Image Processing Techniques in Emission Tomography - Correction Techniques in Emission Tomography - page 132

(d) ResultT opt (a) ReferenceR (b) TemplateT (c) Grid

FIGURE 7.10: The template image T in (b) is registered non-linearly to
the reference image R in (a) using FAIR [43]. The resulting transformation
is expressed by the grid in (c). T is resampled at the grid points yielding the
result T opt in (d).

Figure 7.10 gives an example of registration in cardiac-gated PET of a
mouse. The template image T showing the heart during the systole is regis-
tered to the reference image R showing the heart during the diastole using
a non-parametric transformation model. The similarity is measured with the
sum of squared differences (see Definition 5). The heart contraction during
the cardiac cycle can be clearly seen in these images. The task is to find an
optimal transformation (grid) such that the warped image T opt is as similar
to R as possible. T opt results from interpolating T (see Section 7.3) at the
irregular transformation grid.

7.4.1.1 Nature of transformation

Transformations can be roughly divided into parametric and non-
parametric ones. While parametric transformations cover rigid, ane or spline
(free-form) deformations, non-parametric transformations denote deforma-
tions that are independent for each voxel. Rigid and ane models are appro-
priate mainly for intrasubject registration tasks while non-parametric models
apply better to intersubject or atlas registration. Nevertheless, there are also
many cases where non-parametric (parametric) models are used in intrasub-
ject (intersubject) studies.
In most registration setups the transformation applies to the whole image
domain. These setups are referred to as global approaches. But in some cases
the transformation only applies to local parts of the image [57].

Parametric registration methods
In parametric image registration the transformation is given in terms of a
parametric function, which is defined by a certain number of parameters. For
example, the 3D rigid transformation parameter vector has six entries: three
for describing the rotation around the three coordinate axes and three for
translation. Hence, the task in parametric registration is to find the parameter