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Description of Task

The continuous research work invested in two separate yet related fields calls for a strategic merger which takes advantage of the best of both. These fields are statistical models of appearance and non-rigid registration whose wide-spread use consequently made them independently usable and powerful. As they deal with problems that have a great deal in common, attempts have been made, and still are being made, to discover how one field is able benefit the other and to what capacity.

The broad field of image registration includes some important techniques that academic and clinical research groups have reasonable interest in [,,,,]. An evident rise can be shown in the number of papers published in the field, medical context being a noticeable focus. It turns out that registration is in many respects highly-applicable to polymorphous bio-medical data as later discussions stress.

Registration is concerned with the assembly of data which is taken either at different points in time or at some arbitrary time instances where changes due to the passage of time can be ignored. Registration sees the most use in scenarios where multiple different objects or subjects^1.1 are being scanned or where the acquisition method varies. In the case of medical imaging, registration is commonly mentioned in one of three distinct circumstances: intra-subject registration, inter-subject registration and multi-modality imaging. This corresponds to the investigation of changes in one specific subject over time, the investigation and comparison between more than one subject and the fusion of data acquired from different modalities (e.g. CT, PET and MRI^1.2) respectively. Most typically, however, only a single subject is involved.

The main problem that registration is determined to overcome is the alignment of several images with the aim of achieving better correspondence across the entire set of images to be dealt with. This quality of correspondence can be evaluated by similarity measures, examples of which are given later ( in Chapter ). With suitable overlap of some given object^1.3 within a group of images, segmentation, analysis and comparison become significantly more straight-forward; these are almost impossible to guarantee in the absence of that overlap. Correspondence is not always simple to achieve algebraically since the object inspected or the aperture^1.4 may change position and angle over time or acquisition site. In reality, additional unwanted effects such as noise, distortion and change in form must be carefully accounted for. In some real-world applications, biological being an ideal exemplar, variability must be handled sensibly in order to understand the changing structures (as in soft tissue in the brain) that are present in an image. Therefore, the correspondence, as well as the permissible degree of freedom, must not be excessively rigid^1.5. It is important to ensure that the chosen analysis mechanism caters for some level of flexibility to enable a rigourous registration process that is immune to high levels of misalignment.

The problem of registration would have been rather simple if it were not for the innate changes that are an integral part of any biological entity, e.g. brain [], spine, etc. Simple alignment is therefore not necessarily sufficient to give good a solution - that is - plausible correspondence. As explained in Chapter cha:Non-rigid-Registration of this report, registration methods can be further broken down into different classes, but their aims remain the same in essence. The methods aspire to find some correlation between two or more images, in which case a new entity is obtained that expresses the informative relations between the distinct images.

Image registration is said to be capable of positively affecting the performance of statistical models; possibly this holds the other way around too. More compact (and hence preferable) models of variability can be constructed if registration procedures are applied to its training data (see [] for more details on learning and training and Section on models). This is obvious because registration clearly minimises the witnessed variability, that variability simply being change or difference in the data. The earlier parts of this report, and in particular the next two chapters, attempt to explain and show the commonality between the two techniques, whereas the latter parts explain in greater depth how the two techniques might (and possibly should) come together. It also insinuates that as soon as one can be incorporated within the other, detrimental issues that recur can finally be resolved.

In some previous work, the formation of appearance models, based on registered images, provided a fair indication of how desirable a prior process of registration was. However, the process was slow and therefrom emerged a need to find better ways of using the two techniques in a cunning and hence more efficient manner.

Quite broadly and even wishfully, some current research activities intend to bring together different phases of the handling of an image, from the moment when images are registered to the point where these are coupled with an appropriate statistical model (and even get segmented and measured). Research that this document describes can hopefully form a small part of such a large-scale goal. Arguably^1.6, it would not be venturous to state that model fitting, shape analysis, non-rigid registration, feature detection and segmentation can and should be put under one single framework. At least a few of these might become inseparable in the future.

In this way, by unifying image analysis phases, more compact and powerful representation of images can be used - images can be described by the parameters of non-rigid transforms that ought to generate them from a basal mean image. This is in fact what makes this unification of several methods quite appealing when compared with stand-alone active appearance models where construction is subjective and time-consuming.