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Overlap-Based Methods

An alternative approach is based on measuring the alignment [3,4], or overlap [4,6] of anatomical structures annotated by an expert, or obtained as a result of (semi-)automated segmentation. Manual annotation is expensive to obtain and prone to subjective error. Reliable automated or semi-automated segmentation is extremely difficult to achieve - indeed if it was available it would often obviate the need for NRR.

We have used an 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 [8] which provides a single figure of merit aggregated over all labels and all images in the set:

$$\mathcal{O} = \frac{ \sum\limits_{\mbox{\small pairs},k}\: \sum\l... ...labels},l}\alpha_{l} \sum\limits_{\mbox{\small voxels},i} MAX(A_{kli},B_{kli})}$$ (1)

where $i$ indexes voxels in the registered images, $l$ indexes the labels and $k$ indexes image pairs (all permutations are considered). $A_{kli}$ and $B_{kli}$ represent voxel label values for 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 fuzzy sets. 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. This means that large structures contribute more to the overall measure. We have also considered the cases where $\alpha_{l}$ weights labels by the inverse of their volume (which makes the relative weighting of different labels equal), where $\alpha_{l}$ weights labels by the inverse of their volume squared (which gives regions of smaller volume higher weighting), and where $\alpha_{l}$ weights labels by their complexity, which we define as the mean absolute voxel intensity gradient over the labelled region.

An overlap score based on a generalisation of the popular Dice Similarity Coefficient (DSC) would also be possible but, since DSC is related monotonically to the Tanimoto Coefficient (TC) by DSC = 2TC/(TC+1) [5] we have not considered this further.