Can cropping a sprite invalidate copyright?

Question

US Law — Can cropping (sub-sampling) a copyrighted work in some cases be considered an original work that I can copyright?

In general, I understand I can't use art from a copyrighted video game for my own commercial purposes. On the top left, I mark the Mario artwork with an X to mark that the work is copyright of Nintendo. — Cropping the image to a 3-color 6x6 block is still recognizably Mario, so I believe the small block in the bottom left is still under their copyright.

In the top center, I mark that color changes have no impact on the copyright status. Nintendo owns copyright over the patterns themselves. — I even assume the cropped one-bit image of 4x5 pixels showing part of a color-swapped Mario's face as under Nintendo copyright because it is arguably still recognizably Mario.

For the third example, I assume that Nintendo still has at least some rights over a derivative work heavily influenced by Mario. The derived 'mario' is wearing a jersey instead of overalls and facing forward. — In this case, however, I don't believe Nintendo has any grounds for a copyright claim over the derived and cropped one-bit 4x5 image of a face. This little face, while it shares some pixels with the original Mario- is no longer recognizably Mario, so I mark it with a green check mark.

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Finally, to the question- is there a point where cropping without derivation is sufficient grounds to be considered my own copyrightable work?

Look at the three business cards on the very right of the image. They all crop elements directly from the color-swapped Mario Sprite, but I've been told they are not recognizably Mario. Would Nintendo have grounds to sue me were I to begin to profit off plumbing, insurance, or my own racing team based on the three fictional companies on the far right?

What are the standards by which these decisions are made? I'm going off the assumption it's recognizability. What else could it be?

Also- I very much welcome answers that:

1. Suggest a change to any red X or green Check above
2. Correct a fundamental mistake in my understanding
3. Answer the specific question of these businesses
4. Answer the general question of cropping artwork

Answer 1

Copyright protection is about certain acts, and not about relationships between products. Copyright law says that the creator of an original work hold the exclusive right to copy and to authorize creation of derivative works. Copyright law does not say that anybody can freely create derivative works as long as they are different to a certain extent. So if you take an original Mario and modify it a teeny bit, that is a violation of copyright; if you take an original Mario and modify it hugely, that is a violation of copyright.

Degree of similarity is relevant on some cases when the factual question arises whether the allegedly-infringing work is based on some protected original. This is most obvious in music cases, where all baroque music has some similarity to all other baroque music, all death metal has some similarity to all other death metal, and so on. There is not a legal quasi-statutory standard for measuring substantial similarity in music. The scientific underpinning of such a standard would be based on (weighted) combinatorics and the idea that there are only so many tunes possible (that would be a huge number, until you get to the "within a genre" condition).

It seems obvious (by your "admission") that the derived works are based on protected works, so Nintendo's permission is required to legally create such works. However, you do or would hold copyright in your unauthorized derived work. Without a trail of evidence such as a SE question pointing to the connection, the derived images might be hard to connect to the originals. In addition, you may be able to avail yourself of a "fair use" defense, in case you get sued by the original creator. Factors favoring such a defense are the insubstantiality of the copying (a small portion) and the "transformativeness" of your creation.