Image Registration Methods in MRI - Advance Image Processing in Magnetic Resonance Imaging - page 203

Equation 22 becomes:

−
∑

N 1

S = S I (, I ) (7.24)

G i i + 1

i = 1

This is equivalent to performing the registration of each image in the sequence
in respect to the previous one. Both the methods are extensively used in image
sequence registration. Regarding the second approach, it is important to note that
two consecutive images in the sequence are often almost similar, so the registra-
tion algorithm can better correct the misalignment. On the other hand, an error
in the registration of one image pair will affect the alignment of the temporal
sequence.
A third approach often used in literature is to create a virtual reference image
as the mean of all images in the sequence and to perform the registration in
respect to the virtual image:

N

N

1

∑

∑

S = S I (,) I (7.25)

I = I

G r i

r i

N

i = 1

i = 1

All these simplified methods go far to guarantee a global optimum in the
registration. It has been empirically showed that the combination of these methods
can increase registration quality [33].
In some cases, the image sequence can be divided in groups of aligned images
with the presence of a misalignment along groups. As an example, in cardiac
perfusion MRI a subject was asked to hold his breath during examination, so that
we might have an initial image group with good alignment. When the contrast
medium is injected, a first subject movement will likely happen, starting a new
image group. A third group will start if the subject breaks the breath-hold state.
A second example is f MRI acquisitions, in which major subject movement is
related to paradigm changes.
In these cases, it may be preferable to perform a registration along qua-
sialigned groups followed by a registration along different groups (hierarchical
registration).

Figure 7.7 shows the main steps of the hierarchical registration algorithm:

the value of the similarity between all image pairs is calculated, then a hierarchical
tree, grouping images pairs with a high value of the similarity function. In the
example, four groups (G 1 , …, G 4 ) are identified at the low level of the hierarchy.
The algorithm performs the registration of all images inside each group. Groups
G 1 and G 2 are aligned, using a representative image extracted from each group
or two virtual images obtained averaging all images in each group. The resulting
group G 5 is registered with the G 3 group, and the obtained G 6 group is registered
with the G 4 group.