       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, bm, {6, 6}], args]

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

Clearly you have to adjust the parameters of the functions above

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},
>
>         pr2 = -2 (Pi*sigmaPix/sizePix)^2;
>
>         RotateRight[
>
>             Abs[
>                 Chop[
>
>                     InverseFourier[
>
>                         RotateRight[
>
>                             Table[r1=
>                                     Abs[stretchFactors[]*x+
>                                         stretchFactors[]*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[]]/Max[Transpose[tmp][]]
>
>
> Out[]=1.93009
>
>
> In[]:= Sqrt[Total[tmp[]^2]/Total[Transpose[tmp][]^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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