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Assessing Non-Rigid Registration

One approach to assessing the results of NRR is to create a set of test images by taking original images and applying known spatial deformations. Evaluation involves comparing the deformation fields recovered by NRR to those known to have been applied [15,16]. This approach can be used to test a given NRR method 'off-line', but cannot be used to evaluate the results when the method is applied to real data as part of a registration-based analysis.

An alternative approach involves measuring the coincidence of anatomical annotations following registration. Variants of this approach include measuring the mis-registration of anatomical landmarks [8,10], and the overlap between anatomically equivalent regions obtained using manual or semi-automatic segmentation [10,15]. These methods are of general application, but are labour-intensive and error prone.

This paper will use a generalised overlap-based approach to provide a 'gold standard' method of assessment. The method requires manual annotation of each image - providing an anatomical/tissue label for each voxel - and measures the overlap of corresponding labels following registration, using a generalisation of Tanimoto's overlap coefficient. Each label for a given image is represented using a binary image but, after warping and interpolation into a common reference frame based on the results of NRR, we obtain a set of fuzzy label images. These are combined in a generalised overlap score [4], which provides a single figure of merit aggregated over all labels and all images in the set:

$$\mathcal{O}=\frac{\begin{array}{c} \\ \sum\\ pairs,k\end{ar... ...{array}{c} \\ \sum\\ voxels,i\end{array}MAX(A_{kli},B_{kli})}$$ (1)

where $i$ indexes voxels in the registered images, $l$ indexes the label and $k$ indexes the two images under consideration. $A_{kli}$ and $B_{kli}$ represent voxel label values in a pair of registered images and are in the range [0, 1]. The $MIN()$ and $MAX()$ operators are standard results for the intersection and union of a fuzzy set. This generalised overlap measures the consistency with which each set of labels partitions the image volume. The parameter $\alpha_{l}$ affects the relative weighting of different labels. With $\alpha_{l}=1$, label contributions are implicitly volume weighted with respect to one another. We have also considered the cases where $\alpha_{l}$ weights for the inverse label volume (which makes the relative weighting of different labels equal), where $\alpha_{l}$ weights for the inverse label volume squared (which gives labels of smaller volume higher weighting) and where $\alpha_{l}$ weights for a measure of label complexity (which we define as the mean absolute voxel intensity gradient in the label).