Image:DOG vs MHF.png
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[edit] Summary
Comparison of Difference of Gaussians and Mexican Hat Function. This file was created at 04:58, 6 December 2005 (UTC) by JustinWick, using Mathematica 5.0. It is intended to illustrate that DoG is a reasonable approximation to MHF.
[edit] Licensing
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[edit] 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.
| date/time | username | edit summary |
|---|---|---|
| 05:22, 6 December 2005 | en:User:JustinWick | (Explaination of how I created this image.) |
| 04:58, 6 December 2005 | en:User:JustinWick | (Comparison of <a href="/wiki/Difference_of_Gaussians" title="Difference of Gaussians">Difference of Gaussians</a> and <a href="/w/index.php?title=Mexican_Hat_Function&action=edit" class="new" title="Mexican Hat Function">Mexican Hat Function</a>. This file was created at ~~~~~ by JustinWick, using Mathematica 5.0.) |
[edit] Historio de la dosiero
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- (del) (cur) 04:58, 6 December 2005 . . en:User:JustinWick JustinWick ( en:User_talk:JustinWick Talk) . . 486x900 (10415 bytes) (Comparison of en: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.)
