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Overlap-based Assessment

The overlap-based approach involves measuring the overlap between of anatomical annotations before and after registration. A good NRR algorithm will be capable of aligning similar image intensities - in particular these which indicate the location of anatomical structures. Alignment of image intensities leads to better overlap between anatomical structures, so the two are closely-correlated.

Similar approaches involve measurement of the mis-registration of anatomical regions of significance [10,12], and the overlap between anatomically equivalent regions obtained using segmentation. This process is either manual or semi-automatic [12,19]. Although these methods cover a general range of applications, they are labour-intensive andare often prone to errors. They also rely one's ability to faithfully extract anatomical structures from the image intensities alone.

This paper explores one such method, which assesses registration using the spatial overlap. The overlap is defined using Tanimoto's formulation of corresponding regions in the registered images. The correspondence is defined by labels of distinct image regions (in this case brain tissue classes), produced by manual mark-up of the original images (ground-truth labels). A correctly registered image set will exhibit high relative overlap between corresponding brain structures in different images and, in the opposite case - low overlap with non-corresponding structures. A generalised overlap measure [6] is used to compute a single figure of merit for the overall overlap of all labels over all subjects.

$$O=\frac{\begin{array}{c} \\ \sum\\ pairs,k\end{array}\begin... ...{array}{c} \\ \sum\\ voxels,i\end{array}MAX(A_{kli},B_{kli})}$$ (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. This means that large labels contribute more to the overall measure. We have also consider 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. We define label complexity rather arbitrarily as the mean absolute voxel intensity gradient in the label.

More formulations of overlap, other than Tanimoto's, have also been investigated. Their results were shown to be less accurate and they are omitted in the interest of brevity. While our main focus remains assessment that requires no ground truth, the approach above provides a good reference to compare against for validity with respect to ground-truth annotation.