IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 21, NO. 5, MAY 2002
What is the Best Similarity Measure for Motion
Correction in fMRI Time Series?
L. Freire*, A. Roche, and J.-F. Mangin
It has been shown that the difference of squares
cost function used by standard realignment packages (SPM and
AIR) can lead to the detection of spurious activations, because the
motion parameter estimations are biased by the activated areas.
Therefore, this paper describes several experiments aiming at
selecting a better similarity measure to drive functional magnetic
resonance image registration. The behaviors of the Geman–Mc-
Clure (GM) estimator, of the correlation ratio, and of the mutual
information (MI) relative to activated areas are studied using
simulated time series and actual data stemming from a 3T magnet.
It is shown that these methods are more robust than the usual
difference of squares measure. The results suggest also that the
measures built from robust metrics like the GM estimator may
be the best choice, while MI is also an interesting solution. Some
more work, however, is required to compare the various robust
metrics proposed in the literature.
Artifact, fMRI, motion correction, robust regis-
tration, spurious activation.
OTION correction in functional magnetic resonance
imaging (fMRI) time series is usually performed
through the retrospective estimation of the subject’s motion
during the experiment. This motion is often modeled by a time
series of three–dimensional (3-D) rigid body transformations,
each transformation aligning one volume of the time series with
the reference volume. The retrospective approach amounts then
to the estimation of these transformations via the maximization
of a similarity measure. A number of different similarity mea-
sures have been proposed in the literature in order to perform
retrospective registration of 3-D data sets. Hence, a usual issue
for the design of a registration procedure is the choice of the
best similarity measure considering the characteristics of the
problem being addressed . This choice, indeed, may highly
influence the procedure robustness and accuracy. This paper is
dedicated to various experiments aiming at selecting the best
similarity measure for motion correction in fMRI time series.
Realignment of fMRI time-series is today considered as a re-
quired preprocessing step before analysis of functional activa-
Manuscript received November 9, 2001; revised February 25, 2002.
indicates corresponding author.
*L. Freire is with the Service Hospitalier Frédéric Joliot, CEA, 91401 Orsay,
France, Instituto de Biofísica e Engenharia Biomédica, FCUL, 1749-016
Lisboa, Portugal, and the Instituto de Medicina Nuclear, FML, 1649-028
Lisboa, Portugal (e-mail: firstname.lastname@example.org).
A. Roche is with the Epidaure project, INRIA, Sophia Antipolis, France and