Image Registration Methods in MRI - Advance Image Processing in Magnetic Resonance Imaging - page 186

the heart shape can occur due to poor EEG synchronization in cardiac MRI. In
practice, we can often suppose that the images to be registered will differ only
for a rigid transformation.
For 3-D rigid-body registration, the mapping of coordinates px y z = [ ]

T

A

into px = ′′′ [ y z ]

T

can be formulated as a matrix multiplication in homogeneous

B

coordinates:

cos βγ cos cos αγ αsin sin + sin βγ cos sin αγ αβγ sin − cos sin cos t x

x
y
z
1

′
′
′

x
y
z
1

− cos βγ sin co s αγ αβγ cos − sin sin sin sin αγ αβγ cos + cos sin sin t y

=

sin β − sin α cos β cos α cos β t z

1

0 0 0

(7.2)

where [ t , t , t ] are the translation vectors and [ α , β , γ ] are the rotation values

x y z

around the three axes.
Because digital images are sampled on a discrete grid, but generally maps

to continuous values, interpolation of intensities is required. The interpolation
process can affect the effectiveness of the registration, so that the choice of an
appropriate interpolation algorithm plays an important role in the development of
the registration procedure. This topic will be extensively covered in the following

T

text. The general registration algorithm between two images is shown in Figure 7.1 .

First, we define a reference image and a floating image, which is the image
to be registered in respect to the reference one. The similarity function between
the reference image and the floating one is evaluated. An optimization algorithm
is used in order to estimate the best transformation function (

) that maximizes
the similarity function; the estimate function is used to transform the floating
image. An interpolation operation is also required. If the result is satisfactory, the
procedure ends; if not, a new transformation function is evaluated, and a new
loop is executed. The key issues in the registration algorithm are the choice of
the similarity metric and the choice of the optimization algorithm. These issues
will be described in the following subsections.
Sometimes, the images involved in registration can be preprocessed in order
to improve the effectiveness of the registration algorithm. The most common pre-
processing step is defining a region of interests in images to exclude structures that
may negatively affect the registration process. Other preprocessing techniques con-
sist of image filtering to remove noise, correction for intensity inhomogeneities,
and image resampling to achieve the same spatial resolution in both images.

T

7.3 SIMILARITY METRICS

The similarity metric for image registration should satisfy some constraints. First,
similarity metrics must be robust; that is, they should converge to a global
maximum at the correct registration. The best registration can be in some cases