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!!!Evaluation of Appearance Models of the Brain

!!Abstract

Appearance models are an applicable approach to the
analysis of anatomical variability. They are able to
distinguish between groups, e.g. normal and diseased,
as a model encapsulates the properties of a group from
which it was derived. The construction of such models
is closely-related to the task of registration and they
require the correspondence, which registration is able
to obtain.

We developed a framework which evaluates appearance
models, based on the statistics of large sets of
images. The framework is capable of distinguishing
between good models of the brain and worse ones.
Furthermore, it provides a method of validating models.
It does so by measuring how well a model and its data
fit together.

Two measures are defined which reflect on the quality
of a model. The first of these -- specificity --
approximates the level to which data generated by the
model fits data from which the model was constructed.
The complementary measure -- generalisation -- is able
to quantify 'distance' between data from which the
model was constructed and model-generated data.

Results show that as models degrade in quality, their
specificity and generalisation ability rise, as
expected. The algorithms are used to compare models of
the brains, which were built automatically by
independent approaches of registration. This greatly
helps in identifying better model construction
algorithms, which are analogous to registration algorithms.

!!1 Introduction

A powerful method for the modelling of anatomy was
introduced by Edwards et al. [Edwards] and it is known as
appearance models -- a natural successor to shape
models [Cootes]. This method requires a large enough set of
data, which is representative of a population and
ideally spans its full variability. Appearance models
are able to learn what characterises inter-subject
changes and determine the prominence of the main
characteristics. Hence, it is able to identify changes
and derive a model that encapsulates change -- all in a
data-driven manner.

Non-rigid image registration is ubiquitously used as
the basis for analysis of medical images. The results
of registration can be used for structural analysis,
atlas matching, and analysis of change. Methods for
obtaining registration are are well-established and
quite uniform. The goal is achieved by warping pairs of
images so that they appear more similar. The similarity
leads to overlap, which allows corresponding structures
to be identified. This problem is complementary to that
of modelling groups of images. A statistical model of a
group of images needs dense correspondence to be
defined across the group; non-rigid registration
provides exactly that.

Since the emergence of appearance models, attempts have
been made to reproduce and improve it. To name a few
such efforts, Stegmann [Stegmann] built 4-dimensional cardiac
models and Reuckert et al. [Rueckert] derived statistical
deformation models from several registrations of the
brain. Models have been built in a variety of ways, but
what is yet lacked is the ability to compare them. It
becomes clear from experience that attempts to
distinguish between them by eyesight is hopeless. More
recently, appearance models were built automatically
using piece-wise affine registration [IPMI - YET TO
ADD]. Evaluation of models in this particular case
enables evaluation of registration algorithms.

The idea of evaluating models is not unexampled. Davies
et al. [Davies] explored the evaluation of shape models and
ultimately developed a robust framework. This paper
outlines a principled approach to the evaluation of
appearance models, which is a challenging task since
their complexity is very high. The approach is shown to
be reliable in evaluation of brain models (FOOTER: Examples from non-medical domains are beyond the remit
of this paper, but they have been very successful.) and it is then used to learn about registration
algorithms, from which appearance models have been derived.
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