Biomedical Engineering Reference
In-Depth Information
Mutual information
I
(
A
,
B
) was proposed for intermodality medical image
registration by several researchers [2, 3, 11] . The formula to compute mutual
information is:
P
AB
(
a
,
b
)
P
A
(
a
)
·
P
B
(
b
)
I
(
A
,
B
)
=
P
AB
(
a
,
b
) log
a
b
where
P
A
(
a
),
P
B
(
b
) denote the marginal probability distributions of the two
random variables,
A
and
B
, and
P
AB
(
a, b
) is their joint probability.
The formulation of normalized mutual information (NMI) as described by
Studholme
et al.
[17] is used:
H
(
A
)
+
H
(
B
)
H
(
A
,
B
)
NMI
(
A
,
B
)
=
where
H
(
A
)
=−
P
A
(
a
) log
P
A
(
a
)
a
and
H
(
A
,
B
)
=−
P
AB
(
a
,
b
) log
P
AB
(
a
,
b
)
a
b
H
(
A
) and
H
(
B
) are the entropies of
A
and
B
, and
H
(
A
,
B
) is their joint entropy.
NMI, devised to overcome the sensitivity of MI to change in image overlap, has
been shown to be more robust than standard mutual information [17]. Image
registration using NMI is performed in the following manner:
1. Take one of the two input images as floating image, the other as reference
image.
2. Choose starting parameters for the transformation.
3. Apply the transformation to the floating image. Evaluate the NMI between
reference image and transformed floating image.
4. Stop if convergence is achieved. If not, choose a new set of parameters,
repeat steps 3 and 4.
When the registration parameters (three translations and three rotations)
are applied to the floating image, the algorithm iteratively transforms the float-
ing image with respect to the reference image while making the NMI measure
calculated from the voxel intensities optimal. While all samples are taken at
grid points of the floating image, their transformed position will, in general, not
