Biomedical Engineering Reference
In-Depth Information
should be able to cope with the resulting changes in intensity and contrast
between the target and the images registered to this target.
A more sophisticated choice of target is to take some kind of average image
from across the time series. For example, re-registering ten images (selected
from equally spaced points along the time series) to the first, taking the aver-
age spatial “position” of these ten images, creating an average image in this
position, and then reregistering all ten to this average image results in a
motion correction target which is in the “average position” for the whole time
series and contains representative “average intensities.” This has the benefit
of minimizing the average “distance” by which all images are transformed
(and therefore minimizing interpolation related blurring—see below).
8.2.2
Interpolation
After the registration phase has determined the transformation parameters
required to correct for head motion, it is then necessary to transform the
images to this new, consistent orientation. This requires (subvoxel) interpola-
tion of the intensities; a critical step in motion correction, since the intensities
contain the information regarding physiological response. Therefore, it is
important to ensure that the least amount of artifact is introduced into the
data by the interpolation stage. Consequently, choice of interpolation method
is significant and, for the reasons described in Section 3.5 of Chapter 3, simple
methods such as nearest neighbor or trilinear are not optimal, as they intro-
duce unwanted blurring (spatial autocorrelation) into the data.
In contrast, the interpolation used within the initial transformation-finding
phase is not particularly critical, as usually the gross features such as brain
background boundaries principally determine the transformations. Since the
existence of these features is robust to the amount of blurring introduced by
interpolation, the transformation parameters found are not usually very sen-
sitive to the interpolation method chosen.
There are many different potential choices for interpolation, as discussed in
Chapter 3. This also includes methods such as the use of multiple shears
applied in Fourier space,
2
which are only valid for the small rigid-body trans-
formations typical of motion correction. However, at present there is no con-
sensus as to which method is best.
One related implementational issue worth mentioning is how areas outside
the image are treated. When estimating motion parameters, this “data” out-
side the image should be treated as nonexistent and not of zero intensity;
otherwise, the estimated parameters will be biased. However, when the end
slices are of interest (i.e., they contain brain) the final applied transformation
will be sensitive to the choice of outside values used by the interpolation
method. It is sensible in this circumstance to “pad” (to a small extent) with a
copy of the end slice. If this is not done, the slightest out-of-slice motion
(including any rotation) results in unnecessary loss of information in the end
slices. With padding, this problem is substantially reduced.
