Biomedical Engineering Reference
In-Depth Information
Two images involved in registration are called reference and floating images.
The floating image has undergone scaling, rotation, and translation to match the
reference image. In the mutual information image registration context, we treat
the voxel values
a
and
b
at corresponding points in two images that are to be
registered as random variables
A
and
B
. Mutual information measures the inter-
dependency between the reference image and floating image. We assume that the
mutual information of random variables
A
and
B
has a maximum value when two
images are registered (i.e., maximum interdependency). That is, the uncertainty
of one image given another image is minimized, and we have more confidence in
using one image to interpret another. Note that, the voxel values
a
and
b
are re-
lated by the registration transformation
T
. The mutual information registration
states that the images are registered under transformation
T
∗
for which
I
(
A
,
B
)
is maximal.
If both marginal pdfs are independent of the registration parameters (i.e., no
matter what
T
is, they would not change much), then mutual information maxi-
mization is reduced to minimization of joint entropy. If either pdf is independent
of the registration parameters, which is the case when one image geometrically
contains another image, maximization of mutual information is reduced to min-
imization of conditional entropy. However, if both images only partially overlap,
which is very likely during the optimization as we will see later, the overlap will
change as the transformation changes and both marginal entropies generally
depend on the transformation. Mutual information takes overlapping explicitly
into account.
Sometimes retinal images are not grayscale images. They have RGB color
channels. One has three options to handle this multichannel registration. (1)
Define the mutual information for each channel and maximize the sum of these
mutual information values. (2) Convert the color images to luminance images
and then register the converted images. (3) Pick a color channel and register this
channel and other two channels are presumably registered once that selected
channel has been registered. Since the green channel has the highest contrast,
it can be registered first if one chooses the third option.
In Fig. 4.1 we illustrate the procedures involved in the mutual information
maximization approach to image registration. In the following sections we
discuss what kind of transformation we pose, how to compute the mutual
information, how to update the transform and what is the criterion for optimal
transform, etc.
