Talk:Radon transform

message: At the moment this page provides little more than a classification, definitions and a bit on applications, but no explanation whatsoever. A description of the transform, preferable in the context of CT reconstruction, would go a great length to making this a proper Wikipedia page.  — Preceding unsigned comment added by 192.16.186.53 (talk) 09:55, 22 August 2012 (UTC)
thread_title: This page lacks any explanation

message: I know people want to keep things abstract, but the vast majority of people referencing this page will want to use the 2D(and rarely 3D) version of the dual transform. They should be given explicitly(in addition to the N dimensional variant).   —Preceding unsigned comment added by 142.90.103.110 (talk) 20:56, 20 March 2010 (UTC)
thread_title: Filter back projection

message: I came to look at this at the request of Sławomir Biały. The first edition of Herman's book is a seminal text in the field and certainly would earn a place in a bibliography (along with Natterer's) book. I have not seen the second edition, but in the 1980s when I first learnt about Tomography herman's book was the first place to go. In as far as I have edited the article it is fair to say that is one of the sources I used. That said, we might want to separate a bibliography, as a guide to where people should start to read about this stuff, as oppose to references which specifically support theorems quoted.Billlion (talk) 18:26, 2 January 2010 (UTC)
replies: text: Ok.  I've added the book back into the references.  Sławomir Biały (talk) 22:36, 2 January 2010 (UTC)
thread_title: Reference to GT Herman book

message: I'm not 100% sure about this, but it looks to me like the statement:
"α is the angle L makes with the x axis"
is not quite correct, since α is the angle between the x axis and the normal vector to the line L.
:--Klubi 16:08, 29 January 2010  —Preceding unsigned comment added by 131.234.89.201 (talk)  
You are right. This error was corrected by 108.3.68.169 a day later.
:--Keilandreas (talk) 01:07, 20 March 2010 (UTC)
thread_title:  Definition 

message: I created a new illustration of the Radon transform as vector graphic (PDF) and uploaded it to Wikimedia Commons at []. I would appreciate comments on the content of this image (if it could be used as a replacement) and how to link it here.
--Keilandreas (talk) 10:40, 20 March 2010 (UTC)
replies: text: I have trouble rendering that image in my browser.  I don't know if this is an issue with how Wikimedia generates thumbnails of PDF files or if it is an issue on my end.  The best supported file format is scalable vector graphics (SVG).  I don't know IPE well, but I believe it supports export to SVG.  I would encourage you to do this. Sławomir Biały (talk) 14:15, 20 March 2010 (UTC)
replies: text: Ipe can only save in its internal format (.ipe), .pdf and .esp. I tried Inkscape to convert the pdf or eps to svg without luck (fonts are not rendered but replaced by some other font). Maybe someone else can help? --Keilandreas (talk) 05:32, 26 October 2010 (UTC)
thread_title:  New Illustration of the Radon Transform 

message: Can somebody please clarify the definition of the dual transform? It seems that the two definitions given are not equivalent. Should the normalization factor \frac{1}{2\pi} really be part of the dual? Keilandreas (talk) 13:06, 20 March 2010 (UTC)
replies: text: A probability measure assigns length one to the circle.  The 1/2π is necessary to get a total length of one, so the two definitions are equivalent.  I can attest that this is precisely how Helgason defines the dual Radon transform, but there may be other normalization conventions in the literature (I don't know).  Sławomir Biały (talk) 14:15, 20 March 2010 (UTC)
thread_title:  Dual/Adjoint of the Radon Transform 

message: Is d sigma just length along the line? Should the equation 
:Rf(L) = \int_L f(x)\,d\sigma(x)
just read
:Rf(L) = \int_L f(x)\, \|dx\|
or perhaps
:Rf(L) = \int_L f(\mathbf{x})\, \|d\mathbf{x}\|
or am I missing something? —Ben FrantzDale (talk) 15:32, 30 March 2010 (UTC)
replies: text: The meaning is actually explained in the text of the definition – sigma is arclength measure. The notation you suggest is sometimes used, but is far from universal. I would suggest leaving it as it is. Hanche (talk) 16:33, 30 March 2010 (UTC)
replies: text:  I saw that in the text, but I was half expecting the integral to be weighted additionally by the radius (integrating over a wedge as in an area integral in polar coordinates rather than a line). I'll be bold and try to add some clarity. In particular, I see d\sigma(x) as implying a dependence on x, which made me think an additional weighting may be going on. —Ben FrantzDale (talk) 19:46, 30 March 2010 (UTC)
replies: text:  |dx| seems fine to me, but you might want to explain the notation.  E.g., "where |dx| is the measure of arclength along the line", or something. Sławomir Biały (talk) 20:50, 30 March 2010 (UTC)
thread_title:  d sigma? 

message: Shouldn't
"...whose value at a particular line is equal to the line integral of the function over that line."
become
"...whose value at a particular point is equal to the line integral of the function over that line."?
Ps: q is the distance from the center of the input image (it is the offset parameter of the line in the normal form erquation)
87.2.112.192 (talk) 10:16, 6 July 2016 (UTC)
thread_title: Doubt...=