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Introduction

he work invested in two separate yet related fields calls for a strategic merger that 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 can benefit the other and to what extent.

The broad field of image registration encircles some important techniques that academical and clinical research groups have an interest in [1,2,3,4,5]. An evident rise can be shown in the number of papers published in the field, medical context being a noticeable focus. I turns out that registration is in many respects valid to biomedical 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 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 MR) respectively.

The main problem that registration is set to overcome is the alignment of several images to with the aim of achieving better correspondence across the entire set of images to be dealt with. This correspondence can be evaluated by similarity measures, examples of which are given later. With suitable overlap of some given object¹ within a group of images, segmentation, analysis and comparison are significantly more constructive; these are usually impossible guarantee in the absence of that overlap. Correspondence is not always simple to achieve algebraically since the object inspected or the aperture² may change position and angle over time or acquisition venue. 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 to understand the changing structures that are present in an image. Therefore, the correspondence expectations, as well as the permissible degree of freedom, must not be excessively rigid³. It is important to ensure that the chosen analysis mechanism caters for some level of flexibility to enable a robust 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 element. Simple alignment is therefore not necessarily sufficient to give good a solution - that is - plausible correspondence. As explained in Section 3 of this report, registration methods cab be further broken down into different types, 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 some informative relations between the distinct images.

Image registration is believed to be capable of positively affecting the performance of statistical models and vice versa. More compact models of variability can be constructed if registration procedures are applied to its training data (confer [6] for more details on learning and training). This is obvious because registration clearly minimises the variability seen. The later sections explain in greater depth how the two techniques come together and how one can be incorporated in the other, whereas the earlier sections attempt to explain and show the commonality between the two.

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

Quite broadly and even wishfully, upcoming research intends to bring together all 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). Arguably , it would not be too optimistic to state that model fitting, shape analysis, non-rigid registration, feature detection and segmentation can and should be put under one single framework. In this way, more compact and powerful representation of images can be used - images can be described by the parameters of the non-rigid transforms that ought to generate them. This is in fact what makes this unification of several methods quite appealing when compared with stand-alone active appearance models.