Talk:Scale space

message: This term N-jets is used without definition.  Can someone please add an explanation of exactly what it is. Dicklyon 05:16, 26 August 2006 (UTC)
thread_title: N-jets

message: The reason for my concern about this article (not just the lead) is that a) scale-space is an important concept within (e.g.) computer vision and b) thanks to User:Tpl and other there is now a set of scale-space related articles in WP.  For these reasons it makes sense to have at least one introductory article to this field which is relatively simple to understand.  Perhaps not for any reader who happens to find it but at least for an undergraduate EE student.  That article appears to be this one.
* Since there was no objection, I take it that it is OK to move the article to new title "Scale-space" (with a hyphen)
:I object.  The hyphen is only appropriate when "scale-space" is used as an adjective.  The notion of scale space as a noun does not need a hyphen.  Basic English grammar. Dicklyon 05:01, 28 August 2007 (UTC)
replies: text: L(x, y, t)\ = g(x, y, t) * f(x, y) where g(x, y, t) = \frac {1}{2{\pi} t}e^{-(x^2+y^2)/2t}.\, 
and t =\sigma^2 is the variance of the Gaussian and also the index of the corresponding scale level.   There are 2 formal issues related to the convolution expression which need to be sorted out: 1) what does it mean to convolve a 3 variable function with a 2 variable function, 2) in this particular formulation it is perfectly possible to be strict and not put the variables inside the convolution operation.  For 1) is it possible to define both L and g as 2D functions with an additional index; e.g.,  L_{t}(x,y) ? This would also help solving issue 2)
This type of scale-space is interesting since it is the only one to satisfy a set of useful properties commonly referred to as the scale space axioms.  Furthermore, the set of 2D functions L(x,y,t), indexed by the scale parameter t, can be shown to be the solution of the heat equation.
Stop lead (missing wikilinks need to be inserted)
-----
The rest of the article can have sections with headings such as
* Motivation/background (in relation to biological vision / physics)
* Applications in computer vision and image processing (move subheadings 2-4 in Further readings to here + stuff now in the lead)
* The scale space axioms (short overview with link to the main article)
* Implementation issues (perhaps expand subheading 5 in Further reading and link it to the main article)
In my view, most of the stuff is there already, we only need to reshuffle a bit and be focused in the lead section, then this could be a great article.  --KYN 22:57, 24 August 2007 (UTC)

text: I think your ideas are pretty much OK, and if you want to start, then I bet tpl and I will be able to help.  We might not leave the lead exactly as you propose, but I agree something like that would be helpful. Dicklyon 05:01, 28 August 2007 (UTC)
thread_title:  More comments 

message: Given the above discussion on how to make the article better, I made a picture of how such an article could look like, at least in terms of structure and separation into sections, perhaps not the detailed content.  It can be found here.  It also includes some comments and questions which need to be taken care of.
There has just been a recent rewrite by Terjen, which seems to go in sort of the right direction, dividing the article into sections, even though many of the issues discussed above and questions in "my picture" are not addressed.  Apparently, Tpl is also making a draft for a new shape of the article.
I will wait a bit for comments from other editors before doing any modifications on the current version.  There's seems to be little idea in making incremental changes until there is an agreement on the direction to go based on an overall structure that seems reasonable.  --KYN 10:02, 3 September 2007 (UTC)
thread_title:  Plan for modifications 

message: Here are some examples of images which can be used for the article.  I have set up a small Matlab script for doing the computatitons which is relatively easy to change.  It uses a sampled Gaussian with two different variances.  If someone has suggestions for improvements, I can try to fix them.  --KYN 12:13, 3 September 2007 (UTC)
replies: text: I'd say start with a more interesting image with some natural grayscale stuff (maybe also the text), and use more scales, at least 0, .5, 1, 2, 4, 8, 16.  Maybe animate the results. Dicklyon 16:38, 3 September 2007 (UTC)
replies: text: Yes, your figures are good, but I also agree that there would be more illustrative to use grey-scale images that show more of the merits of scale-space. When I've written about scale-space previously, I've often combined a few levels in scale-space with the output of a feature detector, in order to make the effects more visible in the respect of how they influence later stage visual processes. Tpl 07:25, 4 September 2007 (UTC)

text: There's too much jump from scale 0 to 1, and not enough from 2 to 3.  I recommend 0.5, 1, 2, 4. Dicklyon 14:22, 12 September 2007 (UTC)
replies: text: I agree, using a linear scale on t has that effect, and quadratic or exponential is probably better.  Will try to fix it soon...  --KYN 18:48, 12 September 2007 (UTC)

text: Your code is probably fine, but my t isn't calibrated to a "pixel unit", which I guess that your t is, rather to some arbitrary scale unit.  --KYN 21:25, 12 September 2007 (UTC)
replies: text: Well, if we're going to illustrate what t does, we ought to be calibrated.  How about I filter your starting images at a few scales for you?  Dicklyon 22:46, 12 September 2007 (UTC)

text: The current set of images have t calibrated in unit pixel^2.  --KYN 05:38, 13 September 2007 (UTC)
thread_title:  Images 

message: This this term that an anon keeps adding make sense to anyone?  Not to Google book search; see  and . Dicklyon 15:11, 19 October 2007 (UTC)
thread_title: Psychological vision

message: Cite: 
:g_t(x, y) = \frac {1}{2{\pi} t}e^{-(x^2+y^2)/2t}\, 
....
This definition of L works for a continuum of scales t >= 0, but typically only a finite discrete set of levels in the scale-space representation would be actually considered.
t is the variance of the Gaussian filter and for t = 0 the resulting filter g becomes an impulse function such that L(x,y;0) = f(x,y), that is, the scale-space representation at scale level t = 0 is the image f itself. 
If you put t = 0 into g you'll get:
g_t(x, y) = \frac {1}{2{\pi} t}e^{-(x^2+y^2)/2 \cdot 0} = BANG\, 
--85.181.131.211 (talk) 14:50, 7 March 2010 (UTC)
replies: text: The statement in the text follows from  \lim_{t\rightarrow 0} g_t(x,y) = \delta(x, y) = \delta(x) \delta(y) , i.e., when t approaches 0, then  g_t  approaches the 2D impulse function.  Since the result of convolving f(x,y) with that impulse funtions is again f(x,y) the statement in the text follws.  I tried to clarify this in the text.  --KYN (talk) 15:45, 7 March 2010 (UTC)
thread_title:  There seems to be an error 

message: In a number of previous edits, the notation for convolution had been changed so that it no longer was correct.
Please, note that from a mathematical viewpoint, one cannot use notation of the form
:L_{x^m y^n}(x, y; t) =  \partial_{x^m y^n} g(x, y;\; t) * f (x, y)
since the convolution operation operates on functions f and g and not on function values in a single specific point f(x, y) and g(x, y;/; t). For this reason, one can usually writes the convolution operation as
:L_{x^m y^n}(\cdot, \cdot;\; t) =  \partial_{x^m y^n} g(\cdot, \cdot;\; t) * f (\cdot, \cdot)
where the dots \cdot are to  interpreted as place holders for the arguments over which the convolution is performed.
In particular, a notation of the form
:L_{x^m y^n}(x, y; t) =  \partial_{x^m y^n} g_{t}(\cdot, \cdot) * f (x, y)
that was used previously, does formally speaking not make any sense at all (although a trained person might be able to convert it to something meaningful). Tpl (talk) 07:12, 28 September 2010 (UTC)
thread_title:  Notation concerning the convolution operation 

message: I notice that most of the links in the article use "scale-space", but the article name is "scale space" (no hyphen).  The article should probably be consistent about this.  70.247.173.254 (talk) 23:27, 22 July 2012 (UTC)
replies: text: We should follow normal hyphenation rules:  hyphenate when the compound is used as an adjective, and not otherwise.  If it's not so, fix it.  Dicklyon (talk) 00:12, 23 July 2012 (UTC)

text: Sure enough, someone went hyphen-happy.  I fixed.  Dicklyon (talk) 00:20, 23 July 2012 (UTC)
replies: text: Appreciate the fix.  Wasn't aware of a policy about hyphens.  Care to point me to it?  70.247.173.254 (talk) 07:34, 25 July 2012 (UTC)
replies: text: I don't think there's a policy, but there is info about normal English hyphenation:  see Compound modifier and WP:HYPHEN.  Dicklyon (talk) 21:50, 2 August 2012 (UTC)

text: I am going to invoke WP:COMMONNAME, since every source in the article uses "scale-space" with a hyphen, including two encyclopedias . There is only one exception. --Enric Naval (talk) 19:05, 2 August 2012 (UTC)

text: I looked at google scholar. "scale-space" uses a hyphen but "scalar space" doesn't . --Enric Naval (talk) 19:18, 2 August 2012 (UTC)
replies: text: Editor User:Tpl has mostly referenced his own work, and he's the one that started the over-use of the hyphen, I think.  He's not from a native English speaking country, so I assume he may have been less familiar with the subtleties of English grammar, and picked up on the hyphen in Witkin's original paper, where "scale-space" was used as an adjective.  The Dutch largely followed him.  Some books, like this one go the other extreme, and omit the hyphen everywhere.  But there's really no reason why WP should follow either form of mis-punctuation, when it serves the user best to use English grammar and punctuation standards to help them parse the phrases correctly.  Dicklyon (talk) 21:43, 2 August 2012 (UTC)

text: I undid the move you did, Enric, which was obviously could not have been considered uncontroversial in light of this discussion.  Also verified that the noun/adj. phrase distinction is in Witkin's original and subsequent papers:  and .   The unhyphenated form was adopted by others independent of Witkin's team, like ,  , .  It's just English; no reason to punish the reader by making the structure more ambiguous.   Dicklyon (talk) 22:02, 2 August 2012 (UTC)
replies: text: So, in "a scale space" it's a noun composed by two words, and in "a scale-space image" it's a a compound adjective that is modifying the noun "image". Yes, i can see how it works. And I see that Witkin's paper does make that distinction. OK, no problem with me, the current title is fine. --Enric Naval (talk) 22:33, 2 August 2012 (UTC)
replies: text: Enric, I don't mind helping you learn a bit about English grammar and punctuation and such, but it has been a real pain trying to do that via RM arguments over the last year or two.  Maybe this is a good step, where you actually learn the logic, instead of pretending that you can just copy what you find in sources and end up in a good place.  Dicklyon (talk) 00:37, 5 August 2012 (UTC)
thread_title:  Scale-space or scale space? 

message: as per lead. fgnievinski (talk) 05:18, 8 September 2020 (UTC)
thread_title:  Move to [[Scale-space theory]]?