Exploratory Experiments in 2-D NRR

I performed many additional experiments with 8 brain images, 357x357 pixels in size each. What follows is a summary and some conclusions that I reached based on qualitative results, not quantitative.

As part of the experiments which investigate optimisation through minimisation of the objective function, I conducted a small survey to compare 3 methods. Figure $[*]$ visually (as opposed to quantitatively) compares the level of refinement reached using the different optimisation methods that I studied. While the imaged brains may show similar results, the time taken to arrive at these results varied significantly. Powell was particularly slow compared to a simple downhill optimisation, which was used in the majority of cases and applied at different scales^5.8. In the experiments which this section will show from now on, the only optimiser used was therefore downhill.

**Figure:** Deciding on an optimiser. A small comparison of different registration optimisation methods. This figure shows the results in the form of chequerboard images or pairs, each corresponding to results of a different optimisation method. The differences are minimal, but the time required to reach these solutions varies significantly depending on the optimisation.

The results showed that improvements were first made around the skull and the ventricles. At the later stages, some improvements were also made to CSF. The duration of this experiment was under an hour on my personal computer.

In the next experiment, the rigid and affine transformation stages remained as before. At the stages of NRR (the later stages), there was a gradual increase from 1 to 5 knot-points; that is a total of 5 iterations. Another 5 iterations were run in the same manner but at a finer scale. The duration of the experiment was 15 minutes for those 20 iterations in total. The results were not as pleasing as in the previous case. CSF in particular was still fuzzy, especially once compared across images. This is not surprising considering the fact that 10 iterations of NRR were used here, compared with 90 in the previous case.

In another experiment, the optimisation regime remained the same for the sake of consistency. To find out how an increase in resolution affects change, the following stages of the NRR were carried out in turn. Here is an evaluation of each of the stages (as judged by the results through visual assessment only):

It was of course taken into consideration that bigger changes will be made at the start.