Biomedical Engineering Reference
In-Depth Information
ensemble of 305 MRI data sets was averaged to create the second-pass mean
MRI brain known as MNI305,
36,38,39
which has been made publicly available as
a standard stereotaxic registration target within the MNI_Autoreg package*
and within the statistical parametric mapping (SPM**) package developed at
the Wellcome Department of Cognitive Neurology.
14.2.2
The Spatial Mapping Function
The
is used to transform coordinates from the native
image volume into the reference space. There are a number of desirable char-
acteristics for such a function. It should be continuous, unique, invertible,
simple to compute, and straightforward to apply. Generally, mapping functions
are divided into linear and nonlinear models.
The simplest case of linear spatial normalization involves a rigid-body
transformation (translations and rotations only, no change in size or shape)
and is normally applicable only for within-subject alignment. In order to
account for differing head sizes, a nonrigid component of scaling can be
included while maintaining shape invariance. A single scaling factor is used
in the classical Procrustes mapping
spatial mapping function
40
(other Procrustes mappings are des-
cribed in Chapter 3), whereas the more general use of three scaling factors
yields a total of nine parameters (three translations, three rotations, and three
scaling factors). These linear models are continuous, unique, invertible, sim-
ple to compute, and easy to apply when resampling data for comparisons. A
variety of methods exist to compute the linear spatial mapping based on
landmark matching,
36,41, 42
43-45
surface matching,
or volume density match-
28,46,47
ing.
See Chapters 2 and 3 for more detailed information on registration
algorithms, in addition to the excellent reviews of van den Elsen,
48
49
Maintz,
50
or Hawkes.
The strict piecewise linear mapping of Talairach has been implemented by
Lemoine
51
using manual identification of the AC and PC landmark and by
52
Verard
with automated landmark localization. This mapping method is rela-
tively straightforward to compute, and it is easy to apply. However, it is not con-
tinuous and is only piecewise invertible. Most groups have moved to a nonlinear
spatial mapping function to account for anatomical variability by allowing more
degrees of freedom in the mapping function. Many of the nonrigid registration
algorithms that are appropriate for intersubject registration (or spatial nor-
malization) are described in Chapter 13.
Among the different nonlinear mapping methods, that developed by
Friston et al.
53,54
is constrained to consist of a weighted linear combination of
smooth basis warps that are defined by discrete cosine transforms. A similar
mapping technique has been developed by Woods
55,56
except that polynomial
basis functions are used. In these two methods a limited number of parame-
ters (say,
3
) is used to define the mapping. Bookstein has promoted a
method to interpolate the 3D mapping between sparse landmarks (such as
n
10
*
http:
www.bic.mni.mcgill.ca
software
mni_autoreg
**
http:
www.fil.ion.ucl.ac.uk
spm
