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Image Registration

As medical imaging methods have developed rapidly over the past decade, the ability to discover clinically significant patterns in large quantities of data has become important. One class of problems involves comparing groups of images. There are two common cases:

1. Intra-subject studies involve analyzing a series of images taken from the same subject and comparing them. These images may be acquired over a period of time, as means of tracking the progression of abnormalities, e.g. []. Alternatively, they may be taken at roughly the same time with different image modalities, elucidating different properties of the tissue being imaged.
2. Inter-subject studies involve a comparison between two (or more) groups of subjects. In a medical context, this makes possible the discovery of symptoms for a certain groups of patients, observing how they deviate from `normals'.

Fundamental to this is the need to compare images. Non-rigid registration (NRR) is commonly used to address problems of this kind [,,]. NRR algorithms warp two or more images into the same frame of reference so that equivalent structures align. The problem is highly under-constrained and many different algorithms have been proposed for solving it with no consensus as to which particular algorithm should be used.

The aim of NRR is to find, automatically, a meaningful dense correspondence between a pair (pairwise registration), or across a group of images (groupwise registration). A typical algorithm requires a representation of the deformation fields that encode the spatial variation between images, an objective function that quantifies the degree of similarity between the registered images, and a method of optimising the objective function wrt the deformation fields.

Since different algorithms generally produce different results when applied to the same set of images [], there is a clear need for methods that evaluate the results of NRR. This way, the differences between methods can be investigated and - for example - quality control (QC) can be exercised on a case-by-case basis in clinical studies.

Various methods of evaluation have been proposed [,,] for assessment of the results of NRR. One approach is to construct artificial test data and then apply known deformations to real or synthetic images. This allows algorithms to be evaluated by attempting to recover the applied deformations, but this does not allow the results of NRR to be assessed for QC purposes in real applications. An alternative approach is to provide anatomical ground truth for the images to be registered, then measure the degree of anatomical correspondence following NRR. One such method is used in this thesis as a gold standard, but the need for expert annotation of the images renders the approach too time-consuming and subjective for routine application. These problems motivate the search for a method of evaluation that can be used routinely in real applications, without requiring ground truth. This can be achieved by exploring the relationship between NRR and statistical model building.