Algorithms for deformable image registration
Like Paul suggested, you may want to ask this question at the signal processing stackexchange as well. They may be able to provide you with more information. I am at best a talented amateur in the field.

Let's start with the biggest problem in image registration: there is no catch-all algorithm that just works for everything. Results are heavily dependent on image modality, site and also what you wish to use it for. 

Luckily for you, brain mri is a fairly standard application. I would have a look at elastix, which is ITK based and used quite a bit at my department. It also has a nice database of parameter files for different applications, including several for brain mri. A quick glance reveals that most use B-spline registration for the brain.

I have mainly used registration for lung, where my personal experience was that Demons performed best. Note that Demons is NOT one single algorithm, although it is often presented as such. Rather it's a plethora of variations of the same basic idea.

Finally, some commercial software has registration algorithms that perform very well for specific applications. If you're associated with a hospital, ask researchers at your radiology or oncology department if they have access to something that works well.