find large scale displacements. The search neighbor-

hood is shrunk iteratively and the computations repeated for

findingfinerscaledisplacements.Inpractice,thisisachieved

throughamultiresolutionapproach.Inotherwords,theimage

is processed in multiple resolution levels using scale-space

theory. The scale-space of a 3D image I(r) is a 4D image

I(r, c) that satisfies the isotropic diffusion partial differential

equation:

?

wT

1Hw1. This does not,

∂I(r,c)

∂c

= ∇2I(r,c)(3)

withtheinitialconditionI(r,0)=I(r).ThesolutiontoEq.(3)

isthescale-spaceoftheimageandisgivenbyI(r,c)=Gc(r)*

I(r,0),whereGc(r)istheGaussianfunctionwithvariance2c

and‘*’denotestheconvolutionoperation(Lindeberg,1994).

Therefore, the initial image is low-pass filtered with Gaus-

sian kernels of various widths to form the scale-space. In

ART, the core registration process that is described above

is repeated in scale-space starting from coarse resolutions

towards the finest resolution at c = 0. At each step, the dis-

placement field found is applied to the subject image before

starting the next iteration. The number of iterations is an op-

tiontotheprogram.Atcoarseresolutionlevels,thealgorithm

is fast because: (1) the image is represented by fewer voxels

with a proportionally larger voxel size; and (2) the search

neighborhood ψrcan be large but comprised of few voxels

because of the larger voxel size. In order to use the displace-

ment field obtained at a lower resolution level as the starting

point for the next stage, the field components (ux, uy, uz)

need to be interpolated to match the voxel size at the higher

resolution level. In the present method, this is achieved by

using a fast digital filter implementation of the cubic spline

interpolation method (Unser, 1999). Overall, the multires-

olution approach improves the speed and robustness of the

algorithm.

An additional strategy for increasing the computational

efficiency of the algorithm was implemented by computing

the template image gradient L2norm, ?∇It(r)?, at the high-

est resolution level and only updating the displacement field

in those voxels where the gradient norm is in a certain up-

per percentile of the gradient magnitude histogram of the

template image. The percentile level can be specified as an

optional argument to the ART program. This is only done

at the iteration corresponding to the finest resolution level

that is the most computationally intensive iteration. The phi-

losophy behind this approach is that voxels with low spatial

derivatives ?∇It(r)? are located in featureless ‘planes’ of the

imageandcontainlittleinformationforguidingthealgorithm

and may even result in errors. The gradient vector ∇It(r) is

calculated by approximating the template image using cu-

bic splines (Unser, 1999) enabling us to easily compute the

necessary partial derivatives.

The next point to consider when implementing the algo-

rithm is the regularization of the displacement field. Intu-

itively speaking, regularization is necessary to ensure that

points that are close to each other in the subject image Is(r)

remain close in the warped image Iw(r). Kjems et al. (1999)

reviewed several methods of displacement field regulariza-

tion. In the present paper, we use simple Gaussian low-pass

filteringofthedisplacementfieldthatisobtainedattheendof

each iteration in the multiresolution algorithm. This method

was also applied by Kosugi et al. (1993) and has worked well

in our experiments.

Another very important issue that needs to be addressed

when solving for the displacement field w = (ux, uy,uz) is

that the algorithm must ensure that the resulting non-linear

transformation is a homeomorphism, that is, a continuous

mapping between two spaces that has an inverse which is

also continuous. Since at each multiresolution iteration, the

displacement field is interpolated using a cubic spline fit, we

can easily compute the partial derivatives of the displace-

ment field components (ux, uy,uz) with respect to the x, y,

and z spatial coordinates using the cubic spline coefficients.

This allows us to compute the Jacobian determinant of the

deformation field r + w(r) at every voxel. We ensure that

the Jacobian determinant is strictly positive at every voxel.

This, together with the fact that the displacement field is kept

to zero at all air voxels surrounding the head, can be shown

to be a necessary and sufficient condition for the transfor-

mation to be homeomorphic (Kaplan, 1973). If the require-

ment of a positive Jacobian everywhere in the image is not

met, we incrementally increase the width of the smoothing

Gaussian kernel and repeat the procedure until the condition

is met. Smoothing is guaranteed to have the desired effect

because at the limit of infinite width smoothing kernel, the

displacement field w(r) approaches a constant and, there-

fore, the Jacobian determinant of the deformation r + w(r)

approaches 1.

Finally,anadvantageofmethodssuchasAIRandSPM99

that represent the displacement fields in terms of basis func-

tions is that the displacement fields can be represented and

stored very efficiently using only a few parameters corre-

sponding to the coefficients of the basis functions. We take

advantage of this fact by approximating the components

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of the displacement fields (ux, uy, uz) by a truncated

Fourier–Legendre series as follows:

u(r) =

M

?

n,m,q=0

cnmqPn(x)Pm(y)Pq(z) (4)

where Pn denotes a Legendre polynomial of degree n

(Kaplan, 1973). The coefficients cnmq of the series are

efficiently computed using the orthogonality property of

Legendre polynomials. The coefficients are stored and can

be recalled later to synthesize the displacement field.

2.2. MRI scans

Three dimensional magnetization prepared rapid acquisi-

tion gradient echo (MP-RAGE) volumetric MRI scans were

conducted on 17 healthy individuals (eight males, nine fe-

males, mean (S.D.) age = 31 (8.85) years) using a 3.0 Tesla

SurreyMedicalImagingSystems(SMIS)scanner.Theacqui-

sitionparameterswere:matrixsize=256×256×128;voxel

size=0.976mm×0.976mm×1.3mm;α=18◦;TE=4ms;

TI = 1100ms; and TR = 3000ms. The data were part of a

larger fMRI study approved by the local Institutional Review

Board. Informed consent was obtained from all subjects.

2.3. Preprocessing

Theextracranialregionswereautomaticallydeletedfrom

the 3D MRI volumes using the brain extraction tool (BET)

software (Smith, 2002). In cases where BET did not com-

pletely remove the non-brain regions, manual editing was

performed using the MEDx software package (Sensor Sys-

tems, Inc., Sterling, Virginia).

2.4. Registration

The seventeen subjects were ranked according to the vol-

umeoftheirintra-cranialcontent.TheMRIscanofthesubject

withthemedianintra-cranialvolumewasselectedasthetem-

plate image set. The remaining 16 subjects were registered

to the template volume using the nonlinear fifth order poly-

nomial registration algorithm of AIR software package, the

spatial normalization algorithm of SPM99, and the nonlin-

ear image registration algorithm in ART. Thus, we obtained

48 spatially normalized volumes (16 for each algorithm). In

all cases, the registered volumes were obtained using linear

interpolation.

Implementation of inter-subject registration in ART was

described above. Algorithms used in AIR and SPM99 are

summarized by Friston et al. (1995) and Woods et al. (1998),

respectively. Both AIR and SPM99 use the least-squared im-

agedifferencecostfunctionasameasureofregistrationaccu-

racy while ART uses the cross-correlation criterion given in

Eq. (1). The fifth order polynomial registration of AIR soft-

ware has 168 parameters. The degrees of freedom used when

applying the SPM99 software was the default of 7 × 8 × 7

= 392 basis functions. The effective degrees of freedom in

ART can be considered to be (M + 1)3, where M is the order

of the truncated Fourier–Legendre series given in Eq. (4). In

the present paper, M = 14, therefore, the degrees of freedom

of ART was 3375.

2.5. Dispersion of homologous landmarks

post-registration

LetL={qi}(i=1,2,...,N)representasetofNlandmarks

identified on each of N = 16 original images before registra-

tion. After spatial normalization, each point is mapped to a

new location riresulting in a new set of points L?= {ri}.

A measure of dispersion of this set can be defined as the

root mean square distance from the mean landmark position

within set L?given by:

CL?=

?

?

?

?1

N

N

?

i=1

?ri− r?2

(5)

Twenty landmarks on each of the 16 original unregistered

imagevolumesweremanuallylocatedbyanoperatortrained

inneuroanatomy.Theselandmarksincludedtheleftandright

frontal poles, the left and right temporal poles, the superior

aspect of the anterior commissure (AC), the superior aspect

of the posterior commissure (PC), the most anterior point of

the corpus callosum (CC), the most posterior point of the

CC, the left and right frontal horns, the left and right occip-

ital poles, right and left anterior and posterior aspects of the

putamen,rightandleftanterioraspectofthecaudatenucleus,

and the right and left inferior aspect of the lateral extension

of the fourth ventricle. Landmarks were located using soft-

ware written in IDL (Research Systems, Inc., Boulder, Col-

orado). Thus, we obtained coordinates for the 20 different

landmarks in each of the 16 volumes. Following landmark

selection, the 16 original volumes were warped using the de-

formation fields obtained from AIR, SPM99, and ART pro-

grams.Thus,weobtain48deformedimagevolumes.Thenew

locations of each of the original 20 landmarks were located

on the 48 spatially normalized volumes. The dispersion of

each set of homologous landmarks was calculated according

toEq.(5),resultingina20×3(landmarks×methods)table,

which was subsequently analyzed using a variety of statisti-

cal tests. It should be emphasized that only one set of land-

marks are manually located on each subject’s original image

volume.

2.6. Sample standard deviation maps

Let the N registered volumes obtained by using a given

algorithm be represented by sets of voxel intensities {vij},

where i = 1, 2, ..., N is the subject index, j = 1, 2, ..., V

is the voxel index, and V is the total number of voxels in

a selected subset of image voxels. Then at each voxel j, a

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B.A. Ardekani et al. / Journal of Neuroscience Methods 142 (2005) 67–76

71

sample standard deviation S.D.jmay be computed as:

S.D.j=

?

?

?

?

N

?

i=1

(vij− ¯ vj)2

N − 1

(6)

where ¯ vjis the mean voxel intensity at voxel j in the N vol-

umes. Let two different methods be denoted by ‘A’ and ‘B’

with their corresponding voxelwise sample standard devia-

tions as S.D.Ajand S.D.Bj. The sample S.D.-map calculated

from a set of registered volumes reflects the degree of suc-

cessoftheregistrationalgorithminreducingtheinter-subject

anatomicalvariability.Underthenullhypothesisthatthetwo

methods have equal registration ability, each algorithm is ex-

pected to have a smaller S.D. in about half of the voxels.

This hypothesis can be tested using a sign test. Let s be a

random variable representing the number of voxels out of V

with S.D.Aj< S.D.Bj. The probability that s > s0is given by:

Pr(s > s0) = 1 −

s0

?

s=0

V!

s!(V − s)!(0.5)V

(7)

This probability measure can be used to test the null hy-

pothesis that two algorithms reduce anatomical variability to

the same extent.

3. Results and discussion

The 16 MP-RAGE volumes were registered to the tem-

plate volume using ART, AIR, and SPM99, resulting in a

total of 48 spatially normalized volumes (16 per method).

The 16 registered volumes obtained from applying each al-

gorithm were averaged. Selected slices from the resulting

three average volumes are shown in Fig. 1. Qualitatively, it

can be clearly seen that the average registered volume cor-

responding to ART (first column) has higher resolution than

those corresponding to AIR (second column) and SPM99

(third column). The gyral patterns can be more clearly iden-

tified in the average images processed by ART. Fig. 2 shows

the S.D.-maps corresponding to the averages in Fig. 1. These

mapsaredisplayedusingthesamegray-levelwindowsothat

their intensity can be directly compared. Qualitatively, it can

be seen that ART has lower variance in general, particularly

in regions around the ventricles. It is also noted that the three

methods have more difficulty in registering the parietal lobe

region between subjects as compared to other cortical re-

gions. Visually, there does not appear to be a significant dif-

ference between the AIR (second column) and SPM99 (third

column) S.D.-maps.

Quantitative comparisons were conducted using the S.D.-

maps. One thousand voxels (V = 1000) were randomly se-

lected across the volume, while ensuring that no two voxels

wereneighbors.Neighborhooddefinitionwasbasedoneight-

connectively, that is, voxels that share at least a vertex were

considered neighbors. The scatter plots for the three compar-

isons are shown in Fig. 3. In these plots, the scattered points

Table 1

Post-registration dispersion of landmarks (mm), with landmarks placed be-

fore registration

Landmark Method

ARTAIRSPM99

Frontal Pole—L

Frontal Pole—R

Temporal Pole—L

Temporal Pole—R

Anterior Commissure

Posterior Commissure

Corpus Callosum—A

Corpus Callosum—P

Frontal Horn—L

Frontal Horn—R

Occipital Pole—L

Occipital Pole—R

Putamen—R A

Putamen—R P

Putamen—L A

Putamen—L P

Caudate Nucl.—R A

Caudate Nucl.—L A

Lat. 4th Ven.—R I

Lat. 4th Ven.—L I

2.64

2.48

2.41

2.88

1.06

1.35

1.77

1.85

1.69

1.93

2.49

2.34

1.98

2.22

1.65

1.76

1.91

2.38

1.09

1.26

5.37

4.94

3.31

3.78

1.20

1.73

1.58

2.28

1.78

1.52

3.70

3.99

2.07

2.42

2.04

2.09

1.81

1.98

1.22

1.31

3.55

2.72

2.60

3.74

1.63

2.07

1.65

2.04

1.67

1.62

2.94

2.75

1.91

1.92

1.91

2.09

1.72

2.46

1.50

1.55

Mean

S.D.

Note: L, left; R, right; A, anterior; P, posterior; I, inferior; Lat. 4th Ven.,

lateral extension of the 4th ventricle.

1.96

0.52

2.51

1.24

2.20

0.66

lie mainly below the y = x line, which indicates advantage of

the method plotted as the ordinate. When comparing AIR to

ART using this approach, in 715 voxels S.D.ART< S.D.AIR

(P ≈ 0; two-tailed). When comparing SPM99 to ART, in 761

voxelsS.D.ART<S.D.SPM(P≈0;two-tailed).Bothresultsin-

dicate that the images registered using ART are significantly

less variable that those obtained using either SPM99 or AIR.

When comparing SPM99 to AIR, in 553 voxels S.D.AIR<

S.D.SPM(P = 0.0007; two-tailed). Therefore, the variance in

images registered by AIR is significantly less than the vari-

ance in images registered using SPM99. However, one must

be careful when interpreting this latter result. The reason is

that the AIR program automatically scales the images in a

way that tends to reduce the variance. Therefore, we cannot

rely on this method for quantitative comparison of AIR. In

contrast, SPM99 and ART do not change the image intensity

and only apply spatial deformation to the original image.

The dispersionofhomologous

registration is shown in Table 1. The values for ART

in the first column are mostly lower than those of AIR and

SPM. Paired t-tests were applied to assess the statistical

significance of the differences in registration accuracy.

Comparison of ART and SPM99 yielded t = −3.07 (P

= 0.006), meaning that the dispersions were significantly

smaller in ART as compared to SPM99. For ART versus

AIR, t = −2.83 (P = 0.011), again indicating greater

accuracy of ART over AIR. Comparing AIR and SPM99

we found t = 1.87 (P = 0.077) indicating no significant

difference. It can be seen that the dispersion of homologous

landmarkspost-

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Fig. 1. Selected slices from the average of 16 volumes registered using ART (first column), AIR (second column), and SPM99 (third column). The images

obtainedbyaveragingthevolumesregisteredusingARTclearlyhaveahigherresolutionindicatingthatagreaterreductionofinter-subjectanatomicalvariability

is achieved by ART as compared to AIR or SPM99.

landmarks post-registration is less sensitive than S.D.-maps

in indicating differences between algorithms. But it should

be noted that the S.D.-maps are quite sensitive to any

changes in image intensities that an algorithm may apply.

For example, since AIR applies an arbitrary scaling factor

to the images, the S.D.-maps of AIR cannot be directly

compared with those of SPM99 and ART. Interpolation

methods also significantly affect this measure and it must

be ensured that the same interpolation method is used in

reconstructing the spatially normalized images obtained

from different algorithms, otherwise the S.D.-maps cannot

be used to compare the accuracy of the methods.

The dispersions ofhomologouslandmarkspost-

registration can been considered to be due to two factors.

Firstly, it can be due to ‘errors’ by the operator in selecting

the landmarks. Secondly, it can be due to inability of the

algorithm to accurately match the landmarks together. Our

objective in using this criterion is to quantify and compare

the latter factor between different registration methods.

The presence of the first factor, however, diminishes the

sensitivity of this approach. To increase the sensitivity,

we must reduce the landmark selection error as much as

possible. One approach is to identify the landmarks after

the images have been registered (Grachev et al., 1999). It

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73

Fig. 2. Voxelwise image standard deviation maps of the slices shown in Fig. 1.

has been our experience that landmarks can be placed more

consistently post-registration. However, the drawback is that

the number of landmarks that have to be placed manually

increase by a factor of M, where M is the number of methods

being compared. For example, if we are comparing M

methods using Q landmarks on data from N subject, we only

need to place Q × N landmarks if the landmarks are placed

before image registration, as compared to having to place Q

× N × M landmarks after registration. We also applied this

second method and found that indeed the sensitivity of the

comparisonincreasesdramatically.Theresultingdispersions

are shown in Table 2. Paired t-tests were applied, yielding

values of t = −8.05 (P < 10−4) for ART versus SPM, and t

= −8.32 (P < 10−4) for ART versus AIR, indicating that the

differences between ART and each of the other programs

is significant. Comparing AIR and SPM we found t = 0.45

(P ≈ 0.66) indicating no significant difference. It can be

seen that placement of landmarks after registration generally

reduces the dispersion measures and makes this criterion

significantly more sensitive to the differences between

registration methods.

Many of the adjustable parameters of the ART algorithm

can be provided as optional inputs to the program. In the

results presented in this paper, we used the following param-

eters: (1) the order of the Fourier–Legendre series M was 14;

and (2) we used four levels of resolution starting with voxels

sizes that were 8, 4, 2, and 1 times the original voxel size.

The variance parameter c for the Gaussian kernel in I(r, c)

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B.A. Ardekani et al. / Journal of Neuroscience Methods 142 (2005) 67–76

Fig. 3. Scatter plots of pairs of image standard deviation values measured at 1000 randomly selected voxels comparing: (a) ART vs. AIR, (b) ART vs. SPM,

and (c) AIR vs. SPM. A greater number of points below the line y = x indicates a greater reduction of inter-subject anatomical variability achieved by the

registration method labeled as the ordinate.

= Gc(r) * I(r, 0) was computed using the method described

by Ardekani et al. (1997). (3) The feature and search neigh-

borhoods Ωrand ψrwere both cubic with size 5 voxels × 5

voxels × 5 voxels and remained fixed for all resolution lev-

els. (4) At the highest resolution level (c = 0), only 50% of

the displacement field voxels were updated, those voxels, for

which the L2norm of the intensity gradient ?∇It(r)? was in

the upper 50th percentile.

It was noted that the different algorithms completed the

registration task at noticeably different speeds. To examine

this, a test was run in which one set of data was analyzed on

the same machine (800MHz Pentium III Dell Precision 420

SuSE 7.3 Linux workstation) three times using the different

algorithms. SPM99 was most noticeably the fastest, com-

pleting the task in 4min and 22s. The ART package com-

pleted the task in 23min and 56s, while the AIR package

took 32min and 49s to complete the task. Although the pro-

cessing time for every image in this study was not recorded

(duetothevarianceofprocessingpowerondifferentcomput-

ers used to process the data), this example is consistent with

the observed trend in processing times (with SPM99 finish-

ing significantly faster than the other two packages, and AIR

taking the most processing time).

It was also observed that the AIR package has difficulty

dealing with situations where the template and subject im-

ages have a significant initial misalignment. In such circum-

stances, the output image produced by AIR was highly dis-

torted while the other two algorithms seemed able to account

for the misalignment and functioned normally. In such cases,

the AIR algorithm was aided by an initial rigid-body regis-

tration of the template and subject images. In addition, the

removal of non-brain regions before starting the registration

processwascriticaltothesuccessoftheAIRalgorithm.With-

out this preprocessing step, AIR simply failed in most cases.

ART and SPM99 were more robust in this respect, but still

benefited from the initial brain extraction step using BET

(Smith, 2002).

The results of this paper showed that ART is significantly

more accurate as compared to SPM99 and AIR in the regis-

tration of multiple high-resolution anatomical images to the

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B.A. Ardekani et al. / Journal of Neuroscience Methods 142 (2005) 67–76

75

Table 2

Post-registrationdispersionoflandmarks(mm),withlandmarksplacedafter

registration

Landmark Method

ARTAIRSPM99

Frontal Pole—L

Frontal Pole—R

Temporal Pole—L

Temporal Pole—R

Anterior Commissure

Posterior Commissure

Corpus Callosum—A

Corpus Callosum—P

Frontal Horn—L

Frontal Horn—R

Occipital Pole—L

Occipital Pole—R

Putamen—R A

Putamen—R P

Putamen—L A

Putamen—L P

Caudate Nucl.—R A

Caudate Nucl.—L A

Lat. 4th Ven.—R I

Lat. 4th Ven.—L I

1.548

1.686

1.998

2.540

0.699

0.834

1.009

1.233

1.482

1.546

1.369

1.565

1.714

1.410

1.663

1.291

1.796

1.209

0.817

1.067

2.062

2.542

3.533

3.621

1.332

1.426

1.848

2.014

1.552

2.042

1.845

2.222

2.273

2.394

2.155

2.281

1.837

1.692

1.425

1.317

1.972

2.683

3.442

2.928

2.065

1.997

1.963

2.025

1.584

1.822

1.885

2.393

2.126

2.231

2.044

2.124

1.971

1.763

1.373

1.611

Mean

S.D.

Note: L, left; R, right; A, anterior; P, posterior; I, inferior; Lat. 4th Ven.,

lateral extension of the 4th ventricle.

1.424

0.437

2.071

0.628

2.100

0.474

same template. This result should not be surprising given

the fact that ART enjoys a much higher degree of freedom

(∼3375 d.f.) as compared to the default SPM99 method (392

d.f.)andthe5thdegreepolynomialmethodofAIR(168d.f.).

Thus, the greater ability of ART in reducing anatomical vari-

ability between subjects can be attributed to its greater de-

grees of freedom, since the essence of the algorithms used

by the three methods are to a large extent similar. However,

the particular non-parametric implementation of ART allows

incorporating a much larger number of degrees of freedom

whilekeepingthecomputationalcostmanageable.Ofcourse,

in SPM99 and AIR, it is possible to use a larger number of

basis functions than what is used in this paper. If our above

assertion is correct, using a larger number of basis functions

inthesealgorithmsshouldimprovetheregistrationresults.In

fact,inapreliminarystudy,weusedasetof11×13×11ba-

sisfunctionsinSPM99andfoundthattheregistrationresults

improved over our current SPM99 method, which uses 7 ×

8 × 7 basis functions but did not reach the quality of ART

registration. However, the nature of the optimization prob-

lem in SPM99 and AIR is such that increasing the number of

degrees excessively increases the computation cost.

Another issue that arises is whether it is desirable to make

all images “look alike”. This is certainly a goal for fMRI and

voxelwise diffusion tensor analyses, where analysis of ho-

mologousvoxelsiscriticalininferringgroupdifferences,but

isexplicitlynotthegoalofvoxelbasedmorphometry(VBM)

(AshburnerandFriston,2000).Inthislatterapproach,images

arematcheduptoacertainpointandthenresidualdifferences

are taken to represent critical comparisons between groups.

Nonetheless, even in these cases the accuracy of registration

is critical, as the VBM algorithm entails an interaction be-

tween the spatial normalization and voxelwise comparisons

(Bookstein, 2001).

Finally, as pointed out in Section 1, an important question

is whether the degree of improvement in registration accu-

racy, as shown in Tables 1 and 2 and Fig. 1, is such that there

is an appreciable impact on the final group analysis results of

MRI data. Ardekani et al. (2004) addressed this question in

the case of fMRI group analysis and showed that increased

accuracy of inter-subject registration in removing anatomic

variabilitybetweensubjectsresultsinsignificantincreasesin

the sensitivity of activation detection and the reproducibility

of activation maps. The results suggest that at least in the

visual oddball stimulation paradigm studied in that paper, a

significant portion of variability in activation across subjects

was due to anatomical variability as opposed to variability

in functional anatomy, and this variability was reduced when

the quality of inter-subject registration improved.

4. Conclusions

Details of implementation of a non-parametric method

(ART) for estimating displacement fields for inter-subject

registration of high-resolution volumetric MRI images were

presented. The ability of ART in reducing anatomical vari-

ability between subjects was compared to the registration

accuracy of two other popular registration programs: AIR

and SPM99. Homologous landmark sets manually identified

on the images before registration were significantly less dis-

persed in ART after registration, as compared to their dis-

persion after registration by AIR or SPM99. There was no

significant difference between AIR and SPM99 with respect

to this measure. It was found that the post-registration spa-

tial dispersion of homologous landmarks measure becomes

significantly more sensitive to the differences between algo-

rithms when the landmarks are placed after image registra-

tion, as opposed to before. Sets of images registered by ART

also showed significantly less voxelwise intensity variance

as compared to the other two methods. Overall, results indi-

catethatnon-parametricinter-subjectregistrationalgorithms

with high degrees of freedom are able to reduce inter-subject

anatomic variability to a greater extent as compared to lower

dimensional parametric methods such as AIR and SPM99,

while keeping the computational cost within acceptable lim-

its.

Acknowledgement

This research was supported by Biomedical Engineering

Research Grant RG-00-0350 from the Whitaker Foundation

to BAA. MJH gratefully acknowledges the support of NIH

R01 MH64783 and a NARSAD Young Investigator award.

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