Talk:Gaussian filter

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Gaussian blur

Can the introductory sentences be simplified? It looks like it's written for people who already understand specialized terminology. Chris (talk) 15:56, 9 August 2013 (UTC)[reply]

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.

The result of this discussion was not merged D O N D E groovily Talk to me 04:03, 21 March 2012 (UTC)[reply]

Is this the same as the Gaussian blur interpolation? - Fredrik Johansson 18:58, 8 September 2006 (UTC)[reply]

No, but they are related. A simple Gaussian filter filters a signal (1D), Gaussian blur is 2D. --84.150.198.254 22:12, 21 October 2006 (UTC)[reply]

It looks like we should not merge Gaussian blur with this one then. Graeme Bartlett (talk) 21:05, 31 March 2009 (UTC)[reply]

No, that's an old discussion. A lot of the material in the filter article applies to the blurring article, plus there's duplicated stuff. Both articles really refer to Gaussian filters (except one current covers the 1D and the other the 2D), so I see no reason why they can't be merged. -Roger (talk) 21:20, 31 March 2009 (UTC)[reply]

I think Gaussian blur should absolutely not be merged with Gaussian filter, even if they use the same theory. They are about totally different contexts. Please keep them separate. A photographer might be interested in gaussian blur, and a radio communications designer in gaussian filters. A "see also" link would be sufficient to link the two articles. --HelgeStenstrom (talk) 13:13, 9 November 2009 (UTC)[reply]

I agree with Helga (above). I was specifically looking for the Gaussian filter as it applied to graphic arts, so I searched for "Gaussian blur", its name in PhotoShop. I wanted to learn about 2D without having to weed my way through the 1D references. Lisa Pickens. —Preceding unsigned comment added by 76.26.110.157 (talk) 09:20, 6 December 2009 (UTC)[reply]

The difference between "filter"and "blur' is the difference between a tool and the application of the tool. In the blur article one could focus on the application in graphics. In the filter article one could describe the filter implementation. --84.150.100.221 (talk) 10:31, 29 December 2009 (UTC)[reply]

A Gaussian blur is an image processing effect accomplished by the application of a Gaussian filter to images. Gaussian filter can be applied to may other types of data and signals. This article should stick to math and information related to filter theory and could generalize to N-dimensions. Hgkamath (talk) 04:28, 8 February 2011 (UTC)[reply]

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

non-causal?

It looks to me like the gaussian filter, as defined here, is non-causal. Is this correct? If so, how does one approximate a gaussian filter in the "real" world? Thanks, Mherndon 16:23, 2 July 2007 (UTC) The usual dimensions in images are spatial and the whole image is available before application. If an image was transmitted then causality would matter as one would have to wait for relevant pixels to arrive before computing the filter. Hgkamath (talk) 04:28, 8 February 2011 (UTC)[reply]

A binomial filter (a FIR filter with binomial coefficients) is an approximation to a gaussian filter. --89.59.137.109 00:16, 3 July 2007 (UTC)[reply]

Digital implementation section

I edited the digital implementation section, but left the tag on because I'm not sure whether the math is correct or not. The first few paragraphs seem OK as far as I know (not sure) but the units seem wrong for the cut-off frequency f/sigma. f is already in samples per second, and sigma would be in seconds, I think. ☺Coppertwig (talk) 22:54, 17 April 2010 (UTC)[reply]

The article may be measuring sd in samples rather than time units, but I agree, the cleanup template should stay: the article is far from clear to technically minded readers, let alone a general reader. It also fails to give its source. SpinningSpark 10:23, 18 April 2010 (UTC)[reply]

Sudden jump to digital image processing

The last paragraph under the Definition subheading suddenly starts talking about image and pixel from the second line. I think this is out of context there. The 2-D Gaussian filter should be described in a generic mathematical context rather than particular application (to graphics/image processing). — Preceding unsigned comment added by Srays (talk • contribs) 09:27, 11 January 2011 (UTC)[reply]

Minimizing the rise and fall time?

The article says "Gaussian filters have the properties of having no overshoot to a step function input while minimizing the rise and fall time.". All filters with non-negative (or non-positvie) impulses have no overshoot. The fastest filter without overshoot is the dirac delta (it is instantaneous). It should probably be the fastest filter subjected to some constraint.LarsPM (talk) 16:13, 16 October 2013 (UTC)[reply]

Kernel size

"A gaussian kernel requires 6{\sigma}-1 values, e.g. for a {\sigma} of 3 it needs a kernel of length 17"

Can you please clarify this? I understand it is somehow derived from the 3-sigma rule to cover approximately 99.7 of the the total area of the Gaussian distribution but this is not stated anywhere. Furthermore it is not stated if this refers to an odd or even kernel and what the purpose of -1 is. If I take an odd kernel of 17 pixels that gives an effective radius for the sampling points (at the pixel centres) of (17 - 1) / 2 = 8 pixels. That is a sigma of 8 / 3 = 2.667 approx. I don't see how from a sigma of 3 one can derive a kernel of 17 pixels. My calculation gives me 18 pixels and if I wanted to make this odd I would go up to 19 pixel giving me a sigma of 3.167 approx which is closer to 3. Maybe I have missed something.

Second frequency response function description is badly worded

A function is given in terms of the standard deviation in time-domain, and then a frequency response function is given. At first, because of poor wording, the frequency response function appears to be the frequency response of the same preceding time-domain function, but upon looking closer I see that the standard deviation for the frequency-domain function is in terms of the standard deviation in frequency units. Either "standard deviation" should mean the same in both functions, or language should be introduced that clarifies that the two functions use a different meaning for standard deviation (sigma and sigma-f are the inverse of each other -- sigma-f = 1/sigma). — Preceding unsigned comment added by 2601:643:201:6351:E1CA:D283:CDEB:13A7 (talk) 19:32, 27 November 2015 (UTC)[reply]

What is $a$ ?

The Definition section mentions $a$ but does not explain what it is. It is not obvious to a non-mathematician. — Preceding unsigned comment added by 184.70.193.174 (talk) 18:54, 26 February 2019 (UTC)[reply]

Incorrect formula for frequency cutoff with arbitrary attenuation

The formula : $f_{c}={\sqrt {2\ln(c)}}\cdot \sigma _{f}$ appears to be incorrect. My derivation, supported by numerical calculations indicates that the proper formula is : $f_{c}={\sqrt {ln(c)}}\cdot \sigma _{f}={\frac {\sqrt {ln(c)}}{2\pi \sigma }}$ Also I found a reference that suggests the proper (rearranged) formula, but regrettably with an improper derivation. I would appreciate help finding other references.

https://www.gaussianwaves.com/2012/05/derivation-of-expression-for-a-gaussian-filter-with-3-db-bandwidth/ --Gnobe (talk) 20:32, 2 September 2019 (UTC)[reply]

Infinite support

@Fgnievinski: re this edit, what do you mean by "infinite support"? Is that a typo? SpinningSpark 15:20, 19 August 2021 (UTC)[reply]

@Spinningspark: I've tried to clarify it now: [1]. fgnievinski (talk) 16:09, 19 August 2021 (UTC)[reply]

Rephrase purpose in introduction?

The introduction says, "It is considered the ideal time domain filter, just as the sinc is the ideal frequency domain filter.[1]" I'm having trouble understanding this: the equivalent of a sinc() in frequency would be a rect() in time domain. A Gaussian in time is a Gaussian in frequency. Sinc() is useful if you care about having absolute cutoff in frequency and are willing to have big tails in the time domain. Gaussian gives the tightest combination of tails in time and frequency domain, e.g., uncertainty principle. I'd like to modify this section to reflect that. David (talk) 00:14, 17 June 2022 (UTC)[reply]