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A paper I wrote was recently accepted for publication. In one of our figures, we report our results juxtaposed against results from another paper published in a different journal. To perform a quantitative comparison, we did the following:

  • Download the PDF of the other paper. The relevant figure is in the style of a "density plot" with an associated color bar. By this I mean that three-dimensional data (x,y,z) is plotted in two dimensions with the z value represented by a color in a color bar with associated numerical values.
  • We reconstruct a data set in the form (x,y,z) by associating the (x,y) coordinates relative to the given axis tick marks, and by associating the colors at each (x,y) to the associated color in the color bar. Details of the method by which we did this is explained in the supplementary material of our paper.
  • We re-plot the resulting data set with our own plotting software to compare it to ours using the same color scheme (a different color scheme from the original).

Importantly, we did not duplicate the figure of the original paper, but converted it into a data set and re-plotted that data. The raw data set was not included as a supplemental to the original publication. (one could argue that we should have simply requested the raw data from the authors of the other paper, but that's a different question)

We just received our proofs from the copy editors, who included the following remark:

Please note that in order to reproduce figures from another journal, authors must show that they have complied with the requirements of the publisher of the other journal, possibly including written agreement of both publisher and author of the originally published work. If a figure is reprinted from another source, copyright information must be included in the caption. Please provide required information.

While we don't wish to dispute the copy editors and will probably simply go through with getting permission from the other journal (which will likely require us to pay around $50 USD), I want to know what the rules/laws regarding what we did are in this case. A few thoughts:

  • It seems to me that we did not "reproduce the figure", i.e. we did not show the same figure as it appears in that paper.
  • If the data set had been included as a supplementary to the paper, then presumably a citation would entirely suffice to use that data and re-plot it (perhaps this would depend whether the paper was paywalled or not?)
  • Assuming the above is true, then extracting data from a figure, which ostensibly is just a compact and intuitive way to represent precisely the underlying data set (i.e. in principle the figure contains the same data as the underlying numerical values), then there should be no difference between what we did (extracting the data from the figure) and simply plotting data obtained as a supplemental to a published paper.

In any case this seems like a rather unfortunate situation for scientific publishing and making scientific results accessible.

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    NB it's irrelevant that you didn't directly copy the existing plots, but you have created a derivative work from them, which is considered pretty much the same thing. Extracting from a plot to create a new plot is not the same level as constructing a new plot from identical data.
    – Nij
    Feb 7 at 5:22
  • In your field, is representing 3D data in two dimensions using color for the third dimension a standard practice or is it a "creative element" in the one you derived yours from?
    – Buffy
    Feb 7 at 14:20
  • @Buffy it is the standard method to show this type of data, which can be seen in hundreds if not thousands of papers. On the theory side, we are plotting a specific correlation function whose z-values depend on the underlying model. On the experimental side, the corresponding plot shows neutron scattering intensity as a function of scattering momentum. It is standard to compare the two, qualitatively and sometimes quantitatively as well. We wrote a theory paper and our plot juxtaposes our result next to the previously reported experimental result, on the left/right (the plot is symmetric)
    – Kai
    Feb 7 at 17:19
  • "simply plotting data obtained as a supplemental to a published paper." Usually, these data when released comes with a separate non-commercial attribution, so the copyright on these data is different than the figures. I think there is a license that guarantee you are releasing something openly, but you allow for further modification and commercial redistribution while requiring referencing to the original open release (BSD, maybe?).
    – EarlGrey
    Feb 8 at 23:23

2 Answers 2

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It's hard to say anything conclusive without comparing the figures, but my guess is that the journal is just being overly cautious. It is simply much easier to ask for, and obtain, permission before publication than dealing with the unlikely situation of the other journal causing an issue later. Better safe than sorry. (And hey, it's a great deal for the journal if they can trade a small risk of having to spend considerable amounts on copyright attorneys for the authors spending $50...)

Sometimes this risk aversion is taken quite far. I was asked for permission in a case where somebody wanted to plot results of their own calculation, because the results showed similar curves to ones I had previously published for the same quantity in a closely related system.


That said, you ask about rules and laws. I am not a lawyer, but I nonetheless think the following will be fairly accurate. The first thing to note is that details will matter. (That is a big part of why copyright litigation is expensive in the first place - details are time consuming.) Under US copyright law, there is a fair use defense for academic use, but relying on that assumes one is willing to deal with litigation. Note that there is no presumption the reuse is fair - if a complaint is filed, it needs to be dealt with and the specific case analyzed.

The analysis involves several factors. One of these is related to how much of the work is copied. This can get complicated quickly, since the legal question really is about which protected elements of the figure were copied. The data would not be protected (paywalled or not, data are considered facts, which are not protected), but creative choices could be. I don't know what case law is most relevant to density plots, but one could probably make an argument that choices of font, aspect ratio, labels, tick placements etc. involve some level of creativity - likely not enough to be protectible in separation, but maybe in combination. In most cases I suspect this would be a losing argument, but beating it in court isn't free.

Now, how similar is your figure to the original one? A recreation in a different plotting software, involving a complicated data extraction step, does not necessarily result in different creative choices. If you painstakingly reproduced it in all or most of these aspects, but used a different color scheme, this would put you closer to the line than if the data was integrated in a completely different figure.


At the end of the day, it's just much easier for the journal to avoid these issues altogether by having a policy requiring permission more broadly than is legally necessary. I think it's unfortunate that journals charge authors for granting this permission, but, then again, some fee is probably necessary to cover costs associated with such paperwork.

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    Good answer except for the assumption that US law applies. The question does not indicate that OP or the publisher are in the US.
    – Roland
    Feb 7 at 6:37
  • @Roland Thanks. I intended it more as an example of law than an outright assumption of jurisdiction, and it seemed potentially relevant at least to the journal with the original figure (since $50 USD is mentioned, but maybe the sum was converted for US sensibilities).
    – Anyon
    Feb 7 at 6:48
  • Internationally, publication fees are usually in US currency (for everyone's convenience). European journals sometimes give them (also) in Euros.
    – Roland
    Feb 7 at 6:50
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There is no shortage of hairsplitting about coypright rules in this forum. However, there is (as far as I know) zero question about actual litigation or legal problem. From which you can deduce that most people (including your copy editors) are overly cautious, and that you do not need to get permission.

Actual copyright litigation is against platforms such as Sci-Hub or ResearchGate, not individual researchers.

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