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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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