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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.

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

Edit #2: move Edit #1 to a new post

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.

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

Edit #1

Referencing @user6726 post #1

Helpfully, user6726 states that any cropping and/or derivation (no matter how major the change) is by default a violation of copyright. They make two interesting counterpoints:

• First, similarity matters when deciding how a work was created. One could basically bring an expert into court who calculates the number of possible images (only 1,048,576 for one-bit 4x5 images) and then weighs the probability of independently creating the image (the fraction of 1,048,576 images that resemble faces) against the evidence that the image was derived from the copyright work. @user6726:

The scientific underpinning of such a standard would be based on (weighted) combinatorics and the idea that there are only so many tunes possible.

• But if (as in this case) the image was admittedly created by several modifications to a copyrighted work:

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.

My last question: What copying is insubstantial and transformative? here is I believe the clearest case is :

It seems to me there are three bars for insubstantial and transformative:

• The lowest bar:
  • No one would notice that your work is based on a part of a copyrighted work.
• The medium bar:
  • You would win a case on fair use grounds if taken to court.
• The high bar:
  • The original author of the work wouldn't bother to sue you because the work copied is so insubstantial and transformative.

Edit #2: move Edit #1 to a new post

• First, similarity matters when deciding how a work was created. One could basically bring an expert into court who calculates the number of possible images (only 1,048,576 for one-bit 4x5 images) and then weights the probability of independently creating the image (the fraction of 1,048,576 images that resemble faces) against the evidence that the image was derived from the copyright work. @user6726:

• First, similarity matters when deciding how a work was created. One could basically bring an expert into court who calculates the number of possible images (only 1,048,576 for one-bit 4x5 images) and then weighs the probability of independently creating the image (the fraction of 1,048,576 images that resemble faces) against the evidence that the image was derived from the copyright work. @user6726: