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Introduction
Geometric registration and motion correction are important stages
in the analysis of functional brain imaging studies.
Consequently, it is important that these stages perform robustly and
accurately. Furthermore, for large imaging studies it is desirable
that they be fully automated.
There has been a considerable amount of research into registration and
motion correction of brain images, and many different methods have
been proposed [14]. Most methods in common usage
are based on the mathematical framework of optimising an
intensity-based cost function. However, although much work has
concentrated on how the choice of cost function affects registration
performance, there has been far less examination of the effect of the
optimisation method. Moreover, when optimisation methods are
discussed, global methods are often ignored and local methods compared
purely on the basis of speed [4].
One of the most common and serious problems for registration methods
is the presence of local minima in the cost function. These cause
local optimisation methods to ``get stuck'' and hence to fail to find
the desired the global minimum. Most registration methods attempt to
solve this problem by incorporating a local optimisation strategy
within a multi-resolution framework. Such a multi-resolution
framework, which typically involves starting with low resolution
images (containing only gross features) and working progressively
through to higher resolutions, aims to avoid the local minima
``traps''. As we show later, this simple multi-resolution approach is
not always sufficient for avoiding local minima, and that by using
more sophisticated optimisation methods, the chances of becoming
``trapped'' in these local minima can be substantially reduced.
Two types of local minima commonly occur for the cost functions used
in image registration: large scale basins and small scale dips. The
first type, the large scale basin, is responsible for large
mis-registrations since the local minimum is often far from the global
minimum. The second type, small scale dips, can cause the
optimisation to get stuck at any stage and so are responsible for
large mis-registrations at low resolutions and for small
mis-registrations at high resolutions.
We propose two methods for dealing with the local minima problem.
These are: cost function apodization, which reduces or eliminates
small scale dips; and a hybrid global-local optimisation technique
which utilises prior knowledge about brain registration
to create an optimisation technique that combines the speed
of local optimisation with the robustness of global optimisation.
The following sections of this paper are: background theory, methods
(including both cost function apodization and the hybrid optimisation
method), results and discussion. The results section contains a
number of experiments on real, whole brain images which demonstrate the
effectiveness of the registration in two different settings: (1)
structural image registration (inter-modal/inter-subject) of an
anatomical image to a standard template; and (2) functional image
motion correction (intra-modal/intra-subject) which registers each
image in a time-series to a particular example image from that
time-series. The first case is examined using a robustness study (as
accuracy is hard to define for inter-subject registration, and robustness is a more
important issue in this context), while the
second case is examined using an accuracy study (as, in this context, it is accuracy
that is more important). In each case real
brain image data is used. Comparisons with some commonly used methods
are also included (in both cases) which demonstrate the superior
robustness and accuracy which can be obtained using this approach.
Next: Materials
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Peter Bannister
2002-05-03