Application Areas

Threshold Multidimensional Data 

In[1]:=

X data = Table[ UnitStep[i - 4, 7 - i] UnitStep[j - 7, 11 - j], {i, 0, 20}, {j, 0, 20}];

In[2]:=

X SeedRandom[11]; noisy[\[Sigma]_] := data + RandomReal[NormalDistribution[0, \[Sigma]], Dimensions[data]]

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X smooth = Composition[InverseWaveletTransform, WaveletThreshold, DiscreteWaveletTransform];

In[4]:=

X plots = Table[{ListPlot3D[noisy[\[Sigma]], PlotStyle -> Yellow, Mesh -> None, PlotRange -> All, Boxed -> False, Axes -> False, ImageSize -> 250, PlotRangePadding -> 0, MaxPlotPoints -> \[Infinity], BoundaryStyle -> Directive[RGBColor[0.25, 0.25, 0.02]]] , ListPlot3D[smooth[noisy[\[Sigma]]], PlotRangePadding -> 0, PlotStyle -> Yellow, Mesh -> None, PlotRange -> All, Boxed -> False, Axes -> False, ImageSize -> 250, MaxPlotPoints -> \[Infinity], BoundaryStyle -> Directive[RGBColor[0.25, 0.25, 0.02]]]}, {\[Sigma], {0.04, 0.1, 0.25}}];

In[5]:=

X Show2DThresholdPlot[name_, info_] := Column[{Style[name, 16, Bold, Opacity[0.9], FontFamily -> "Helvetica"], Row[{info[[1]], \!\(\* GraphicsBox[ {Thickness[0.05263157894736842], FaceForm[{RGBColor[ 0.597284, 0.585138, 0.0490272], Opacity[1.]}], FilledCurveBox[{{{0, 2, 0}, {0, 1, 0}, {0, 1, 0}, {0, 1, 0}, {0, 1, 0}, {0, 1, 0}}}, {{{9.9999, 18.}, {9.9999, 13.5}, {-0.00009999999999976694, 13.5}, {-0.00009999999999976694, 4.5}, {9.9999, 4.5}, { 9.9999, 0.}, {18.9999, 9.}}}]}, AspectRatio->Automatic, ImageSize->{60., 31.}, PlotRange->{{0., 19.}, {0., 18.}}]\), info[[2]]}]}, Alignment -> Center, Spacings -> {0, 0}]

In[6]:=

X Column[MapThread[ Show2DThresholdPlot, {Table[ "\[Sigma] = " <> ToString[\[Sigma]], {\[Sigma], {0.04, 0.1, 0.25}}], plots}], Spacings -> {0, 0}]

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