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Non-rigid registration (NRR) of both pairs and groups of images is used widely as a basis for medical image analysis. Applications include structural analysis, atlas matching and change analysis [1]. The problem is highly under-constrained and many different algorithms have been proposed.
The aim of non-rigid registration is to find automatically a meaningful, dense correspondence between a pair (pairwise registration), or across a group (groupwise registration) of images. A typical algorithm consists of a representation of the deformation fields that encode the spatial variation between images, an objective function that quantifies the degree of misregistration, and a method of optimising the objective function. As different algorithms tend to produce different results when applied to the same set of images [2], there is a need for methods to evaluate the results of NRR.
Various methods of evaluation have been proposed [3,4,6,7]. One approach is to construct artificial test data, applying known deformations to real or synthetic images. This allows algorithms to be evaluated by attempting to recover the applied deformations, but does not allow the results of NRR to be assessed 'in-line' 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. We have used one such method in this paper 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 the need for ground truth.
The approach we have adopted is based on the observation that, given a set of non-rigidly registered images - however obtained - it is possible to construct a statistical model of appearance that takes account of both the shape and texture variation across the set. Models of this type have been used extensively as a basis for image interpretation by synthesis [9,10]. We build models by exploiting the dense correspondence across the set of images established by the NRR. The key idea that underpins our approach is that, if the correspondence is poor, the resulting appearance model will be unsatisfactory. This observation allows us to transform the problem of evaluating non-rigid registration into one of evaluating the model generated from the result of registration.
The structure of the paper is as follows. We first provide a brief description of the background to both the assessment of registration, and the construction of appearance models, explaining in more detail the link between the two. We then define two quantitative measures of model (and thus registration) quality, and discuss their implementation. The behavior of these measures is investigated by measuring the effect of deliberately perturbing the registration of an initially registered set of images The results are compared to those obtained using a 'gold standard' method of assessment, based on measuring the overlap of manually annotated ground truth. The results demonstrate that our new measures are closely correlated with those based on ground-truth, and that the proposed approach is actually more sensitive to misregistration. Finally, we use the measures we have developed to compare various NRR algorithms applied to the registration of sets of 2D MR brain images, demonstrating the superiority of fully groupwise registration over a repeated pairwise approach.