Retrieve geometric transformation of moving image's coordinates in image registration (using imregtform, imwarp etc.)

The problem I'm trying to solve is how to access the geometrical transformation which imregister (and the functions that it calls) apply to the moving image. The alignment I'm doing is on a set of particle locations (with (x,y) coordinates) with should be aligned with another image of the objects whose borders they are supposed to be inside of.

This is an image of the particles:

This is an image of the objects:

This is after registration with imregister with default parameters:

So this alignment works pretty well. However, I need the geometrical transformation itself and not the registered image as explained in the following. In a later step in the analysis the particles are organized into clusters, and so a lot of information about their locations is lost and the alignment would be very unreliable with the clusters themselves. I want to get the transformation's parameters when aligning the particles image with the objects image, and then apply it to the clusters' coordinates.

I've tried digging into the code of imregister, imwarp and interp2 to find out how the registered image is constructed but I got lost in interp2, primarily because it relies on internal functions. I've tried exporting the various "tform"s constructed along the way in these functions, and applying them to the data but they don't seem to do the trick.

I'd appreciate any assistance or guidance in the matter.