Google Images thumbnails were ruled infringing by one US court and overturned by another some time ago. More recently, the US also is the venue where Robin Thicke and Pharrell Williams ended up paying the Gaye estate royalties and naming Marvin Gaye a writer because Blurred Lines was apparently the result of Thicke saying he wanted to write a song that sounded like Got To Give It Up, and Williams using his knowledge of songcraft and what was distinctive about Got To Give It Up's groove to compose an original song with different words, note patterns and beat which nevertheless sounded similar, so I'm not sure there's much grounds for the absolute confidence most HNers seems to have that fair use defences will prevail in the US because of novelty and "learning".
Copyright law rulings are all over the place, and I think it's quite likely creators of such tools will be ruled infringing by one court and overruled by another, infringing in one region and OK in another, one diffusion model ruled non-infringing and another more commercially-oriented one ruled infringing, and perhaps others where either the creators or the users of the tool are deemed infringing but not necessarily both.
As far as I know, all standing case law in the USA says that web crawling for search indexing is fair use. I'd be interested in a citation to a counter example. I've been unable to find any.
Also interested in specifics of any actual court cases involving News Corp vs Google in Australia; I can't find any references to lawsuits, only to the threat of legislation (which changes the law if passed, but I don't think it was passed in the end?)
The France thing is interesting. I know less about EU copyright law. Did Google pay the fine and... then what? Did they stop indexing news orgs in France, start paying for it, or just keep doing the infringing thing, or what? The ruling only applied to news organizations?
One USA case from back in the day that ruled that Google Indexing (and caching) was fair use, was Field v. Google, from 2006. http://www.eff.org/IP/blake_v_google/google_nevada_order.pdf
Another USA case that ruled that Google Image indexing, and using thumbnails in search results, was fair use was Perfect 10 v. Google (2007). https://cyber.harvard.edu/people/tfisher/IP/2007%20Perfect%2...
It's true it hasn't been super extensively litigated, and never made it to the supreme court. Perhaps because in fairly short order content owners realized they actually wanted to be indexed in google. And because Google (if not everyone) would respect a robots.txt to keep them out if they didn't.
The Google Books case is also probably relevant. (Which Google also, eventually, won).
There are other cases not specifically involving Google that are relevant, one for example with an index of tv news broadcasts that provided keyword search and let users view clips. The court ruled this was fair use too. Fox News v. TVEYES, Inc., 43 F. Supp. 3d 379 (S.D. N.Y. 2014).
I don't think I can find any USA cases that suggest indexing for a search engine would be a copyright violation and not fair use. Let alone against Google specifically. When you say courts have ruled against Google, can you cite any particular cases? Maybe they were from other jurisdictions than USA?
And yet, GP's description applies just as much to google indexing images. Google makes money off of a search index that copies copyrighted content without explicit permission or compensation.
In the USA, where OP suit is filed, I am not a lawyer but I think these image AI's are going to have a pretty good case for fair use, even if it what they did counts as "making a copy" (which I think isn't totally clear). It is a very transformative use. I think convincing a court that the AI's will result in lost revenue (for the specific works used as training data, not in general for the field) would probably be necessary, but not sufficient, to overcome a fair use defense -- and I don't think that argument is even a slam dunk. And is still just one factor in fair use; the transformative nature of the use has lately been given a lot of weight in the law, and seems pretty overwhelming here.
Of course, sometimes courts do surprising things.