File:DOG vs MHF.png
| Description | Comparison of Difference of Gaussians and Mexican Hat Function, intended to illustrate that DoG is a reasonable approximation to MHF. |
| Date | (UTC) |
| Source | Originally uploaded to en.wikipedia. Generated using Mathematica 5.0. Category:PNG created with Mathematica#DOG%20vs%20MHF.png |
| Author | JustinWick |
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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. |
Notes on Generation
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.
File history on en.wikipedia
- Description page history
| date/time | username | edit summary |
|---|---|---|
| 05:22, 6 December 2005 | JustinWick | (Explaination of how I created this image.) |
| 04:58, 6 December 2005 | JustinWick | (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.) |
- 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.)