Hello. I have some conceptual understanding of registration and very little of its math so I’m looking for a practical solution. Thank you in advance for any help offered.

Say I registered 3D image A to 3D image B in a 2-step process by first finding the best-fit affine transform and then a deformation field on top of that. Applying these two transforms (affine first then dense deformable as a composite transformation) will warp the whole of image A to the space of image B.

How do I use this composite transformation to now map an arbitrary subset of image A to that of image B? For example, how do I warp a 2D slice of image A to the space of image B? What if I just wanted to map a point (1D)?

One solution is to put that subset of points into the same 3D space of image A and then apply the transform as I would on a full image of A. I have tried this and it works as it should. However, that’s costly in terms of memory and, I suspect, computationally. How do I strictly work on an arbitrary and smaller subset of image A?