Biomedical Engineering Reference
In-Depth Information
list of methods but to present generic and up-to-date methods. The interested
reader will refer to [19, 60, 61, 87, 90, 91, 140, 143, 151] for a complete survey
on this subject. This section will therefore be restricted to an overview with
classification of non-rigid registration methods, more particularly applied to
non-rigid registration of brains of different subjects.
Methods can generally be classified according to the following criteria:
Features that will be matched. This includes both the dimension of the
data (classically from 2
D
to 4
D
) as well as the homologous structures that
are chosen for matching.
Transformation type. This includes the transformation domain: local or
global. A transformation is called “global” when the modification of one
parameter affects the entire image. This also includes the transformation
type (rigid, affine, projective and so on).
The similarity measure. The similarity models the interaction between the
data (features used for matching defined above) and the variables to be
estimated (parameters of the transformation for instance).
The regularization. The regularization can be implicit (regularized trans-
formation model for instance) or explicit (first-order regularization for
instance).
The optimization method. Once the registration problem has been formal-
ized, the optimization plays a crucial role in estimating the registration
variables.
We have chosen to divide non-rigid registration methods into two classes:
geometrical methods that are based on the extraction and matching of sparse
features; and photometric (or intensity-based) methods that exploit luminance
information directly.
8.2.2
Geometric Methods
The amount of data in a 3D MR image is enormous: it contains more than 10
million voxels. The computation of a dense deformation field is a tough problem:
more than 40
.
10
6
variables have to be estimated. This complexity has motivated
geometric methods: sparse anatomical features reduce the dimension of the
