Biomedical Engineering Reference
In-Depth Information
constrained by the skull. However, there are many other applications where
nonrigid transformations are required to describe the spatial relationship
between images adequately. For example, in intrasubject registration non-
rigid transformations are required to accommodate any tissue deformation
due to interventions or changes over time. Similarly, in intersubject registra-
tion, nonrigid transformations are often required to accommodate the sub-
stantial anatomical variability across individuals.
In contrast to rigid registration techniques, nonrigid registration tech-
niques are still the subject of significant ongoing research activity. The goal of
this chapter is to give an overview of the different nonrigid registration tech-
niques and the current state of the art in this fast-moving area. A recent over-
view of hierarchical approaches to nonrigid registration can be found in
Lester and Arridge.
1
13.2
Techniques
Any nonrigid registration technique can be described by three components: a
transformation which relates the target and source images (images
as
defined in Chapter 3), a similarity measure which measures the similarity
between target and source image, and an optimization which determines the opti-
mal transformation parameters as a function of the similarity measure. The
main difference between rigid and nonrigid registration techniques is the
nature of the transformation. The goal of rigid registration is to find the six
degrees of freedom (three rotations and three translations) of transformation
A
and
B
T
) which maps any point in the source image into the cor-
responding point in the target image. An extension of this model is the affine
transformation model which has twelve degrees of freedom and allows for
scaling and shearing:
(
x
,
y
,
z
)
(
x
,
y
,
z
a
00
a
01
a
02
a
03
a
10
a
11
a
12
a
13
a
20
a
21
a
22
a
23
0001
x
x
y
z
1
y
T
x
,
y
,
z
(
)
(13.1)
z
1
These affine or linear transformation models are often used for the registra-
tion of images for which some of the image acquisition parameters are unknown,
such as voxel sizes or gantry tilt,
2,3
or to accommodate a limited amount of shape
4
By adding additional degrees of freedom (DOF), such a linear
transformation model can be extended to nonlinear transformation models.
Figure 13.1 shows some examples of the different types of transformations com-
monly used for image registration.
variability.
