Point cloud, surface mesh, and (binary) image registration are different problems. You also need to mention that you are looking into deformable registration.
Since your inputs are already images, and among the three, binary image registration is the easiest problem, I would recommend registering distance maps computed from the binary images. This is already very fast and you can make it faster by utilizing GPU (by computing the registration metric on the GPU).
For reference, see this related discussion on the VTK forum: https://discourse.vtk.org/t/vtk-point-set-registration/2599/6