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Re-optimising with Perturbations

Following the search with 8mm cubed voxels, a progressive refinement is required, starting with 4mm voxel size.

Since the 8mm solution may not lie inside the 4mm basin of attraction, a 7 DOF optimisation is run at 4mm on the optimised solution found in 8mm. Furthermore, several perturbations of the un-optimised 8mm solution are also treated similarly. These perturbations attempt to correct for typical registration errors, with the perturbations being: $\pm \frac{1}{2} \Delta \theta_{fine}$ in each rotation angle and $\pm \Delta s , \pm 2 \Delta s$ in scale, giving a total of 10 different perturbations, where $\Delta \theta$ and $\Delta s$ are the step sizes evaluated for the 8mm resolution. It has been found that this simple, relatively inexpensive procedure, corrects for the majority of mis-registrations.

It has also been found that, on occasion, the relative rankings of corresponding minima change between sub-samplings. This is especially true when the cost values are very similar for two competing minima. Therefore, the global minimum for the 4mm case may not correspond to the global minimum for the 8mm case. To correct for this change in minima ranking, the best 3 solutions from the 8mm case are used, rather than just the single best solution. This has been found, empirically, to compensate for the next major case of mis-registration.

Overall, therefore, a total of 33 optimisations with 7 DOF are performed at the 4mm resolution. This acts as a local search about each of the most promising local minima found by the previous (8mm) stage. The time taken to complete this stage is typically less than 10 minutes but it is a critical stage in eliminating many common mis-registrations.


next up previous
Next: Refining the Transformation Up: Initial Search Previous: Initial Search
Mark Jenkinson
2000-05-10