Image Processing Reference
In-Depth Information
also discuss some optimization techniques, from the classical ones (i.e., simplex
and Powell methods) to the more advanced (i.e., genetic algorithms). Because
registration of image sequences is often needed in the MRI field, we cover exten-
sion of the standard registration procedures. Finally, we describe two examples of
the application of registration procedures to MRI data (fMRI images and cardiac
perfusion MRI images).
7.2
THE REGISTRATION PROBLEM
In the following, we assume that an image can have two or three dimensions.
Let
denote the spatial transformation that maps coordinates (spatial locations)
from one image or coordinate space to another image or coordinate space. Let
T
p
denote coordinate points (pixel locations) in images A and B, respec-
tively. The image registration problem is to determine
and
p
A
B
T
so that the mapping
Tp
:
→⇔
p
Tp
(
)
=
p
(7.1)
A
B
A
B
results in the best alignment of A and B. The domain where
T
is defined is named
the
of the registration problem. The function that defines the quality
factor for the alignment is named the
search space
similarity metric
or
registration metric
. The
algorithm used for the search of the function
T
that maximizes the chosen metric
is named the
.
In the most general case, two medical images may differ from another by any
amount of rotation about an axis, by any amount of translation in any direction,
may differ in scale, and nonrigid transformation can be present. Moreover, these
features may vary locally throughout the volumetric extent of the images. The nature
of the
search strategy
transformation characterizes the search space of the registration problem,
ranging from nonlinear transformation, with virtually infinite degrees of freedom,
to rigid registration with six degrees (for 3-D volumes) of freedom. Intermediate
cases are affine transformations, in which the images can be scaled and sheared.
It is important to note that MRI are codified in digital image format, typically
the Digital Imaging and Communications in Medicine (DICOM). The DICOM format
includes some information that can be useful for image registration, as the position
and the orientation of the image in respect to the acquisition device and in respect
to the patient (as well as the voxel size) so that a preliminary registration can be
performed using this geometrical data, reducing the image misalignment. In the
unimodal registration of MRI images, the absence of image scaling can be ensured
by the use of the same acquisition device with the same acquisition parameters.
Moreover, because the pixel dimension in both images is known from the acqui-
sition parameters, the scaling factor can be easily computed and image scaling
can be easily applied. The main sources of nonrigid distortions in MRI are due
to the subject's breathing during acquisition. These kinds of distortions affect
cardiovascular and abdominal MRI, whereas they are negligible in brain imaging.
Moreover, because heart movement is not rigid in nature, some deformation of
T
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