What considerations determine copyright infringement? In copyright case law, what roles do process versus output play in determining infringement via creation of a similar work. By process I mean, "How much access did the creator of the new work have to the putative base work?" By output I mean, "How similar, textually, is the new work to the older work?" I am primarily curious about the USA.
One principle of copyright law is that if you can prove independent authorship, there cannot be liability no matter how similar your work is to the prior work. "If by some magic a man who had never known it were to compose anew Keats's 'Ode on a Grecian Urn,' he would be an 'author,' and if he copyrighted it, others might not copy that poem, though they might of course copy Keats's." (Sheldon v. MGM Pictures Corp., 81 F.2d 49, 54 (2d Cir. 1936)). Now, of course, the challenge is proving that you've never heard a given piece of music, or never read a particular work of fiction. If you have, even unconscious copying exposes to liability. And if the plaintiff can prove that you had access (such as the scriptwriter who sent a copy to a movie studio), they will have an even easier time proving the copying. If there is no proof of copying or not-copying, the copying can be proved circumstantially either through expert testimony or the jury's evaluation. The expert might testify something like "There is an identical tonal progression in these two songs, even though they were written in different keys. There were a million different ways the songs could have been written, but they are identical in this respect." The jury can consider that information and find the defendant liable. Or, the judge may simply tell the jury, "You may listen to these two songs, and find the defendant liable if you find them to be substantially similar to the extent that it is more likely than not that the defendant copied the plaintiff." TL;DR: The process can be conclusive, but if it isn't, then the output will be the evidence that the jury will consider.
Musical compositions can be, and if recent almost always are, protected by copyright. This is separate from the copyright on a recording of a performance of the work. If you reuse a musical passage, the new work may be a derivative work, that is a work based on an earlier work. Or an extended musical quotation could be considered to be copyright infringement. If this is in the united-states the use of a section from a previous work might be considered to be a fair use (fair-use). This is a specifically US concept in copyright law, although several other countries have a concept of fair dealing which is somewhat similar, although narrower. Whether a use is a fair use is an inherently fact-based determination. There is no clear and simple bright line for what is and is not a fair use. US law (17 USC 197) specifies four factors which are to be weighed by a court in considering the matter: The purpose and character of the use. If your use is commercial that weighs against fair use, but does not at all preclude it. This factor also includes whether the use is transformative or not. A transformative use is one that takes the part used for a very different sort of purpose than the original. Parodies are normally transformative, for example. A quote for purposes of commentary and analysis, or criticism is normally transformative. Transformative uses are more likely to be considered fair uses. The nature of the copyrighted work. Creative works such as fiction and music are more strongly protected than works such as textbooks and news stories. This probably weighs against fair use in the case described. The amount and substantiality of the portion used in relation to the copyrighted work as a whole. If only a short section of a longer work is used, that weighs in favor of fair use. However very short quotes can still fail, to be held to be fair uses. In Harper vs Nation a quote of about 300 words from a 500 page book was held not to be fair use because it was &quot;the heart of the book&quot;. The effect of the use upon the potential market for or value of the copyrighted work. A use that significantly harms the market value of the original, or serves as a replacement for it, weigh strongly against fair use. This was a major factor in Harper vs Nation. Each case of claimed fair use is evaluated by looking at all four factors, and the specific facts of the case. From the description in the question, such a use might well be held to be fair use. Musical quotations often are. But there is no way to be sure unless a court evaluates the specific case. A lawyer specifically experienced in not only copyright law, but copyrights on music, might be able to give more specific advice. Or you could, of course, seek permission from the copyright holder, quite likely the original composer or artist. If you get permission, there is no further issue. There might be a charge, but when the use is minor, and has no commercial effect, the charge might be small or even zero provided that the source is acknowledged.
Person A has to have created the data to hold copyright; for most kinds of data this has no legal effect because facts are not protected by copyright. A mineable database probably does not have the necessary creative elements for copyright. An algorithm is not protected by copyright (it might be patented). Person C's program is copyrighted. The product created by D is probably copyrighted, depending on what degree of creativity is involved in their transformation. If the transformation is automatic then no, but if creative judgments are applied to the output of the program then maybe. Though the resulting product is another database of facts, and the facts cannot be protected. In terms of "using the model", only C and possibly B have any control. If it is necessary to validate the software using A's data and A has kept the data secret, C might negotiate with A to use the data, in order to complete his program, and that could give A some interest in the program.
Here's where you went wrong legally: Suppose I legally obtain some digital image created by somebody else (e.g., by downloading from a public website). That, right there, is copyright infringement- unless the copyright owner has granted permission or the image is public domain you cannot copy it - this breaches "the right to make reproductions". By posting it on the web (assuming that it isn't itself an infringing copy) they have given implied permission for you to look at it in a web browser but not to copy it into a presentation even if that presentation is never presented. If it is presented then that makes the infringement worse - it adds breaches of "the right to communicate to the public" and "the right to use the work as a basis for an audiovisual work". How is this different from the computer wallpaper? It isn't. If you are using the one of the defaults that shipped with the OS then the license gives you permission. If you are using someone else's copyright without permission then it's a breach. There are defenses to copyright infringement but these are quite nationally variable - search this or other sites for "fair dealing" and "fair use".
Fair use is a four-factor test. Whether the use is commercial is part of just one of the four factors. Fair use is determined on a case by case basis, and it would be rather silly to assume that everything a user could post would be covered by fair use. Rather than just rely on the possibility of fair use, you may want to utilize the DMCA protections. Doing so can protect you from copyright liability for the user-generated content. You will have to register a DMCA agent, and expeditiously respond to takedown notices and counternotices.
I would argue that no, there is no copyright for the restored work. Independent copyright is only possible for any original material added, as previously discussed on this site. In this case, the added work was a technical process rather than a creative process, and technical processes cannot be protected by copyright. Copyright licenses would therefore be ineffective. However, I believe one could still impose a license based on owning the copy as opposed to the copyright (contract might be a better term in this case). However, if a third party managed to obtain a copy through some other avenue, any such contract would not be binding on them and nothing could be enforced against them unlike with copyright laws. Another way a license might be imposed is through patent protections, as technical processes can be protected via patents. However, I'm not as familiar with patent law, and this doesn't appear to be the claim being made.
Copyright infringement is just one of several ways to violate a person's intellectual property rights. Others include patent infringement, trademark infringement, and misappropriation of trade secrets.
This sounds like a case where there can be differences as to if something is a design that can be copyrighted or if it is a matter of a trademark held by the artist who drew the circle. If someone began a copyright infringement action against you, claiming copyright of the shape of a circle, your defense could be the Threshold of originality (Wikipedia). The threshold of originality is a concept in copyright law (Wikipedia) that is used to assess whether a particular work can be copyrighted. It is used to distinguish works that are sufficiently original to warrant copyright protection from those that are not. In this context, "originality" refers to "coming from someone as the originator/author" (insofar as it somehow reflects the author's personality), rather than "never having occurred or existed before" (which would amount to the protection of something new, as in patent protection). Obviously, circles, squares, triangles, pyramids, etc., even straight lines, have all existed for a long time. Simple shapes can, of course, be included as part of a more complex design, and that design as a whole is copyrighted as soon as you complete the design. You don't need to claim copyright; you already have it. If you did a design that was fairly simple and were accused of copyright infringement, it might come down to a court case to determine the threshold of the threshold of originality. Now, if you did a painting of a circle that looked like another painting of a circle, then you could be accused of trademark infringement, because the artist you allegedly copied could say that they have such a distinctive style that is is their trademark. A trademark, trade mark, or trade-mark is a recognizable sign, design, or expression which identifies products or services of a particular source from those of others...Trademarks (Wikipedia) Trademarks are also designs, of course, but are protected in a different method different than copyrights. So many decisions about copyright infringement come down to the judgement and opinions of a jury, because of the fungibility of what exactly constitutes originality and what constitutes a copy, part of a copy or a derivative. Trademark infringement hinges on how recognizable that design as a mark is and if there can be confusions between the two. For a much more in depth outline of copyright, see I have a question about copyright. What should I read before I ask it? - Law Meta Stack Exchange.