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Re: blurry ellipse

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92063] Re: blurry ellipse
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Thu, 18 Sep 2008 07:31:41 -0400 (EDT)
  • References: <gat9g4$ec5$1@smc.vnet.net>

Hi,

you function are exceptional long winded.

Try:

makeImage[todraw_] :=
  Rasterize[
   Graphics[{White, todraw}, Background -> Black,
    AspectRatio -> Automatic, PlotRangePadding -> 1],
   ColorSpace -> GrayLevel]

gauss[s_] :=
  Table[N[Exp[-(x^2 + y^2)/(2*s)]/(2 Pi*s)], {x, -10, 10}, {y, -10,
    10}]

and

makeImage[Circle[{0, 0}, 1]] /.
  Raster[bm_, args___] :>
   Raster[ ListConvolve[gauss[2], bm, {6, 6}], args]

makeImage[Circle[{0, 0}, {1, 0.5}]] /.
  Raster[bm_, args___] :>
   Raster[ ListConvolve[gauss[2], bm, {6, 6}], args]

Clearly you have to adjust the parameters of the functions above
to fit your needs.

Regards
   Jens


Solomon, Joshua wrote:
> NB: This is a mathematical problem, not necessarily a Mathematica problem.
> 
> I need a rasterized, blurry ellipse, i.e. an ellipse convolved with a
> Gaussian. I already know how to make a blurry circle. You take the Fourier
> transform of a circle (i.e. a Bessel function), the Fourier transform of a
> Guassian, multiply them, and transform them back. No problem. Since an
> ellipse is just a circle that has been squashed in one dimension, I figured
> I could make a blurry one the same way as I make blurry circles. I just
> needed to squash the Bessel function first. And I was right. The code below
> works just fine, *except* the intensity varies as you go around the elipse.
> If anyone could tell me how to fix that problem, I'd be very grateful!
> 
> BlurryEllipse[sizePix_, radiusPix_, sigmaPix_,stretchFactors_: {1, 1}] := 
> 
>     Module[{half = sizePix/2, x, y, f, r, a, pr2}, 
> 
>         f = 2*Pi*radiusPix/sizePix;
>         pr2 = -2 (Pi*sigmaPix/sizePix)^2; 
> 
>         RotateRight[
> 
>             Abs[
>                 Chop[
> 
>                     InverseFourier[
> 
>                         RotateRight[
> 
>                             Table[r1=
>                                     Abs[stretchFactors[[1]]*x+
>                                         stretchFactors[[2]]*I*y];
>                                  r2 = Abs[x + I*y];
>                                  BesselJ[0, f*r1] Exp[pr2 (r2^2)],
>                                 {y, -half, half-1} , {x, -half, half-1}],
>                             {half, half}]]]], {half,half}]]
> 
> size = 64; rad = 24; scale = 3;
> tmp = BlurryEllipse[size, rad, scale, {1, .5}];
> Show[Graphics[Raster[tmp/Max[Max[tmp]]]], ImageSize -> 400]
> 
> Intensity varies around the elipse. We can compare amplitude (or power)
> ratios between major and minor axes:
> 
> In[]:=Max[tmp[[33]]]/Max[Transpose[tmp][[33]]]
> 
> 
> Out[]=1.93009
> 
> 
> In[]:= Sqrt[Total[tmp[[33]]^2]/Total[Transpose[tmp][[33]]^2]]
> 
> Out[]= 1.98887
> 
> 
> 
> I was surprised these numbers weren't closer to 2. How can we make intensity
> invariant around the ellipse?
> 
> 


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