Biomedical Engineering Reference
In-Depth Information
on the type of interpolation used, hence the use of
rather than
T
as the
T
superscript.
Many of these voxel similarity measures involve analyzing level sets, or
isointensity sets, within the images. For a single image
A
, an isointensity
set with intensity value
a
is the set of voxels in
A
, such that:
{
x
A
A
A
x
()
a
}
(3.3)
a
Some algorithms do not work on isointensity sets corresponding to a sin-
gle intensity value but on isointensity sets corresponding to small groups,
or bins, of intensities. For example, a 12-bit image may have its intensities
grouped into 256 four-bit bins. We use
a
to mean either individual intensi-
ties or intensity bins, as appropriate.
It is important to remember that
is the isointensity set within all of image
a
A
. As stated above, for registration using voxel
similarity measures, we work within the overlap domain
that is within the domain
A
T
.
The level set
A
,
B
within this overlap domain is, of course, a function of
T
. To emphasize this
T
dependence, we define the isointensity set in image
A
with value
a
within
T
as:
A
,
B
a
T
T
{
x
A
A
,
B
A
x
()
a
}
(3.4)
is
always the image that we consider transformed, so the definition is slightly
different than for image
Similarly, we can consider an isointensity set in image
B
. Image
B
. We consider the isointensity set to be the set of
voxels in the overlap domain
A
T
B
T
A
,
B
that have intensity
b
in image
.
T
T
B
T
x
()
{
x
A
A
,
B
b
}
(3.5)
3.2.1
Image Field of View
For intrasubject registration, the object being studied is the same for both
images, but the domains
and
may be different in extent, and are always
A
B
different in position and
/
or orientation. The domain over which the transfor-
T
mation
is valid is
A
,
B
. This domain is, in general, smaller than either
or
T
A
. The latter point is impor-
tant and sometimes overlooked. It is true even if the images
, and also is a function of the transformation
T
B
A
and
B
have
identical fields of view, since any translation or rotation of image
B
with
respect to image
will alter the overlap domain. For registration algorithms
that make use of corresponding geometrical features, the difference in field
of view of images
A
can cause difficulties, as features identified in one
image may not be present in the second. The dependence of
A
and
B
T
is,
however, not especially important in these algorithms. For registration
algorithms that make use of image intensity values to iteratively determine
A
,
B
on
T
,
greater difficulties arise. The isointensity sets used by these algorithms are the
T
