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BACKGROUND

E xample plots are included in this section, which attempts to illustrate the general aims and add some context. We are investigating plots which depict a certain measure $m$ versus the extent of mean pixel displacement. These plots typically reflect on some measure of 'goodness' as data is degraded.

Mean pixel displacement is closely-related to the degree of mis-registration in the set of images under investigation. In simple terms, as we move rightwards in the plots, the overlap (or correspondence) among the images is made worse. We expect our measure $m$ to be able to detect these overlap changes, preferably with a linear response too, which implies robustness. Below are 2 blended figures which practically visualise that. In the former case, overlap between label in the images is used as our measure, whereas model-based measures are used in the latter.

It is worth noticing that all curves are sampled at 8 separate points. Each such point corresponds to one particular value of mean pixel displacement. The value measured, namely $m$, is calculated over 10 instantiations of an image set, from which the average has been derived. This repeatability factor will later enable us to argue that the methods work consistently, so no handpicking or fluke are involved.

We are interested in two separate 'sources' of error (uncertainty):

1. Error that is associated with the instantiation process. As the number of instantiation is finite, our measures are susceptible to some fluctuation. We absolutely must account for bias, which is due to the random instantiation process. In our circumstance, we have 10 instantiations to consider.
2. Error that is associated with the calculation of the value $m$. To obtain the values which we seek, a set of synthetic images is generated. Since that set is limited in term of its size, corresponding error bars need to be bound.