Talk:Projection-slice theorem

Cleanup
This article is a bit of a dog's dinner at the moment. The first part is too informal in style for an encyclopaedia, and the brief explanation of the theory is better in Radon transform. I am going to try to do a bit of tidyingBilllion (talk) 19:05, 6 April 2011 (UTC)

I think this article doesn't need a cleanup anymore and I removed the note. Any objections to this? Gromobir (talk) 19:43, 11 October 2014 (UTC)

Misleading Figure
The figure is confusing. It illustrates that the projection is taken along the x direction, but the text reads that it is a projection onto the x-axis. It technically is not a projection onto the x-axis since there is no particular location to which the projection belongs. I suggest removing the figure until a better one is made. hovden (talk) 14 June 2018 —Preceding undated comment added 14:51, 14 June 2018 (UTC)

Misleading Use of term "Projection"
I came across this page hoping to find some quick information on the scope of the projection-slice theorem. Unfortunately it doesn't help much. The use of "projection", combined with the link to Projection (mathematics) as the only definition of projection, is seriously misleading. Projection (mathematics) defines a projection as any idempotent mapping, however that is clearly not the definition used in this theorem: it is not valid, for example, for min or max projections, though it's possible there might be other transforms they could combine with to give a valid theorem. It means that the page is only useful to people who already know most of the theory (in particular, which specific projections the theorem covers - unfortunately that doesn't include me). I don't know the theory well enough to edit it, because I don't know how to delineate exactly which projections and transforms it does hold for - clearly integral projections, but is it valid for any other projections, maybe in conjunction with other transforms? For example, I think it probably holds for sum projections and DCTs, and there might well be Boolean analogues. Could someone who does know the theory well enough please clarify this. If it only holds for integral projections (or if other transforms are required for other projections) please say so. Thanks for any help. Urilarim (talk) 05:48, 22 June 2018 (UTC)

I added a link to the radon transform to clarify the meaning of projection. This should have solved the issue. BigAndi (talk) 04:32, 8 October 2019 (UTC)

Unfortunately it doesn't actually solve the problem, because it still doesn't delineate which projections the theorem applies to (e.g. Radon) and which it doesn't (e.g. min or max). I came to this page because I had read a discussion using the theorem where I thought it was unlikely to apply (I can't recall the detailed context now). The page did not help with this. For this reason, I support the proposal by ECMJohnson (below) that would fully resolve the issue Urilarim (talk) 01:08, 21 July 2021 (UTC)

Overview Figure
I uploaded a nice overview figure on Wikimedia Commons that is available under CC 4.0 BY. I think, it explains the concept very well and would nicely fit this article. Please decide whether you think it is an appropriate addition. — Preceding unsigned comment added by BigAndi (talk • contribs) 15:28, 7 October 2019 (UTC)

Reply 7-OCT-2019
Regards, Spintendo  18:05, 7 October 2019 (UTC)
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Request edit
Thanks for your patience with me. The figure is located on page 154 and does not state a different license. The PDF is available here: https://link.springer.com/content/pdf/10.1007%2F978-3-319-96520-8.pdf Please let me know whether this is formation is sufficient. BigAndi (talk) 19:37, 7 October 2019 (UTC)


 * The tag has not been filled out correctly. The tag's User1 parameter is blank. The COI editor has not stated whether or not they have been paid for the edits they are suggesting. If they have been paid, the tag's U1-client and U1-employer parameters need to be filled out, while the template needs to be used. This information needs to be provided. Regards,  Spintendo  13:31, 8 October 2019 (UTC)


 * I have not been paid for suggesting this edit. BigAndi (talk) 14:21, 8 October 2019 (UTC)
 * ✅ Spintendo  05:56, 9 October 2019 (UTC)

Over specificity of theorem as presented
I don't understand why this article presents such a specific version of the theorem (i.e. 2D to 1D for projection and slice operators) and also doesn't define the "slice" operator. I think, we should lift the presentation of the fully generalized fourier-slice theorem from as the main definition of this theorem. Ng's article provides specific mathematical definitions for all the operators and then in a section we can present the more commonly encountered 2D with Radon Transform (i.e. $$N = 2$$, $$M = 1$$, $$B = R_\theta$$) case as a special case of this theorem. Additionally, we could also present the proof from Appendix A of Ng's article in addition to the simpler 2D proof (which can be considered as a proof in the case $$B = I$$). Any thoughts on this? ECMJohnson (talk) 15:13, 13 December 2019 (UTC)