How do I efficiently determine if the connected components from, say 3 images, are overlapping?

Supposing I want to check if there is overlap between n 3D volumes each containing 1 or more connected components, what would be the most efficient to do it?

In addition, I would also be interested in determining how much overlap there is between these components.

In answer to a comment in this blog post, Steve, suggests this:

" ... For each object in one image, use its PixelIdxList to index into the other image. Pass the result to unique, and that’ll give you a list of the objects in the second image that overlap with the object in the first image."

But I don't really understand what is being suggested here.

Thanks in advance, N