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>*Reply-to*: cfo at lanl.gov

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> > > > >