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Part 1 - Atlases and Deformable models
Much attention has been given to the problem of atlas matching of
medical images. The problem can be stated as follows. Given a
standard
image dataset (either from one individual or a population
average),
which has labels identifying the structures of interest, find the
transformation which best matches that dataset to a particular
individual. We may then apply the labels from our atlas to the
individual. The transformation clearly meeds to be a non-rigid
warping
of the atlas. Deformable models and correlation methods have
been
proposed to solve this problem
1,2.
We concentrate instead on the problem of matching multiple images
from
the same patient where the tissue is seen to have deformed. Since
the
process of tissue deformation is physical, a physical model seems
appropriate. Our simplified model is summarised in the next
section
and will be discussed in detail in future presentations.
The model we propose has three simple components - rigid,
deformable
and fluid. The rigid components do not move. The deformable
regions
obey some energy constraints, in this case behaving as a network
of
spring-like elements. The fluid regions have no energy associated
with
their deformation and effectively move freely. The model moves
under the
influence of landmarks chosen in each of the images and provides
a best
fit of the model to the landmark data.
An example set of springs is shown in Figure 1. The blue regions
are
rigid and do not move. The green sections are stretched by the
landmarks. The region in the centre is considered fluid and
deforms
freely.
a) 
b) 
Figure 1. An example spring deformation a)
relaxed,
and b) deformed. Regions are rigid (blue) deformable (green) or
fluid (black).
This model can be applied to registration where tissue has
deformed if the
tissues representing bone, soft tissue and fluid can be
identified. The
segmentation process will be considered in the next section.
A physical model such as the one described above requires a
segmentation of an individual's scan which separates the tissues
based
on their physical properties. A further requirement is that the
boundary conditions between different tissues be described. In
the VHD,
for example, there are regions where the outer brain surface and
the
inner surface of the skull appear in adjacent voxels. The
boundary
condition between these voxels must be labelled as unconnected.
In
other regions where soft tissue is attached to bone it must be
labelled
accordingly.
An atlas based segmentation is ideally suited to this sort of
problem.
In the atlas all the tissues must be painstakingly identified
along
with their respective boundary conditions. A transformation
between
this atlas and the individual needs to be established. This could
perhaps be achieved using one of the algorithms already mentioned
1,2
and would
provide all the necessary labels to create a model for the
individual.
This model may then be used to match different scans of the
patient or
register preoperative scans to the patient in-theatre. This two
stage
registration approach is shown schematically in Figure 3.
Figure 3. Two stage registration approach - Atlas match
provides
labels for the individual model, then this model is used to
register the individual's scans.
There are several reasons why the VHD is a particularly
appropriate
dataset with which to create such an atlas. The high resolution
nature
of the data means that small regions of connecting tissue
relevant to
the model will not be overlooked. Also, the cryosections provide
good
contrast data about both bone and soft tissue in the same
dataset,
whereas the same cannot be said of CT or MRI.
Next: VHD as Source of Test Data
Up: Title and abstract
Previous: Introduction