Biomedical Engineering Reference
In-Depth Information
modification proposed by Studholme
et al.
[72], normalized mutual information
(NMI), has been found to be slightly more robust
H
R
+
H
F
H
RF
.
S
NMI
=
(11.3)
There are many different implementations of both MI and NMI, using different
numerical methods to estimate the image entropies. While some use continuous
methods such as Parzen windowing [77, 80], others estimate the entropies from
discrete two-dimensional histograms [36, 71]. The latter techniques are more
easily implemented and more common.
11.3.2
Rigid Registration
The first iteration of intersubject registration, such as registration of an image
to an atlas, usually aims at correcting for positioning, orientation, and global
size differences between the individual images. Consequently, we initially apply
a 9 degree-of-freedom (DOF) affine registration algorithm that performs appro-
priate translation, rotation, and scaling. A technique described by Studholme
et
al.
[71] has been found to produce highly accurate (rigid) transformation in an
independent, blinded evaluation study [82]. The algorithm optimizes the NMI
similarity measure described above using a simple but robust multiresolution
optimization strategy with hierarchically resampled images. For details about
our particular implementation of this algorithm the interested reader is referred
to [48, 49, 50, 62].
11.3.3
Non-Rigid Registration
There is typically considerable inter-individual variability in the shapes of
anatomical structures in the brains of humans and animals. Figure 11.3 illustrates
this for the microscopy images of bee brains that we are using to demonstrate the
methods in this chapter. For MR images of human brains, Fig. 11.4 provides an
analogous illustration. Therefore, in order to be effective, any registration-based
segmentation method requires a registration algorithm that can compensate not
only for different pose and size, but also for inter-individual shape differences
between raw image and atlas (i.e., a non-rigid registration algorithm).
Many different non-rigid registration methods have been published. Some
of these, such as methods based on optical flow [73] and most methods using
elastic [38, 9] or fluid models [10, 32], typically require both images to be from the
