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OVERLAP-BASED ASSESSMENT

Overlap-based assessment relies on labels (anatomical mark-up in our case), embedded in a group of images. The principal idea is that of computing overlap between corresponding labels in image sets which have been registered. Such labels, which are transformed along with the images that embody them, often reflect rather well on the correspondence among the images themselves. Thus, labels can infer registration quality in the images are less prone to error in the case of coarse anomalies.

For each displacement value, we take the error associated with overlap, which has been accumulated over all labels. To get a value that is representative of all 10 instantiations, we take the average over the 10 instantiations. This accounts for the error (uncertainty) in the measure, which in this case is label overlap.

Another error we must consider is due to varying values of the measured overlap. Each instantiation gives us a slightly different value. We derive the standard deviation of the overlap quantities for each displacement value and divide by $\sqrt{N-1}=9$, i.e. divide by 3 to get the errors.

The way these two errors should 'blended' is somewhat ill-comprehended. There are arguments to suggest that the two errors are entirely independent, but contrary arguments have been raised as well.

The evaluation of the error bars is a very crucial detail as it eventually leads to the derivation of sensitivity plots. Correct error bars will be a pre-requisite for impartial comparison between NRR assessment methods.

To associate a standard deviation with the overall overlap we assume that each pair of registered images represents a sample from a normal distribution. Therefore N pairwise comparisons gives a standard deviation associated with the N intersections and unions, accumulated over all the labels. The standard deviation and standard error for the total overlap are then estimated using standard error propagation formulas. The figure below depicts the effect of degrading the quality or registration on the overlap-based assessment method.