Re: Re: blurry ellipse

• To: mathgroup at smc.vnet.net
• Subject: [mg92275] Re: [mg92253] Re: blurry ellipse
• From: "Curtis F. Osterhoudt" <cfo at lanl.gov>
• Date: Thu, 25 Sep 2008 05:33:19 -0400 (EDT)
• References: <gat9g4\$ec5\$1@smc.vnet.net> <gavqku\$emm\$1@smc.vnet.net>

```We could also go about it in a different way, by producing a function
f(x,y) which yields a "density" of 1 when directly on the original
ellipse, and tapers off (perhaps as a Gaussian) when inside or outside of
that ellipse. I'm envisioning an elliptical crater, with a flat plane
outside of it and a flattish valley inside. It should give one a smooth
density plot, with no pixel artefacts.

>
>
> Hi Solomon,
>
> I think this is an artefact of the original coarse grained picture. The
>
> convolution treats every block (square) of pixels equally. But look at
>
> the original picture. If you imagine some small square, you will see
>
> that there are more or less white pixels inside the square, depending on
>
> where the squre is placed. This differences will persits, because the
>
> convolution will simply smear the "total white" on a larger surface.
>
> To improve, we therefore need a more fine grained original.
>
> Daniel
>
>
>
> Solomon, Joshua wrote:
>
>> thanks. but notice, intensity also varies as you go around your ellipse.
>
>> j
>
>>
>
>>  On 19/09/2008 10:16, in article gavqku\$emm\$1 at smc.vnet.net, "dh"
>
>> <dh at metrohm.ch> wrote:
>
>>
>
>>> n=100;
>
>>>
>
>>> pict=Table[0,{n},{n}];
>
>>>
>
>>> Scan[(pict[[Round[n/2+n/5  Sin[#]],Round[n/2+2
>
>>>
>
>>> n/5Cos[#]]]]=1)&,Range[0,2Pi,0.01]];
>
>>>
>
>>> Graphics[Raster[pict]]
>
>>>
>
>>> kernel={{1,1},{1,1}};
>>> pict=ListConvolve[kernel,pict];pict=pict/Max[pict];
>
>>>
>
>>> Graphics[Raster[pict]]
>
>>>
>
>>> kernel={{1,1,1},{1,1,1},{1,1,1}};
>
>>>
>
>>> pict=ListConvolve[kernel,pict];pict=pict/Max[pict];
>
>>>
>
>>> Graphics[Raster[pict]]
>
>>>
>
>>> kernel={{1,1,1,1},{1,1,1,1},{1,1,1,1},{1,1,1,1}};
>
>>>
>
>>> pict=ListConvolve[kernel,pict];pict=pict/Max[pict];
>
>>>
>
>>> Graphics[Raster[pict]]
>
>>
>
>>
>
>
>
>
>
> --
>
>
>
> Daniel Huber
>
> Metrohm Ltd.
>
> Oberdorfstr. 68
>
> CH-9100 Herisau
>
> Tel. +41 71 353 8585, Fax +41 71 353 8907
>
> E-Mail:<mailto:dh at metrohm.com>
>
> Internet:<http://www.metrohm.com>
>
>
>
>

```

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