DescriptionDOG vs MHF.png	Comparison of Difference of Gaussians and Mexican Hat Function, intended to illustrate that DoG is a reasonable approximation to MHF.
Date	6 December 2005, 04:58 (UTC)
Source	Originally uploaded to en.wikipedia. Generated using Mathematica 5.0.  This diagram was created with Mathematica.
Author	File:DOG vs MHF.png by JustinWick
Other versions	English .svg English .png Russian .svg

File:DOG vs MHF-en.svg is a vector version of this file. It should be used in place of this PNG file when not inferior. File:DOG vs MHF.png → File:DOG vs MHF-en.svg For more information, see Help:SVG. In other languages Alemannisch ∙ العربية ∙ беларуская (тарашкевіца) ∙ български ∙ বাংলা ∙ català ∙ нохчийн ∙ čeština ∙ dansk ∙ Deutsch ∙ Ελληνικά ∙ English ∙ British English ∙ Esperanto ∙ español ∙ eesti ∙ euskara ∙ فارسی ∙ suomi ∙ français ∙ Frysk ∙ galego ∙ Alemannisch ∙ עברית ∙ हिन्दी ∙ hrvatski ∙ magyar ∙ հայերեն ∙ Bahasa Indonesia ∙ Ido ∙ italiano ∙ 日本語 ∙ ქართული ∙ 한국어 ∙ lietuvių ∙ македонски ∙ മലയാളം ∙ Bahasa Melayu ∙ မြန်မာဘာသာ ∙ norsk bokmål ∙ Plattdüütsch ∙ Nederlands ∙ norsk nynorsk ∙ norsk ∙ occitan ∙ polski ∙ prūsiskan ∙ português ∙ português do Brasil ∙ română ∙ русский ∙ sicilianu ∙ Scots ∙ slovenčina ∙ slovenščina ∙ српски / srpski ∙ svenska ∙ தமிழ் ∙ ไทย ∙ Türkçe ∙ татарча / tatarça ∙ українська ∙ vèneto ∙ Tiếng Việt ∙ 中文 ∙ 中文（中国大陆） ∙ 中文（简体） ∙ 中文（繁體） ∙ 中文（马来西亚） ∙ 中文（新加坡） ∙ 中文（臺灣） ∙ +/−

 

This work has been released into the public domain by its author, JustinWick at English Wikipedia. This applies worldwide. In some countries this may not be legally possible; if so: JustinWick grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.Public domainPublic domainfalsefalse

To reproduce this plot in mathematica, use the following code:

<< "Statistics`NormalDistribution`";
DOG[mu_, s1_, s2_][x_] := PDF[NormalDistribution[mu, s1], x] - PDF[NormalDistribution[mu, s2], x]; 
MHF[x_] := ((2/(Sqrt[3]*Pi^(1/4)))*(1 - x^2))/E^(x^2/2);
Show[Plot[c*DOG[0, a, b][x] /. {a -> 1.3383326406221043,  b -> 0.7477302449634321, c -> -3.812773094633841}, {x, -5, 5}, 
PlotRange -> {-1,  1}, Frame -> True, Axes -> False, PlotStyle -> {RGBColor[0, 0, 1]}, PlotLabel -> "Difference of Gaussians"], 
Plot[MHF[x], {x, -5, 5}, PlotRange -> {-1, 1}, Frame -> True, Axes -> False, 
PlotStyle -> RGBColor[1, 0, 0], PlotLabel -> "Mexican Hat Function"], PlotLabel -> "Difference of Gaussians and Mexican Hat Function"]

Note, to fit the DoG best to the MHF, I utilized the following code:

NMinimize[{Hold[NIntegrate[Abs[c*DOG[0, a, b][x] - MHF[x]], {x, -5, 5}]], {a > 0, b > 0}}, {a, b, c}]

This uses least squares fitting, which may be slightly suboptimal.

Description page history

File versions

• 04:58, 6 December 2005 . . JustinWick . . 486x900 (10415 bytes) (Comparison of Difference of Gaussians Difference of Gaussians and Mexican Hat Function. This file was created at 19:02, 18 March 2006 (UTC) by JustinWick, using Mathematica 5.0.)