So the copyright belongs to google, even if you run it on your own photographs on your own machine? That doesn't seem right.
Now consider if you trained the NNet with the same two images, such that it was highly overtrained and basically produced a combined replica of the inputs. This is essentially the same as doing it manually in photoshop. That a computer done it does not take ownership away from the creators of the two images.
A NNet isn't trained with two images though, but millions. Do we abandon copyright because of scale? Should the NNet operator not be required to keep the entire training set such that copyright can be traced? Do we invent an entire new industry on determining the probability that a particular image was used to train a NNet (and by how much it affected it), such that it's owner can claim royalties on anything the NNet produces?
The question isn't about google versus operator, it's about whether or not we're going to continue investing in the madness of copyright for machines designed to mimic human brains, and if so when will it apply to ourselves - for we can't archive our own training set.
It doesn't matter whose images they were trained on. As long as you are not reproducing the images exactly it's not violating copyright.
But if it does, then I believe it was Flickr that provided the images.
This is an interesting question. I wonder if, due the number of items in the training set and the minimal impact of each individual creative work, it would be considered fair use.
If your training set significantly consists of images from someone else's training set in the same domain, you might have a conflict. But for arbitrary images, it may be analogous to search engines indexing (and learning from) copyrighted material, which is generally protected.